Options-Pricing-Two-Assets-Correlation-Options.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6233 Option Pricing and StochasticCalculus in Finance\n",
    "# Final Project: Two Assets Correlation Options"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conducted by: Chen, Yinqi He, Zicheng Quan, Shuning Zhang, Duanyang Zhang, Yaqian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math\n",
    "from scipy import stats\n",
    "from scipy.integrate import dblquad,quad\n",
    "from tqdm import tqdm\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analytical solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pricing Option Value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to price option\n",
    "def M(a,b,rho):\n",
    "    \"\"\"\n",
    "    double intergral M in pricing\n",
    "    \n",
    "    \"\"\"\n",
    "    coef =  1/(2*np.pi*np.sqrt(1-rho**2))\n",
    "    dbintergral = dblquad(lambda y,x:np.exp((-x**2 + 2*rho*x*y - y**2)/(2 - 2*rho**2)), ##f\n",
    "                          -np.inf,       ## x lower bound\n",
    "                          b,             ## x upper bound\n",
    "                          -np.inf,       ## y lower bound\n",
    "                          a)[0]          ## y upper bound\n",
    "    return coef * dbintergral\n",
    "\n",
    "\n",
    "def Pricing_Correlation_Option(S1, S2, K1, K2, sigma1, sigma2, r, rho, tao): #定价方程\n",
    "    \"\"\"\n",
    "    Payoff:max(S2(T)-K2,0) if S1(T)>K1  otherwise 0\n",
    "    \n",
    "    \"\"\"\n",
    "    y2 = (np.log(S2/K2) + (r - 1/2*sigma2**2) * tao) / (sigma2 * np.sqrt(tao))  # y2 = dz\n",
    "    y1 = (np.log(S1/K1) + (r - 1/2*sigma1**2) * tao) / (sigma1 * np.sqrt(tao))  # y1 = dx\n",
    "    V = S2 * M(y2 + sigma2*np.sqrt(tao), y1 + rho*sigma2*np.sqrt(tao), rho) - K2 * np.exp(-r*tao) * M(y2,y1,rho)\n",
    "    return V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate Analytical Delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Analytical Delta\n",
    "def dM1(a,b,S1,sigma1,rho,tao):\n",
    "    f = lambda z: np.exp((-b**2 + 2*rho*b*z -z**2)/(2 - 2*rho**2)) / (sigma1 * np.sqrt(tao) * S1)\n",
    "    dmds1 = quad(f, -np.inf, a)[0]/(2 * np.pi * (1-rho**2))\n",
    "    return dmds1\n",
    "\n",
    "def dM2(a,b,S2,sigma2,rho,tao):\n",
    "    f = lambda x: np.exp((-a**2 + 2*rho*a*x -x**2)/(2 - 2*rho**2)) / (sigma2 * np.sqrt(tao) * S2)\n",
    "    dmds2 = quad(f, -np.inf, b)[0]/(2 * np.pi * (1-rho**2))\n",
    "    return dmds2\n",
    "    \n",
    "\n",
    "def Delta1 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao):\n",
    "    dz = (np.log(S2/K2) + (r - 1/2*sigma2**2) * tao) / (sigma2 * np.sqrt(tao))\n",
    "    dx = (np.log(S1/K1) + (r - 1/2*sigma1**2) * tao) / (sigma1 * np.sqrt(tao))\n",
    "    A = dM1(dz + sigma2*np.sqrt(tao), dx  + rho*sigma2*np.sqrt(tao), S1, sigma1, rho, tao)\n",
    "    B = dM1(dz, dx, S1, sigma1, rho, tao)\n",
    "    D1 = S2 * A - K2 * np.exp(-r*tao) * B\n",
    "    return D1\n",
    "\n",
    "def Delta2 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao):\n",
    "    dz = (np.log(S2/K2) + (r - 1/2*sigma2**2) * tao) / (sigma2 * np.sqrt(tao))\n",
    "    dx = (np.log(S1/K1) + (r - 1/2*sigma1**2) * tao) / (sigma1 * np.sqrt(tao))\n",
    "    C = dM2(dz + sigma2*np.sqrt(tao), dx  + rho*sigma2*np.sqrt(tao), S2, sigma2, rho, tao)\n",
    "    D = dM2(dz, dx, S2, sigma2, rho, tao)\n",
    "    D2 = M(dz+sigma2*np.sqrt(tao), dx+rho*sigma2*np.sqrt(tao), rho) + S2 * C - K2 * np.exp(-r*tao) * D\n",
    "    return D2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analytical solution on real data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read data, change path here to load your own data\n",
    "path1 = 'C:/Users/63438/Desktop/HP.csv'\n",
    "path2 = 'C:/Users/63438/Desktop/DLTR.csv'\n",
    "\n",
    "# Calculate annulized vol (sigma1,sigma2) and rho\n",
    "df1 = pd.read_csv(path1,usecols=['Date','Close'],index_col=0).rename(columns={'Close': 'First'})\n",
    "df1['firlogret']=np.log(df1.First) - np.log(df1.First.shift(1))\n",
    "sigma1 = np.std(df1['firlogret'])*(252**0.5)\n",
    "\n",
    "df2 = pd.read_csv(path2,usecols=['Date','Close'],index_col=0).rename(columns={'Close': 'Second'})\n",
    "df2['seclogret']=np.log(df2.Second) - np.log(df2.Second.shift(1))\n",
    "sigma2 = np.std(df2['seclogret'])*(252**0.5)\n",
    "\n",
    "df = df1.merge(df2, left_index=True, right_index=True)\n",
    "rho = np.corrcoef(df.firlogret[1:], df.seclogret[1:])[0][1]\n",
    "\n",
    "# set up K, tao, r\n",
    "K1, K2 = df['First'][0],df['Second'][0]\n",
    "r = 0.0083\n",
    "df['tao'] = range(252,0,-1) \n",
    "df['tao'] = df['tao'] /252\n",
    "\n",
    "# Price option on each day's stocks price\n",
    "df['OptionPrice'] = 0\n",
    "for index, row in df.iterrows():\n",
    "    S1 = row.First\n",
    "    S2 = row.Second\n",
    "    tao = row.tao    \n",
    "    df.loc[index,'OptionPrice'] = Pricing_Correlation_Option(S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.410965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>10.624699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>10.042789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>9.856477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>9.843518</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  OptionPrice\n",
       "Date                                                                          \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000    10.410965\n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032    10.624699\n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063    10.042789\n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095     9.856477\n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127     9.843518"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Delta From Analytics\n",
    "df['Delta1'] = 0\n",
    "df['Delta2'] = 0\n",
    "for index, row in df.iterrows():\n",
    "    S1 = row.First\n",
    "    S2 = row.Second\n",
    "    tao = row.tao    \n",
    "    df.loc[index,'Delta1'] = Delta1 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "    df.loc[index,'Delta2'] = Delta2 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "      <th>Delta1</th>\n",
       "      <th>Delta2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.410965</td>\n",
       "      <td>0.167616</td>\n",
       "      <td>0.296651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>10.624699</td>\n",
       "      <td>0.170831</td>\n",
       "      <td>0.299488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>10.042789</td>\n",
       "      <td>0.177025</td>\n",
       "      <td>0.284728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>9.856477</td>\n",
       "      <td>0.176792</td>\n",
       "      <td>0.281367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>9.843518</td>\n",
       "      <td>0.173348</td>\n",
       "      <td>0.283304</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000   \n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032   \n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063   \n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095   \n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  \n",
       "Date                                         \n",
       "2019-05-15    10.410965  0.167616  0.296651  \n",
       "2019-05-16    10.624699  0.170831  0.299488  \n",
       "2019-05-17    10.042789  0.177025  0.284728  \n",
       "2019-05-20     9.856477  0.176792  0.281367  \n",
       "2019-05-21     9.843518  0.173348  0.283304  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Delta From Numerics\n",
    "df_num = df.copy()\n",
    "df_num['NumDelta1'] = 0\n",
    "df_num['NumDelta2'] = 0\n",
    "chg = 0.1\n",
    "for index, row in df_num.iterrows():\n",
    "    S1 = row.First\n",
    "    S1up = row.First + chg\n",
    "    S1down = row.First - chg\n",
    "    S2 = row.Second\n",
    "    S2up = row.Second + chg\n",
    "    S2down = row.Second - chg\n",
    "    tao = row.tao  \n",
    "    df_num.loc[index,'NumDelta1'] = (Pricing_Correlation_Option(S1up, S2, K1, K2, sigma1, sigma2, r, rho, tao) \n",
    "                           - Pricing_Correlation_Option(S1down, S2, K1, K2, sigma1, sigma2, r, rho, tao)) / (2 * chg)\n",
    "    df_num.loc[index,'NumDelta2'] = (Pricing_Correlation_Option(S1, S2up, K1, K2, sigma1, sigma2, r, rho, tao) \n",
    "                           - Pricing_Correlation_Option(S1, S2down, K1, K2, sigma1, sigma2, r, rho, tao)) / (2 * chg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th></th>\n",
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       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "      <th>Delta1</th>\n",
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       "      <th>NumDelta1</th>\n",
       "      <th>NumDelta2</th>\n",
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       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.410965</td>\n",
       "      <td>0.167616</td>\n",
       "      <td>0.296651</td>\n",
       "      <td>0.155785</td>\n",
       "      <td>0.296651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>10.624699</td>\n",
       "      <td>0.170831</td>\n",
       "      <td>0.299488</td>\n",
       "      <td>0.158773</td>\n",
       "      <td>0.299488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>10.042789</td>\n",
       "      <td>0.177025</td>\n",
       "      <td>0.284728</td>\n",
       "      <td>0.164530</td>\n",
       "      <td>0.284728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>9.856477</td>\n",
       "      <td>0.176792</td>\n",
       "      <td>0.281367</td>\n",
       "      <td>0.164313</td>\n",
       "      <td>0.281367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>9.843518</td>\n",
       "      <td>0.173348</td>\n",
       "      <td>0.283304</td>\n",
       "      <td>0.161112</td>\n",
       "      <td>0.283304</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000   \n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032   \n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063   \n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095   \n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  NumDelta1  NumDelta2  \n",
       "Date                                                               \n",
       "2019-05-15    10.410965  0.167616  0.296651   0.155785   0.296651  \n",
       "2019-05-16    10.624699  0.170831  0.299488   0.158773   0.299488  \n",
       "2019-05-17    10.042789  0.177025  0.284728   0.164530   0.284728  \n",
       "2019-05-20     9.856477  0.176792  0.281367   0.164313   0.281367  \n",
       "2019-05-21     9.843518  0.173348  0.283304   0.161112   0.283304  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_num.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Using monte carlo to validate prcing formula\n",
    "### 2. Using Numerical Delta to validate Delta1 and Delta2 formula"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First, Fix K1, K2, Sigma, Sigma2 with S0_1 ∈(0, 200), S0_2 ∈（0, 200）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "  0%|                                                                                           | 0/20 [00:00<?, ?it/s]\n",
      "\n",
      "  5%|████                                                                            | 1/20 [04:28<1:24:57, 268.29s/it]\n",
      "\n",
      " 10%|████████                                                                        | 2/20 [08:57<1:20:32, 268.45s/it]\n",
      "\n",
      " 15%|████████████                                                                    | 3/20 [13:26<1:16:08, 268.71s/it]\n",
      "\n",
      " 20%|████████████████                                                                | 4/20 [17:55<1:11:41, 268.84s/it]\n",
      "\n",
      " 25%|████████████████████                                                            | 5/20 [22:27<1:07:25, 269.68s/it]\n",
      "\n",
      " 30%|████████████████████████                                                        | 6/20 [26:57<1:02:57, 269.81s/it]\n",
      "\n",
      " 35%|████████████████████████████▋                                                     | 7/20 [31:24<58:18, 269.10s/it]\n",
      "\n",
      " 40%|████████████████████████████████▊                                                 | 8/20 [35:51<53:42, 268.52s/it]\n",
      "\n",
      " 45%|████████████████████████████████████▉                                             | 9/20 [40:18<49:08, 268.05s/it]\n",
      "\n",
      " 50%|████████████████████████████████████████▌                                        | 10/20 [45:02<45:26, 272.66s/it]\n",
      "\n",
      " 55%|████████████████████████████████████████████▌                                    | 11/20 [49:35<40:56, 272.90s/it]\n",
      "\n",
      " 60%|████████████████████████████████████████████████▌                                | 12/20 [54:07<36:21, 272.63s/it]\n",
      "\n",
      " 65%|████████████████████████████████████████████████████▋                            | 13/20 [58:39<31:46, 272.35s/it]\n",
      "\n",
      " 70%|███████████████████████████████████████████████████████▎                       | 14/20 [1:03:08<27:07, 271.31s/it]\n",
      "\n",
      " 75%|███████████████████████████████████████████████████████████▎                   | 15/20 [1:07:35<22:30, 270.19s/it]\n",
      "\n",
      " 80%|███████████████████████████████████████████████████████████████▏               | 16/20 [1:12:06<18:01, 270.30s/it]\n",
      "\n",
      " 85%|███████████████████████████████████████████████████████████████████▏           | 17/20 [1:16:37<13:31, 270.50s/it]\n",
      "\n",
      " 90%|███████████████████████████████████████████████████████████████████████        | 18/20 [1:21:05<08:59, 269.86s/it]\n",
      "\n",
      " 95%|███████████████████████████████████████████████████████████████████████████    | 19/20 [1:25:32<04:28, 268.83s/it]\n",
      "\n",
      "100%|███████████████████████████████████████████████████████████████████████████████| 20/20 [1:29:59<00:00, 269.95s/it]\n"
     ]
    }
   ],
   "source": [
    "## Validation process:\n",
    "### 1. Using monte carlo to validate prcing formula\n",
    "### 2. Using Numerical Delta to validate Delta1 and Delta2 formula\n",
    "def SimulateSP(sigma1,sigma2,T,S0_1,S0_2,r,delta,rho):\n",
    "    stockprice1 = []\n",
    "    stockprice2 = []\n",
    "    stockprice1.append(S0_1)\n",
    "    stockprice2.append(S0_2)\n",
    "    S2 = S0_2\n",
    "    S1 = S0_1\n",
    "    for i in range(delta):\n",
    "        w1 = np.random.normal(0,math.sqrt(T/delta))\n",
    "        w2 = np.random.normal(0,math.sqrt(T/delta))\n",
    "        w3 = rho*w1+np.sqrt(1-rho**2)*w2\n",
    "        deltaprice1 = (r-0.5*sigma1**2)*(T/delta)+sigma1*w1\n",
    "        deltaprice2 = (r-0.5*sigma2**2)*(T/delta)+sigma2*w3\n",
    "        S1 = S1 * np.exp(deltaprice1)\n",
    "        S2 = S2 * np.exp(deltaprice2)\n",
    "        stockprice1.append(S1)\n",
    "        stockprice2.append(S2)\n",
    "    return stockprice1,stockprice2\n",
    "         \n",
    "\n",
    "def PricingByMc(K_1,K_2,r,T, s1, s2, sigma1, sigma2, rho):\n",
    "    twoassetprice = []\n",
    "    for i in range(5000):\n",
    "        stockprice1,stockprice2 = SimulateSP(sigma1,sigma2,T,s1,s2,r,delta,rho)\n",
    "        if stockprice1[-1] > K_1:\n",
    "            twoassetprice.append(max(stockprice2[-1]-K_2,0)*np.exp(-r*T))\n",
    "        else:\n",
    "            twoassetprice.append(0)\n",
    "    return np.mean(twoassetprice)\n",
    "\n",
    "# Fix K1, K2, Sigma, Sigma2 with S0_1 ∈(0, 100), S0_2 ∈（0, 100）\n",
    "K_1 = 95\n",
    "K_2 = 90\n",
    "r = 0.1\n",
    "sigma_1 = 0.20\n",
    "sigma_2 = 0.30\n",
    "rho = 0.75\n",
    "delta = 252\n",
    "T =1\n",
    "S0_1 = np.linspace(1, 200, 20)\n",
    "S0_2 = np.linspace(200, 1, 20)\n",
    "chu = 0.1\n",
    "\n",
    "McPrices = []\n",
    "AfPrices = []\n",
    "NDelta1 = []\n",
    "AfDelta1 = []\n",
    "NDelta2 = []\n",
    "AfDelta2 = []\n",
    "for s2 in tqdm(S0_2):\n",
    "    for s1 in S0_1:\n",
    "        McPrices.append(PricingByMc(K_1,K_2,r,T, s1, s2, sigma_1, sigma_2, rho))\n",
    "        AfPrices.append(Pricing_Correlation_Option(s1, s2, K_1, K_2, sigma_1, sigma_2, r, rho, T))\n",
    "        NDelta1.append((Pricing_Correlation_Option(s1 + chu, s2, K_1, K_2, sigma_1, sigma_2, r, rho, T) - Pricing_Correlation_Option(s1 - chu, s2, K_1, K_2, sigma_1, sigma_2, r, rho, T)) / (2*chu))\n",
    "        NDelta2.append((Pricing_Correlation_Option(s1, s2 + chu, K_1, K_2, sigma_1, sigma_2, r, rho, T) - Pricing_Correlation_Option(s1, s2 - chu, K_1, K_2, sigma_1, sigma_2, r, rho, T)) / (2*chu))\n",
    "        AfDelta1.append(Delta1 (s1, s2, K_1, K_2, sigma_1, sigma_2, r, rho, T))\n",
    "        AfDelta2.append(Delta2 (s1, s2, K_1, K_2, sigma_1, sigma_2, r, rho, T))\n",
    "McPrices = np.array(McPrices).reshape(20,20)\n",
    "AfPrices = np.array(AfPrices).reshape(20,20)\n",
    "NDelta1 = np.array(NDelta1).reshape(20,20)\n",
    "AfDelta1 = np.array(AfDelta1).reshape(20,20)\n",
    "NDelta2 = np.array(NDelta2).reshape(20,20)\n",
    "AfDelta2 = np.array(AfDelta2).reshape(20,20)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(McPrices, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "#ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Pricing By Monte Carlo\", xlabel = \"S1\", ylabel = \"S2\")\n",
    "plt.savefig(\"McPrices_1\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(AfPrices, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "#ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Pricing By Analytical Formula\", xlabel = \"S1\", ylabel = \"S2\")\n",
    "plt.savefig(\"AfPrices_1\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(NDelta1, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "#ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Delta1 By Numerical Methods\", xlabel = \"S1\", ylabel = \"S2\")\n",
    "plt.savefig(\"NDelta1_1\")\n",
    "    \n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(NDelta2, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "#ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Delta2 By Numerical Methods\", xlabel = \"S1\", ylabel = \"S2\")\n",
    "plt.savefig(\"NDelta2_1\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(AfDelta1, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "#ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Delta1 By Analytical Formula\", xlabel = \"S1\", ylabel = \"S2\")\n",
    "plt.savefig(\"AfDelta1_1\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(AfDelta2, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "#ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Delta2 By Analytical Formula\", xlabel = \"S1\", ylabel = \"S2\")\n",
    "plt.savefig(\"AfDelta2_1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fix K1, K2, S0_1, S0_2 with sigma1 ∈(0, 1), sigma2 ∈（0, 1）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Process: 0.01\n",
      "Process: 0.02\n",
      "Process: 0.03\n",
      "Process: 0.04\n",
      "Process: 0.05\n",
      "Process: 0.06\n",
      "Process: 0.07\n",
      "Process: 0.08\n",
      "Process: 0.09\n",
      "Process: 0.10\n",
      "Process: 0.11\n",
      "Process: 0.12\n",
      "Process: 0.13\n",
      "Process: 0.14\n",
      "Process: 0.15\n",
      "Process: 0.16\n",
      "Process: 0.17\n",
      "Process: 0.18\n",
      "Process: 0.19\n",
      "Process: 0.20\n",
      "Process: 0.21\n",
      "Process: 0.22\n",
      "Process: 0.23\n",
      "Process: 0.24\n",
      "Process: 0.25\n",
      "Process: 0.26\n",
      "Process: 0.27\n",
      "Process: 0.28\n",
      "Process: 0.29\n",
      "Process: 0.30\n",
      "Process: 0.31\n",
      "Process: 0.32\n",
      "Process: 0.33\n",
      "Process: 0.34\n",
      "Process: 0.35\n",
      "Process: 0.36\n",
      "Process: 0.37\n",
      "Process: 0.38\n",
      "Process: 0.39\n",
      "Process: 0.40\n",
      "Process: 0.41\n",
      "Process: 0.42\n",
      "Process: 0.43\n",
      "Process: 0.44\n",
      "Process: 0.45\n",
      "Process: 0.46\n",
      "Process: 0.47\n",
      "Process: 0.48\n",
      "Process: 0.49\n",
      "Process: 0.50\n",
      "Process: 0.51\n",
      "Process: 0.52\n",
      "Process: 0.53\n",
      "Process: 0.54\n",
      "Process: 0.55\n",
      "Process: 0.56\n",
      "Process: 0.57\n",
      "Process: 0.58\n",
      "Process: 0.59\n",
      "Process: 0.60\n",
      "Process: 0.61\n",
      "Process: 0.62\n",
      "Process: 0.63\n",
      "Process: 0.64\n",
      "Process: 0.65\n",
      "Process: 0.66\n",
      "Process: 0.67\n",
      "Process: 0.68\n",
      "Process: 0.69\n",
      "Process: 0.70\n",
      "Process: 0.71\n",
      "Process: 0.72\n",
      "Process: 0.73\n",
      "Process: 0.74\n",
      "Process: 0.75\n",
      "Process: 0.76\n",
      "Process: 0.77\n",
      "Process: 0.78\n",
      "Process: 0.79\n",
      "Process: 0.80\n",
      "Process: 0.81\n",
      "Process: 0.82\n",
      "Process: 0.83\n",
      "Process: 0.84\n",
      "Process: 0.85\n",
      "Process: 0.86\n",
      "Process: 0.87\n",
      "Process: 0.88\n",
      "Process: 0.89\n",
      "Process: 0.90\n",
      "Process: 0.91\n",
      "Process: 0.92\n",
      "Process: 0.93\n",
      "Process: 0.94\n",
      "Process: 0.95\n",
      "Process: 0.96\n",
      "Process: 0.97\n",
      "Process: 0.98\n",
      "Process: 0.99\n",
      "Process: 1.00\n"
     ]
    }
   ],
   "source": [
    "# Fix K1, K2, S0_1, S0_2 with sigma1 ∈(0, 1), sigma2 ∈（0, 1）\n",
    "K_1 = 95\n",
    "K_2 = 90\n",
    "r = 0.1\n",
    "sigma_1 = np.linspace(1,0.1, 100)\n",
    "sigma_2 = np.linspace(0.1,1, 100)\n",
    "rho = 0.75\n",
    "delta = 252\n",
    "T =1\n",
    "S0_1 = 100\n",
    "S0_2 = 100\n",
    "chu = 0.1\n",
    "\n",
    "McPrices = []\n",
    "AfPrices = []\n",
    "NDelta1 = []\n",
    "AfDelta1 = []\n",
    "NDelta2 = []\n",
    "AfDelta2 = []\n",
    "count = 1\n",
    "for sg2 in sigma_2:\n",
    "    for sg1 in sigma_1:\n",
    "        print(\"Process: {:.2f}\".format(count / 10000))\n",
    "        count += 1\n",
    "        McPrices.append(PricingByMc(K_1,K_2,r,T, S0_1, S0_2, sg1, sg2, rho))\n",
    "        AfPrices.append(Pricing_Correlation_Option(S0_1, S0_2, K_1, K_1, sg1, sg2, r, rho, T))\n",
    "        NDelta1.append((Pricing_Correlation_Option(S0_1 + chu, S0_2, K_1, K_2, sg1, sg2, r, rho, T) - Pricing_Correlation_Option(S0_1 - chu, S0_2, K_1, K_2, sg1, sg2, r, rho, T)) / (2*chu))\n",
    "        NDelta2.append((Pricing_Correlation_Option(S0_1, S0_2 + chu, K_1, K_2, sg1, sg2, r, rho, T) - Pricing_Correlation_Option(S0_1, S0_2 - chu, K_1, K_2, sg1, sg2, r, rho, T)) / (2*chu))\n",
    "        AfDelta1.append(Delta1 (S0_1, S0_2, K_1, K_2, sg1, sg2, r, rho, T))\n",
    "        AfDelta2.append(Delta2 (S0_1, S0_2, K_1, K_2, sg1, sg2, r, rho, T))\n",
    "McPrices = np.array(McPrices).reshape(100,100)\n",
    "AfPrices = np.array(McPrices).reshape(100,100)\n",
    "NDelta1 = np.array(McPrices).reshape(100,100)\n",
    "AfDelta1 = np.array(McPrices).reshape(100,100)\n",
    "NDelta2 = np.array(McPrices).reshape(100,100)\n",
    "AfDelta2 = np.array(McPrices).reshape(100,100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(McPrices, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Pricing By Monte Carlo\", xlabel = \"Sigma1\", ylabel = \"Sigma2\")\n",
    "plt.savefig(\"McPrices_2\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(AfPrices, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Pricing By Analytical Formula\", xlabel = \"Sigma1\", ylabel = \"Sigma2\")\n",
    "plt.savefig(\"AfPrices_2\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(NDelta1, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Delta1 By Numerical Methods\", xlabel = \"Sigma1\", ylabel = \"Sigma2\")\n",
    "plt.savefig(\"NDelta1_2\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(NDelta2, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Delta2 By Numerical Methods\", xlabel = \"Sigma1\", ylabel = \"Sigma2\")\n",
    "plt.savefig(\"NDelta2_2\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(AfDelta1, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Delta1 By Analytical Formula\", xlabel = \"Sigma1\", ylabel = \"Sigma2\")\n",
    "plt.savefig(\"AfDelta1_2\")\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(5,5))\n",
    "im = ax.imshow(AfDelta2, cmap='rainbow')\n",
    "plt.colorbar(im, fraction = 0.045)\n",
    "ax.set_yticklabels([0, \"\", 80, 60, 40,20])\n",
    "ax.set(title = \"Delta2 By Analytical Formula\", xlabel = \"Sigma1\", ylabel = \"Sigma2\")\n",
    "plt.savefig(\"AfDelta2_2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Extreme cases\n",
    "### Case 1. Zero correlation, correlation = 0\n",
    "### Case 2. Perfect correlation, correlation = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Coding\\Anaconda\\lib\\site-packages\\scipy\\integrate\\quadpack.py:865: IntegrationWarning: The integral is probably divergent, or slowly convergent.\n",
      "  **opt)\n"
     ]
    }
   ],
   "source": [
    "## Validation process:\n",
    "### 3. Extreme cases\n",
    "# reset params, using historical data\n",
    "rho = np.corrcoef(df.firlogret[1:], df.seclogret[1:])[0][1]\n",
    "\n",
    "K1, K2 = df['First'][0],df['Second'][0]\n",
    "r = 0.0083\n",
    "\n",
    "df_test1 = df.copy()\n",
    "df_test2 = df.copy()\n",
    "\n",
    "### case1. zero correlation, correlation = 0\n",
    "df_test1[\"rho\"] = 0\n",
    "for index, row in df_test1.iterrows():\n",
    "    S1 = row.First\n",
    "    S2 = row.Second\n",
    "    tao = row.tao \n",
    "    rho = row.rho\n",
    "    df_test1.loc[index,'OptionPrice'] = Pricing_Correlation_Option(S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)  \n",
    "    df_test1.loc[index,'Delta1'] = Delta1 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "    df_test1.loc[index,'Delta2'] = Delta2 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "     \n",
    "### case2. perfect correlation, correlation = 1\n",
    "df_test2[\"rho\"] = 0.99 # when rho = 1, formula divide by 0, and we get NaN, so try 0.99 here \n",
    "for index, row in df_test2.iterrows():\n",
    "    S1 = row.First\n",
    "    S2 = row.Second\n",
    "    tao = row.tao\n",
    "    rho = row.rho\n",
    "    df_test2.loc[index,'OptionPrice'] = Pricing_Correlation_Option(S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)  \n",
    "    df_test2.loc[index,'Delta1'] = Delta1 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "    df_test2.loc[index,'Delta2'] = Delta2 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "      <th>Delta1</th>\n",
       "      <th>Delta2</th>\n",
       "      <th>rho</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.351866</td>\n",
       "      <td>0.138233</td>\n",
       "      <td>0.202095</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>6.506398</td>\n",
       "      <td>0.141150</td>\n",
       "      <td>0.204799</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>6.032042</td>\n",
       "      <td>0.142100</td>\n",
       "      <td>0.191900</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>5.895573</td>\n",
       "      <td>0.141194</td>\n",
       "      <td>0.188996</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>5.906352</td>\n",
       "      <td>0.139343</td>\n",
       "      <td>0.190661</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000   \n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032   \n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063   \n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095   \n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  rho  \n",
       "Date                                              \n",
       "2019-05-15     6.351866  0.138233  0.202095    0  \n",
       "2019-05-16     6.506398  0.141150  0.204799    0  \n",
       "2019-05-17     6.032042  0.142100  0.191900    0  \n",
       "2019-05-20     5.895573  0.141194  0.188996    0  \n",
       "2019-05-21     5.906352  0.139343  0.190661    0  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "      <th>Delta1</th>\n",
       "      <th>Delta2</th>\n",
       "      <th>rho</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.275267</td>\n",
       "      <td>0.530100</td>\n",
       "      <td>0.515126</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>18.607971</td>\n",
       "      <td>0.557782</td>\n",
       "      <td>0.516585</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>18.093454</td>\n",
       "      <td>0.680801</td>\n",
       "      <td>0.495948</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>17.850428</td>\n",
       "      <td>0.690245</td>\n",
       "      <td>0.491931</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>17.721354</td>\n",
       "      <td>0.640717</td>\n",
       "      <td>0.496008</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000   \n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032   \n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063   \n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095   \n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2   rho  \n",
       "Date                                               \n",
       "2019-05-15    18.275267  0.530100  0.515126  0.99  \n",
       "2019-05-16    18.607971  0.557782  0.516585  0.99  \n",
       "2019-05-17    18.093454  0.680801  0.495948  0.99  \n",
       "2019-05-20    17.850428  0.690245  0.491931  0.99  \n",
       "2019-05-21    17.721354  0.640717  0.496008  0.99  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case3. S1 << K1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "### 3. S1 << K1\n",
    "df_test3 = df.copy()\n",
    "rho = np.corrcoef(df.firlogret[1:], df.seclogret[1:])[0][1]\n",
    "K1 = 1000\n",
    "\n",
    "for index, row in df_test3.iterrows():\n",
    "    S1 = row.First\n",
    "    S2 = row.Second\n",
    "    tao = row.tao \n",
    "    #rho = row.rho\n",
    "    df_test3.loc[index,'OptionPrice'] = Pricing_Correlation_Option(S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)  \n",
    "    df_test3.loc[index,'Delta1'] = Delta1 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "    df_test3.loc[index,'Delta2'] = Delta2 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "      <th>Delta1</th>\n",
       "      <th>Delta2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.009175</td>\n",
       "      <td>0.000726</td>\n",
       "      <td>0.000176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>0.009179</td>\n",
       "      <td>0.000727</td>\n",
       "      <td>0.000174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>0.007283</td>\n",
       "      <td>0.000615</td>\n",
       "      <td>0.000139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>0.006802</td>\n",
       "      <td>0.000582</td>\n",
       "      <td>0.000130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>0.006874</td>\n",
       "      <td>0.000583</td>\n",
       "      <td>0.000132</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000   \n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032   \n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063   \n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095   \n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  \n",
       "Date                                         \n",
       "2019-05-15     0.009175  0.000726  0.000176  \n",
       "2019-05-16     0.009179  0.000727  0.000174  \n",
       "2019-05-17     0.007283  0.000615  0.000139  \n",
       "2019-05-20     0.006802  0.000582  0.000130  \n",
       "2019-05-21     0.006874  0.000583  0.000132  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test3.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case4. S1 >> K1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "### 4. S1 >> K1\n",
    "df_test4 = df.copy()\n",
    "df_test4['VanillaOptionPrice'] = 0\n",
    "df_test4['VanillaOptionDelta2'] = 0\n",
    "rho = np.corrcoef(df.firlogret[1:], df.seclogret[1:])[0][1]\n",
    "K1 = 5 \n",
    "\n",
    "def Pricing_Vanilla_Call(S,K,sigma,T,r):\n",
    "    d1 = (math.log(S/K) + (r+sigma*sigma/2)*T)/(sigma*math.sqrt(T))\n",
    "    d2 = d1-sigma*math.sqrt(T)\n",
    "    C = S*stats.norm.cdf(d1,0,1)- np.exp(-r*T)*K*stats.norm.cdf(d2,0,1)\n",
    "    return C,stats.norm.cdf(d1,0,1)\n",
    "\n",
    "for index, row in df_test4.iterrows():\n",
    "    S1 = row.First  \n",
    "    S2 = row.Second\n",
    "    tao = row.tao \n",
    "    #rho = row.rho\n",
    "    df_test4.loc[index,'VanillaOptionPrice'] = Pricing_Vanilla_Call(S2,K2,sigma2,tao,r)[0]  \n",
    "    df_test4.loc[index,'VanillaOptionDelta2'] = Pricing_Vanilla_Call(S2,K2,sigma2,tao,r)[1]  \n",
    "    df_test4.loc[index,'OptionPrice'] = Pricing_Correlation_Option(S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)  \n",
    "    df_test4.loc[index,'Delta1'] = Delta1 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "    df_test4.loc[index,'Delta2'] = Delta2 (S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "      <th>Delta1</th>\n",
       "      <th>Delta2</th>\n",
       "      <th>VanillaOptionPrice</th>\n",
       "      <th>VanillaOptionDelta2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.814356</td>\n",
       "      <td>0.001330</td>\n",
       "      <td>0.598290</td>\n",
       "      <td>18.831622</td>\n",
       "      <td>0.599159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>19.192353</td>\n",
       "      <td>0.001330</td>\n",
       "      <td>0.603790</td>\n",
       "      <td>19.209607</td>\n",
       "      <td>0.604651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>18.851077</td>\n",
       "      <td>0.001585</td>\n",
       "      <td>0.599353</td>\n",
       "      <td>18.870928</td>\n",
       "      <td>0.600348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>18.616131</td>\n",
       "      <td>0.001592</td>\n",
       "      <td>0.596418</td>\n",
       "      <td>18.635869</td>\n",
       "      <td>0.597414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>18.407299</td>\n",
       "      <td>0.001469</td>\n",
       "      <td>0.593860</td>\n",
       "      <td>18.425556</td>\n",
       "      <td>0.594789</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000   \n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032   \n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063   \n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095   \n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  VanillaOptionPrice  \\\n",
       "Date                                                              \n",
       "2019-05-15    18.814356  0.001330  0.598290           18.831622   \n",
       "2019-05-16    19.192353  0.001330  0.603790           19.209607   \n",
       "2019-05-17    18.851077  0.001585  0.599353           18.870928   \n",
       "2019-05-20    18.616131  0.001592  0.596418           18.635869   \n",
       "2019-05-21    18.407299  0.001469  0.593860           18.425556   \n",
       "\n",
       "            VanillaOptionDelta2  \n",
       "Date                             \n",
       "2019-05-15             0.599159  \n",
       "2019-05-16             0.604651  \n",
       "2019-05-17             0.600348  \n",
       "2019-05-20             0.597414  \n",
       "2019-05-21             0.594789  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test4.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Values vs Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### 4. values vs correlation\n",
    "def twoassetvalue_rho(rho):\n",
    "    return Pricing_Correlation_Option(S1, S2, K1, K2, sigma1, sigma2, r, rho, tao)\n",
    "\n",
    "df_test3 = df.copy()\n",
    "S1 = df.First[0]\n",
    "S2 = df.Second[0]\n",
    "K1 = S1\n",
    "K2 = S2\n",
    "tao = 1\n",
    "\n",
    "x = np.arange(-0.95,0.95, 0.05)\n",
    "y = []\n",
    "for i in x:\n",
    "    y.append(Pricing_Correlation_Option(S1,S2,K1,K2,sigma1,sigma2,r,i,tao))\n",
    "fig0 = plt.figure(figsize=(10,6))\n",
    "plt.title(\"Value of Two Asset Option relative to the correlation\",fontsize = 15)\n",
    "plt.xlabel('rho')\n",
    "plt.ylabel('Option Value')\n",
    "plt.plot(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BackTest on historical data\n",
    "## PNL calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "      <th>Delta1</th>\n",
       "      <th>Delta2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.410965</td>\n",
       "      <td>0.167616</td>\n",
       "      <td>0.296651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>10.624699</td>\n",
       "      <td>0.170831</td>\n",
       "      <td>0.299488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>10.042789</td>\n",
       "      <td>0.177025</td>\n",
       "      <td>0.284728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>9.856477</td>\n",
       "      <td>0.176792</td>\n",
       "      <td>0.281367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>9.843518</td>\n",
       "      <td>0.173348</td>\n",
       "      <td>0.283304</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000   \n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032   \n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063   \n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095   \n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  \n",
       "Date                                         \n",
       "2019-05-15    10.410965  0.167616  0.296651  \n",
       "2019-05-16    10.624699  0.170831  0.299488  \n",
       "2019-05-17    10.042789  0.177025  0.284728  \n",
       "2019-05-20     9.856477  0.176792  0.281367  \n",
       "2019-05-21     9.843518  0.173348  0.283304  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# BackTest : Pnl calculation\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['PNL'] = 0\n",
    "df['PNL_Option'] = df['OptionPrice'] - df['OptionPrice'].shift(1)\n",
    "df['Price_diff1'] = df['First'] - df['First'].shift(1)\n",
    "df['Price_diff2'] = df['Second'] - df['Second'].shift(1) \n",
    "df['PNL_Hedge'] = df['Delta1'].shift(1) * df['Price_diff1'] + df['Delta2'].shift(1) * df['Price_diff2']\n",
    "df['PNL'] = df['PNL_Option'] - df['PNL_Hedge']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>First</th>\n",
       "      <th>firlogret</th>\n",
       "      <th>Second</th>\n",
       "      <th>seclogret</th>\n",
       "      <th>tao</th>\n",
       "      <th>OptionPrice</th>\n",
       "      <th>Delta1</th>\n",
       "      <th>Delta2</th>\n",
       "      <th>PNL</th>\n",
       "      <th>PNL_Option</th>\n",
       "      <th>Price_diff1</th>\n",
       "      <th>Price_diff2</th>\n",
       "      <th>PNL_Hedge</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>57.930000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.199997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.410965</td>\n",
       "      <td>0.167616</td>\n",
       "      <td>0.296651</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>58.080002</td>\n",
       "      <td>0.002586</td>\n",
       "      <td>100.889999</td>\n",
       "      <td>0.006863</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>10.624699</td>\n",
       "      <td>0.170831</td>\n",
       "      <td>0.299488</td>\n",
       "      <td>-0.016099</td>\n",
       "      <td>0.213734</td>\n",
       "      <td>0.150002</td>\n",
       "      <td>0.690002</td>\n",
       "      <td>0.229833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>55.480000</td>\n",
       "      <td>-0.045799</td>\n",
       "      <td>100.389999</td>\n",
       "      <td>-0.004968</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>10.042789</td>\n",
       "      <td>0.177025</td>\n",
       "      <td>0.284728</td>\n",
       "      <td>0.011994</td>\n",
       "      <td>-0.581910</td>\n",
       "      <td>-2.600002</td>\n",
       "      <td>-0.500000</td>\n",
       "      <td>-0.593905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>55.009998</td>\n",
       "      <td>-0.008508</td>\n",
       "      <td>100.059998</td>\n",
       "      <td>-0.003293</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>9.856477</td>\n",
       "      <td>0.176792</td>\n",
       "      <td>0.281367</td>\n",
       "      <td>-0.009149</td>\n",
       "      <td>-0.186312</td>\n",
       "      <td>-0.470002</td>\n",
       "      <td>-0.330001</td>\n",
       "      <td>-0.177163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>55.529999</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>99.769997</td>\n",
       "      <td>-0.002902</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>9.843518</td>\n",
       "      <td>0.173348</td>\n",
       "      <td>0.283304</td>\n",
       "      <td>-0.023294</td>\n",
       "      <td>-0.012958</td>\n",
       "      <td>0.520001</td>\n",
       "      <td>-0.290001</td>\n",
       "      <td>0.010335</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                First  firlogret      Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  57.930000        NaN  100.199997        NaN  1.000000   \n",
       "2019-05-16  58.080002   0.002586  100.889999   0.006863  0.996032   \n",
       "2019-05-17  55.480000  -0.045799  100.389999  -0.004968  0.992063   \n",
       "2019-05-20  55.009998  -0.008508  100.059998  -0.003293  0.988095   \n",
       "2019-05-21  55.529999   0.009408   99.769997  -0.002902  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2       PNL  PNL_Option  \\\n",
       "Date                                                                \n",
       "2019-05-15    10.410965  0.167616  0.296651       NaN         NaN   \n",
       "2019-05-16    10.624699  0.170831  0.299488 -0.016099    0.213734   \n",
       "2019-05-17    10.042789  0.177025  0.284728  0.011994   -0.581910   \n",
       "2019-05-20     9.856477  0.176792  0.281367 -0.009149   -0.186312   \n",
       "2019-05-21     9.843518  0.173348  0.283304 -0.023294   -0.012958   \n",
       "\n",
       "            Price_diff1  Price_diff2  PNL_Hedge  \n",
       "Date                                             \n",
       "2019-05-15          NaN          NaN        NaN  \n",
       "2019-05-16     0.150002     0.690002   0.229833  \n",
       "2019-05-17    -2.600002    -0.500000  -0.593905  \n",
       "2019-05-20    -0.470002    -0.330001  -0.177163  \n",
       "2019-05-21     0.520001    -0.290001   0.010335  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'PnL from Option and Hedge Part')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GGxkcHGT16tWF5Zdddhn9/f11bVdKWTWz1Fv+1re+lXA4TDgc5vWvfz1bt26ls7Oz6jY3bNhQEJbXXXcd0WiUeDwOwJve9CaCwSDBYJDe3l6Gh4fp6+ura8yNRAs6jaaBxOOQTjd6FBqNRjN7vBi6yQSDwcLvPp+PbDZb13Yvvvhinn766bJlhw4dorW1lba2NmBqKZGZSotUSqjw3jN5vLZt1zXeRqNdrhpNA7EsOM2+MzQajeaU8M53vpMNGzbw+OOPA8oS+OEPf5ibb765sM6DDz6IYRhEo1HWr1/PFVdcQVtbG8lksuI2X/e613HHHXcAsH79ehYtWkR7e/vJP5hTgBZ0Gk0DMU3I5xs9Co1Gozm1vP/976evr4++vj6uvPLKiuuEw2EefPBBbr31Vi688EIuueQSrrjiCj70oQ8V1nnNa17Dm970Jn7913+dT33qUyxfvpxXvvKV+P1+Lr30Ur785S+XbXPdunVs27aNV77ylXziE5/gu9/97kk9zlOJmKmey6nm8ssvl9u2bWv0MDSaU8KXvgQHD8Ltt8MCL0Ku0WgWIHv37uUVr3hFo4fRENatW0draysf//jHT9k+K51vIcR2KeXlp2wQVdAWOo2mgViW+n+BPVdpNBqN5jRDJ0VoNA3ENNX/tg2BQGPHotFoNI1g165dvOtd7ypbFgwG2bJly7TvW7du3Ukc1emHFnQaTQPxLHQ6jk6j0ZypXHLJJRWzZDX1oV2uGk0D8Sx0WtBpNBqNZi5oQafRNBAt6DQajUYzH2hBp9E0CNsGxyn+rtFoNBrNbNGCTqNpEF78HGgLXa0cPgyZTKNHodFoNAsPLeg0mgbhuVtBC7pakBJuuw2efLLRI9FoNKX4fD7Wrl3LmjVruP7668nM8NT1nve8h3vvvXfG7fb397NmzZqyZevWreO2226ra3ytra11rX+6ogWdRtMgtIWuPmxb/UxMNHokGo2mFK+X6+7duwkEAtx+++2NHtIZyUkvWyKE+C/gzcCIlHLNTOtrNGcK2kJXH945SiQaOw6NZqFy991w7Nj8bnPlSvijP6p9/WuuuYadO3fS39/P7/7u73L11VezadMmVqxYwYMPPkg4HJ63sR08eJCbbrqJ0dFRIpEI3/rWt7jooos4fPgw73jHO7Btm9/5nd8prO84Dh/60Id46qmnWL16NY7jcMMNN/D2t7+d7du387GPfYxUKsWiRYv4zne+w7Jly+ZtrKeCU2Gh+w7wOzOtpNGcaWhBVx92TsKjPyP57IuNHopGo6mAbds88sgjXHLJJQAcOHCAm266iT179tDZ2cl9991X9zYPHjzI2rVrCz+l1r/3ve99/Nu//Rvbt2/ntttu44Mf/CAAH/nIR/jABz7As88+y9KlSwvr33///fT397Nr1y6+/e1vs3nzZgByuRx/9Vd/xb333sv27du54YYb+OQnPzmXU9EQTrqFTkr5tBBi1cnej0ZzuqFdrvVhGzYcOUJijw+4qNHD0WgWHPVY0uaTbDbL2rVrAWWhu/HGGxkcHGT16tWF5Zdddhn9/f11b/vcc88tKzrsdYdIpVJs2rSJ66+/vvCa6T4lb9y4sSAe3/Wud3HLLbcAsGHDBq6//nqamppYunQpr3/96wHYt28fu3fv5o1vfCMA+Xz+tLPOge4UodE0DG2hq498VingZNxp8Eg0Gk0pXgzdZILBYOF3n89HNpudt306jkNnZ2fVDhNCiCnLZJWm2VJKLr744oLF7nRlQSRFCCHeJ4TYJoTYNjo62ujhaDSnhFILna5DNzN2Rp0wM50rE8MajebMo729ndWrV3PPPfcASpQ9//zzAFx11VXcddddANxxxx2F91x99dXcd999OI7D8PAw69evB+DCCy9kdHS0zAW7Z8+eU3g088OCEHRSym9KKS+XUl6+ePHiRg9HozklaAtdfdjZnPolmyWZbOxYNBrN3Hj/+99PX18ffX19XHnllbPaxh133MF//ud/cumll3LxxRfz4IMPAvDVr36Vr3/961xxxRXE4/HC+m9729vo6+tjzZo1vP/97+e1r30tHR0dBAIB7r33Xm655RYuvfRS1q5dy6ZNm+blOE8lopoJcl53omLoHqoly/Xyyy+X27ZtO+ljOt3wLlMFK7LmNOWxx8CLEX7/++HVr27seBY6RzYO8PmrH4ZwmFt2/xnnnNPoEWk0jWfv3r284hWvaPQwThtSqRStra1Eo1Fe85rXsHHjxrLEiZmodL6FENullJfP91jr5aRb6IQQPwA2AxcKIQaEEDee7H2+HNm1McHHfm+vdjW9jNBJEfWRNzwLnaHj6DQazax485vfzNq1a7nmmmv41Kc+VZeYW+iciizXPz3Z+zgTGP7hejI/O0HmyCKCF2i39EJmeFiJtZUrp1/PNIETJ2BsjHz+klMyttMZ2/ACDSWJgQS8qrOh49FoNPPDrl27eNe73lW2LBgMsmXLlnnflxc393JEZ7meQl58EZYvh/b2+t9rJpU5J5/RJrqFzg9/CKkU/N3fTb+eaQL79sGRfi3oaqBgoQOSA3FACzqNBlRCQKWsztOFSy65pGq26kLiVISozYUFkRRxuvDcYyN882OzK2oqJXzta/D447Pbt5VR1onSSU2zMBkdpaagfdMEv5WGvKNdrjWQyxZTgRODqQaORKNZOIRCIaLR6IIXG6c7Ukqi0SihUKjRQ6mKttDVwb6vPc6vHskg//miupMT8nnIWZJEHKD+J6mCoDN1fYuFjJQwPg4+38zrWhaErQRJJ6/LltRAmYVuKN3AkSjyeYjFoKen0SPRnMn09fUxMDCALvl18gmFQvT19TV6GFXRgq4OzKSFtPPY2RzNkea63pvLAXfdRSq2Av78dfXvO6NMOIXSDZoFSTJZbCKfz08v7EwTIuYEScdHPuegDebT48XQtZIiMdr40IMt67Pc+fUJ/vkHyympn6rRnFKam5tZvXp1o4ehWQDoGaQOPFFlTmTqfq+VzUMyQerI2Kz2bRkqq68YGK5ZiESjxd8zM9wmlgURQ70hb+nrOhOedbqLCRLRxj/YjN/zBLkHHiIXTTR6KBqNRqMFXT2YWSWqZiPocgnV8iQZm125BSurxKSOoVvY1CPoTEMSybiCTgv1GfEeZroZJxlrfNBhNpoGJNLSn0mNRtN4tKCrA0/QWfH6+9FZCQOAVHJ2gaumod6Xtxo/kWmqMz5e/D09Q5iXmTAJyQwCueAtr4OD8KUvgWE0bgy2qe79Ll+SdDLf8ESSbEJdM2nrz6RGo2k8WtDVgSeqzHj9s5on6Iz07ALgTVPte6FP/Gc60Sjwwh547rmZXa4JgyAmPvIL3vJ68KD6KbVAnmoKFrpevyou3OD2X9mkGo9j6yLHGo2m8WhBVweeqJqLhQ7DIDWLiguWGwOeNxf2xH+mMz4Owb07YN++mix0ASwl6BZ4DJ13z5Z2tzjVeNbpzmXhBdHPNZtW49EWOo1GsxDQgq4OTFOVGzET9WfYFQSdZZIar39W9CbSvKknj4VMdMRmxcRuMIyZLXQps8RCt7AFXWbPYbjnbqxo41SU53Lt7otANkuiwbkImbR6wJOOrv+l0WgajxZ0dWBY6nRZqfoFXa7kPamBWN3vNy0lJm0t6BY00QMT9DlHwTJJx6pbUx0H7LRVYqFb2Nc1teswTEyQOzLYsDHYZh6BpGNVF9g5kiP1W8rnk6wr2LWFTqPRLAS0oKsRKcHMeRa6WVjYUsX3pI5N1P9+d9+6sPDCJZMBY2iCxYwSwiAzXN2aZZqAWRJDt8Cva3pC3b+zeZiZL/JWHj827eeqXsaJY/GGjQUg6xrdZV7H0Gk0msajBV2N2IZd+OIuFWe1YqWL1prUifrcVlIWBZ220C1cxseBaJQeorSQJj1cPVjSNAHDPH0EnWtttJK13/tSwj33wKFD8zMG21SCLrhqGc3kSB5vrM81a6ivTyevXa4ajabxaEFXI+Z4McLdTNWfmFBmoRuqLyvCzsmCW2ehu+Zervz32x/mxx95Ytp1olH1T09TjAgZMmPVg+gsCzCN08blmo4rwVnPw4xtq97F99wzP2Owcw5+4SCWL6OdBImh+utBzhe2DbalkyI0Gs3CQQu6GiktJlxqbasV7z0BrLpjf6ykCeg6dI3k0Poj9D9+oPD3yAh897/yytLmoix043RftlpZ6MaqX+dSC50fe8FbXtPJ+q3TXs26Q4fmx0pnW1K1UuvtpY1kQ2PosnELrxCettBpNJqFgBZ0NVJmoUvX7x7LZXMIJJ3ESE0z0Vfcd6y4vm3peJ1GYJoCyyhO3Pvu2Mamv/wev/h+MUkgenCCZiNB22//hrLQTVSPNytY6HyOstDlFu51lRJSaeXyr+dhplTsPjG9cbMm8lYev09Cb68SzOONq3KcHSmGTWgLnUajWQhoQVcjxkRRVHk9XevBSts0k6MtbJMar8/CV2od1Ba6xmDmmgqFpQHMw4OQs3jsK3sK5Umiu07QzTji2v9Fi8iSjle/zgUL3aK2Be9yNU1wDGWZy2Vqv3c9C92SJbB9+9yLEts5ic8vIBQiEpJkYo0ripcZKYZN6KQIjUazEDgjBF101OErHznM44/mZyz2Wo3S7hBeX9V6yGVtmrFp7QqQitVn4SvUsEMLukbgJaWYJfrBcz1mXujn8R+MAjC+f4xuxmHtWiLtfjIJG1nFG6eyXE2CSzoXvKBLpymoMytT+71rmsCOHfz2it0IAevXz20cBQsdEOloJh1v3DnLjhW/SHQdOo1GsxA4IwTdwTueYe+/PsY9f3wPt7ztAAf21/8FPFdBZ2XzBJodWjv9dfdzVTF0CjunJ49TTd60cRyJ5dYCBOV2b8LhMn7F4/+2l699DY4ezLGoy4GeHiKdAeyMRa6KQcuyAMMgsLTbdbkuXEGXitmFViVWtnZBZ8RN2LqFpR/+I1Zl9nD06NzGkcuB369+j3QGyKbyVQXzySYbLVrNtctVo9EsBM4IQWeMqPIGH4h8j9yjv+DIDzbVvQ2vO0SkycTMzuxiyeXKA8GVoIPW7gDJlKhrItIWusbiubxL216ZGZugL8/vvz2Is/sFhu9+iteN3sdvvXoMgJbuIGSrd4swM3mwLILLuhd8DF1mqFgexKoj3MCLOw025Qj+z7extu2c0zjytlMm6BzDLIvTO5Vkx4shGDopQqPRLATODEHnFgK+8PGvI5Bk+4fr3oYn6NpaHCxz5sl3yxb40pcouHgtwyHQLGntCZLPWnVNRKWtxuwFPPG/XLFiSpWZueLHxcrkCQYcln3ug3y1+eN87pfX8qfyTnr/5DoAIotUe6pqLn5rIg1IAisWuy7Xma/r/v1w++2ccqtUalAJuiYcLKN2QWe4Qjj02b8juKgd65lfzWkchRg6oKU7AKY56xCKuZKdKD5k6Rg6jUazEDgjBJ3pFkMNnb2EoLDIxKsHU6dS8MVPpRgdLV9uJJXvrL0dzBqS69Kbnkfecy/pqBt7ZEoCQWhbEoGcRSpau6IrLRVRy8Q/Hfk8Vd2Amsp4CTF2HhxbnX8zkycQAC64AF8sqgqTxWLwF38BQEtvy7T9XM0xlSUZ7Ftcs4Vu78+O8Nw3tmKZp1bRpYfUWDuIk6tD0JnueQv2LSawqH3O1rR8TuJvVr9HeiJgmDP2yz1ZaEGn0WgWGmeEoDNSNkEsRCRMJJgnm6geBzSwoZ9Dt97JvnvK3UOeqGrr8tU0MVkvHoLxKNmjShnmTIfmQBOtS1sASB4Zr3n83r6bcMjbc5vMH3wQ/vmf57SJMw4rnp3yu2U4BAPuwmAQVSCtSKS3ddp+ruZ4Cj82vr5lqg5dDbGR2ae2wo7nsBOnVsWkR5QZrJNYWemWmfDiTkPdEYLhpkI/4tli2xK/a6GLLIqAnWtYpms2Ubyu2uWq0WgWAmeEoDPTNqGAA0IQDkkyyepWhtSBE4Bk9LmB8m2kcjSLPKG2QFksVTVybvC4Me7GX5mSQABal3eo/dTRz9XrTBFuMuecFDHy3w8z9h/zVLq/QWQyypI6Hfk8OPNkOClLiPHcr1mHQKi6QGlxr3NmMFbxdWs8TQALenvxCVmThc4TEbn0qRUx6bEsIQwiIYll1H5SjbhJEw7+rjYC4R/je30AACAASURBVKaaPjfTYdvga1ZfWZHeVgAyJyqf35NNqaDTFjqNRrMQOCMEnZHOEwy45Q7CkE1VF3SeNWL0cLliMNJ5QoE8wYgPMzezpcHLhDWianuWJQmEmmjrcwXdYO19KL1CxpGQM+fgeePoCNZoY5uaz5X/WXeQb9+8f9p1/u2jB7n7tjmmVbqUJqV4CRKmIQmFqr8nsrwTKE8oKMWMZQliQnc3Pp8K+J8J70HETp/aTIB01KCFNM1dreSsOix0CdUJQ7S3EQj7sXJzi/+zbVF0uS5pAyAzTb/ck0k2WbTyz1XQ5XLFmn0ajUYzW84MQZdxCAXVTBJuEWQz1WeV9KiasEcHy11lZtom2CwJRPxYNQg6L9bIy4azLAiEmmg9uweA5InaJyIrncOPTSDkq2ninw4z62Dl6suyXWhE71tP4sEnp13n6PefZvTOx2a1/UwG/ud/ipOsWdKQ3uvaYZrqelYjtKKHJpxC/FkyWf66Fc8qC11PD77mJvK1uFzT6trbmVNroUuNW7T4DAId4bri94ykpURrWxuBiB/HdrxuWbMiX+Jy9Syg6UYJupKHwrkKunvvhS9/ea4j0mg0ZzpnjqALq9/DLT6y2eqTkpesMDpabk0wsw7BIAQiPuzczHEz1hRBJwiEmgiuWIQfm9RI7XFQVsYmQA5f0I89x4QGIyuRdv60rmeXTslp4xgtU5JO5smV1Avcv9vi5nccqymIft+j/Wx433fp33gcKBd0nrXOsiTBaQSdWNJLmCyZ0TT79sHHPw7HjxdfNxMGQSzo6MDvV/FhM5FNuxa6Uyzo0nGblhYlYK16LHTJHCEMaG8n2OKHnD0nt6ttgz+gznlwaRdNOGRGG5Pmms04Sqwy9xi6wQef5fi9m07rhyyNRtN4zgxBZ0DIjXcKt/rIZKsfdmpCKaZs3CSTLmn1lHUIhgTBlmZAlrnhKpFzY42MuPrSz+WgOexDdHbQ2pQlNVa7j0VlVEr8fuacFKGsTrKsWPHpRibDtMIg1h+DfL7MPXjirqeI/+CnnNh6bMbtJ3ccBMMg++IRoDzL2CshY1qCQMRX8f0ALF6s+o2OZdn0eAa2bmFisKR9XMIiGG4Cn692C50rRk+5oEvkaWltojnsKyuuPBNm2laip6WFQEszSKfsXNaLnS/G0ImebiJkSEfr64s8X2QzEGlWbte5Wuhi2w6Q27N/xrjQejFN2Ldvfrep0WgWLmeEoDMNqSZPINLuJ2tWdzkWshJzOUYPFAOuTcMVdK0qiKe0v2olPNdUNmGp1lG2IBD2gxC0tkhS47VPbFY2T7BZ1eCqxZJTij0podcw3Sbr8cZMhHPFcSBriGnd3rH9IwBlgk7VfYPxPSdm3EfihFrXs656SSkAVlIJcdNqIhjxV99IVxcRYRAbzfHcD/fBjh1lhXXNpEXAvZd8fkG+BitPxlDHbGdPbd2ZdFrS2uEjEPLVFG7gYaRsFerQ1KQEHUWX9WzI54sWOnp6iJAhM9GgLNcsRMLqms1F0EkJ8RhgmowPzG/28ub1Jl++ZWiKu1+j0bw8OSMEnWEKQhF1qOGOANLKlTVaLyWVcOhECbnRncXJ3zAgFBYEWlWtipkEXc4tPmwkLCWqbJuAKwBa20TBElgLXlFin1/UZaEbG4O/+RvVGB3U5GFY6jycroIuGzORtj1tHODEQVUSxio5xV7W8diBmbOLE8PZwr5gsqBTAj2Xg+B0FrqmJlpa4aXBCOa+fvXeEuuUlc651l7wBXzkZ+ioJSUYDRB0UkImDS2dzQQifmxb1pw9bGbyBF3LeLBNfW7mct/Z+aaChY5IhIjfIhObH0vz3XfDj35U+/pZQ9CiKhDNqZerYRTvr/G99Rc8n47ofeuRD/64rhJJGo3m9OWMEHSmJQi1qMk33BkEKct6MZaSTknO7lBZoKMvjhW3YUIg7CtOTDO4XD0LnZG0VUNzx6E5rARdpN0/bemUKeM3JIGgcF2uNb+N++9XE8awO0/YOYljqQ2croIuPaiujZOvnvE7cUStU1pA2WsqH+2f2VyRGFMiIeu6y70sY1CWNStlgXQK4r4akTY/cmSUwIgqgVPq5jYzNoG2IKAsdE7emTaGyshKpKtQT6Wgy2RAGiYt3UECYR/Yds2FqVWYgvqKCcxR0EmpXK4FCx3QEoFMvI4PxDQ8/zwcOFDburkc2JZDpFWNZS69XGPDZqFS+cRL0VlvpxITR5OAJHVUCzqN5kzgZS/opAQzJ1RQNhDuUpNodqTyxJ5KC7rP7aKDOKMHi+tYprLIeJOwGTewLFi3Dl58cep2vBivbMouTGKe2ynS7iedqd11ZRkqIcPnF9Q6dxw8CNufzcOuXWQH1ERhxE2QSgTNJEgXKpkTxZIr1cRBbEC5THMl7kHPQjc+OPNxJ8bdhBa3o4iVzeNDLTNTuWKPUtdlWo2WzmYYj3I52wrv9TANCvekL+CD/PQZoJlotnDtvGM5FaRTEkyDlp6Qun/z+Zpr0RlZWbCMB0s+N7PBcYC8gz9YtIpG2nx1PRhNt+3xcWruZJFNO5DL0dKuxjKXpIjYgWJLmvHD81tTLzaq7rfUCe1z1WjOBF72gs40lH8s1Opax7pVumt2dGoEsorPgtZlbSyOZBg9Vpx8DKuJUIuPYIcqPmYlDMbG4MTuKC/tnWqyyLlB7kbaIZdwBZ3rcm3pbCaTrb10iGm6zQiaRU0WOinh7rscOjc+TGTz46rDAGBGi8c8V0H33/8Njzwyp03MCq8MCFQXdBND6tjKLHSuCBkbnlkAJOJqXa+jiJnJ0xZwxV06VxToMwi6SLcSMVetVq77MtetVXTZ+gJNkM9PK+hKH0DyxvxY6AxD9YedjvRQEqSktTdCc0Qdb61WNtOUBF3LuPcgNNtkHDsnwcmXWegi7X7S6bklCQHE4+C8dBBrV20ZBOq7QxJpV5/nubhc44fUw5Yfm/Fj8xtDF4uqG8qrranRaF7evOwFnREzQEpCbWoyCvdEACqWO0jHbbAsWnpCLF4iGB1SX4hOXpKzlUUm2O5OTAmD+OFxuP8+4j/dOGVbnpjIZooZsZ6LLtIZwDbtmou0ejXs/M3TB8/ncvDEE/DZzzj0/8/TvHXvF2gjWYgF84ocw+wnVo8DTw5waNPQnLYxG0onJ69rw2QmRl23sl28vb26gOMTMxe3TSSVZc9IudvJ5om0gEAJOi+w33O/V+Py8+L8Hj/l3L98I35srLS6KRwHcnZR4PuafeDULuhsY34sdL/4hap/Np0L1XNxR3pbCxZm7wFlOqRUDyIh1woZ6FAPUl6WcL3kTXXMvkCJha6jmWxGzrncRzQKbNuOuWl7Tet71yLSqa6/M4fakDE3POBsjjB+Yv4yz6WEWFzdx6nR0zO8QqPR1MfLX9C5IibU7oqpxSqS2ctgLCV1XH25ti4Os7gvRGzcIZdzxY+UBFv8BNqVhc5MmsT3DYGUxI9O7bzglXeoKOh6wiAlmZHa6hRYliQQ9uHzN2Hnq7tqf/pTuPvbCQLf+zbv3vd3XPmpNxIOQSZZ3oYMmFP5CIDcw49h/OTnc9rGbPAKP0P1jMnYhJrhHUcWJltP0OVSJsmJ6oLINCRmxrXQucVjTcMhGBQE/XnMtF0i6ILTjnXFxZ28tfkRxLv+DwFyBUFnmcpq7Llc/YGmGV2upTGfuXkSdIMPPotzxw8K8YWVSJ9QnS5al7UV7t9arLumCVi5glu6YNme5X3nlWopc7l2BXEMq2ZXaTWiow4kEzXXyPOuRcQN35iLhS42kCRChqXLmhgfqy4M621ll8lAzu0okoqenuEVGo2mPl7+gm7CnXxdy1p4sdsDskL9qtSAimFp7Y2weHUrpJKMDecLojDYFiDQqSx8ZtIifkStHxuZOqN41iHDLFrDmlvVGFoWKWtFaTzYdJhWE4GwZ6Grvt7ehw5y3n1f5G+j/5ff+M+/QHxmHZEWQdaNM/LOBcxd0FmmnLaF2skiPVZyDBWsjPk8JBKiUPS1UAjYzTpGSqIvVM8mTA7EwXFj6NyOIqYhVVHpgMTK2EWB3j5N7y+AD34Qdu6EZcvUe91CxyqpQhYEkq+5aUYLXWasKOhsY37O+9BzJyCZwI5Vf7BIDat7v2V5R/2CLpcrWMY9C91sLcP57FRB19ITAtNUcX5zIPrSBOTzmDXW2MuOuefE/RzPpWxJ7IRBhy9N97ldJGLOlDJDHt/6Fnz723VsdyBVML2m6yiRpJmeiYnpa2BqNI3kjBF0oQ5X0PWqHpDZiamTkhef1bK0jcUXdoPjMPrCaDEIvi1AsNOdmFI59aUJxMfLJ1gpi/XfDEMUJjEvjsizEnrWj1IGBsprx3k17IJhVYDWtitPOqYJR548xPmR47B7N9xwAwhBpEUUCiSXCrrSeK7ZkLMFxjQdN04WmYmiIKgkLOIjJtIwWBx2EyNc92DOlKprARDdO1J1+4nDKqYpiFk4Pq/NV7BZYmadQmC/95BQlUgELroIgECzisWDYskbz3rlC/pnjqErsSjPh8tVShg+MXMrsfRIGoEkvKK7IOhyqZlFmWEAOatwjgoPQrO873IZ9T5fsFj7L7IoAs7cu0VE96ls9nxu+mtgGOqz6V2LyCJ1THOy0I1adHZC18pWZCpdsC6XIiXsfWKQ/U8er7CFKtt9SR2TQJKKzXy/SKmKEL9cu1U4Tu3Hls9XT5D5/Ofhnnvmb1wazXzyshd0nnss1KWEWPOiDvzYhQzGUry+kC3L2lm8ZgkAo7uHi9voCBLoUmLMTOWIn1ATczwuytwhOUspuhAGtuUU9lUQdL2ulXCSyzWbhX/8R9iypbjMtkHm8gQiftVRoIoxoL8fnKERzvv1RbByZWF5uNVX6AHqda2AuVnoHEc1k29EQ/F0SSHZStYeL2uwd4kSvrmkZ6GTLG1V5zt6oHoZB8/quiScJOsen2VCMCwIBiSW4RT264n7WggGZSExoyDo2kosdDO5XEseQGxz7ha6WKxYbNlOVxdoyTGDCBmaFvfUldhgJkxwnEKog68tQhPOtO7d6ShY6EIlLtfFbjzs4NyyQ6OHXEt5zp7WffvFL8I3vgGZcXUtWnrVd8GcLHTjDp09TXSv7gAnz/hLU+/NkREwnthI8uebay4SHDuktrOYUdKJme+XnTvhX/4FDh2qa/gF1q+Hn5/6CIya+da34Pbba1v3rrvgC1+YutwwIPH9H7P928/NqSexRnOyWJCCzguoridmpBpGzLWmeJNvaythjIqCzuuv2trXScuvnU0LaU68GC/GTHWE8LeFCxNT3HW1ynSaZKL4+JdLW4Ckw58BJ098uNxF17KsHZiafWaa4IzHGB8pTnqW4UBeFSX2B5rIV4mhO7BpFJFOcs5vnlO2PNzmLwiTMkE3y4kV3BiwfL4hgi6TyKmm9lQWFhMHlGWi9yx1rj1rkmVB29JWImSmrUWXHFCT+5KlgqxbyNe0IBhqIhAUykLn9nYNdkVqHncgIAr9fQtZsu794Av6wclXdbcBZGIWzbh16OZB0A0dzkJaCVzP+lWJkWHJYjEGnZ00t7lxcLUIOs+q7cbOidYWAliFOMJ68Wrv+UstdK61PTM8t7IcUS+7NJer6k7LZmHwuGTn85LNu1uV1dLd/2zLlkipHgY7e4N0X7AIgPEXp1qP+180lK9vIsbx/trOn5dssSIyQSo58/iOH3NgZJjDh+s4gBK2PjrBo3fHF6SFb2wMnnsOjs3c9Q/Lgi0/7Gfwp89NSRaKj1owdIL0zpdmzA7XaBrBghR02zdbfPjGNMMDcy/P4GXVeRY6hCASzJNJTJ0901EDPzaBpd2Is89ipTjO0QNmmaCjqYmg38FM28SieRWrZdvEjhbdp54rsF3pNhJDasLwJvDI8k6gPC4KwJ5Iwr33kH50Q3H83r5blYXOdpoq+g5eWj/ACo4TufY1ZcvDHQFyhorNMRKulQN7ToLOs3rlLDmtCDkZpBMOXRGvhMjU2XfCreXVe66abD3xkbMkza1BeiIG0YHqWX9e26/FZ4UxTWV5VW2+fKo5vSkLgs6LC6uFQEhgud1JCtfUdUfWUocum8gRIYsPZ15crkO/Giz8Pp3LdWQElrRmVPuu9toTGwxX0IU63TjDQICgyM3eQueWavGHSgTdsg4AMlVqStaClDA+nFPdYWRRrE/m+HHgoZ8Q3vwLjg83E8SkqVt9jmfrck0mJE46S+eyMN0X9QIwfnBqJ5MjvzyKDxucPANbanO7xo6naSNJx1mdpGrwSA89thN+9COOPDk7E51x70Mkf/REoYj5qeTFF+HJJ6u/vmEDyJ27iK9/bkbB+fzzYG54Frb/irHR8pXjB91C8+PjbH90rMK7NZrGsiAFXXDjL+CO7xdaJs0FT8SEuovWlHCYigH9qXGTVpFBdHZAczMrV8LxQ0YhbivoisJgcx4zkycel5wlVBeA+EvFAqEFQdepTq/XSqq5Xb0/vKwTgSQ9KfssH0+B45AaLBGHcU/QBfAFfEjAyZWP3XHg0PMJzgscg0svLXst0hkAyySbVYkczeQI+ecm6Ap1yOxcIS7sVJFOSbq61O9mcqrgjw2kaCZH5wVqgvQsdLmcJBBqYtFiQXS4+rHHh7K0iCytK7vAzpFN5bFyqsRIMCQwzWIcWLC7peZxB4JNhXZzk5Mqaomhy8RzhEMSv09iW9VN15s2wTe/OfN4hvYUJ6Rqgi6Xg/Fhm96+QNl4a7GymW5GdakVM9AsZ32/eBa60hi6lhVKUKVHZl+/LZEAO55mGapWYLVSOAP7M3BiiL/Y/RGaXtpPWJiI1rm5XONH45C36ehro/ncs2glxcSRqXG1/dvGWEU/bSQ5vr22UkGxYYPOQIbWpa1kMzN7O4ZeUC7aI89Wjy+dDjOVg7ExDjw/v7X0auHp7xzigf+3t6JYy+dh42NpmrZsxt67n/QM4nbrj47TNDEGeZvRF8s7d3gtBfsY4LkfH5sXD5JGM58sTEHnukdn6pdaC0Yyh0AS6G4tLAuHIZuuIOgmbFrCDgjlajtrbTf2cJQjx9xq925gdyAA8WQTubTFWWerdeOHix9+z4LV3qMmn8SYa9Fx3y8iYcI+qyzAH4qTVmmcmBeAH2gNFIqqevFEHseOgXk8yvlrgtBcXuw23BkE2yYTs1SzdJ+t3H/Z2Qsx7/gAjLHaSq/MF+mMoKvXLXBbyUI3mKXLl6R5mXJhedYkK9dEINRE99IA0fHqAdLJMZOOlhzhLiVeUkMpnJyjStaEmrAslenahIOvrXaXazAksNy6g57V2LvPPZfrtBa6VJ5I2BN01VfcddcenvvG1hktEcMHkgjUStVaiY2OArEYS85T1k7vgcQTdJs2VY+58kIdSh+kggGVVDIbCi7XcPH+Di7toglniqW7HqJRIJFguU8JmWrfOQNbBmghxcXtA7x9/Btc0fICTc0qnq8eC51tw9e/rs6bFx7QuaoTenro9icZP15uPXYcOLY/y6qWMVY0DXH8hdoy4ydGbDo6BC3dQaRpkZnmFEkJQ0ctfOQZPpgiW8WAnU7DxqklNwE3CQbJgZ/31zS++ST+s02Y6zeXhb147NwJiWde4LXOJkiliU0TbplMwu6fHuNKNgMwuqtcPHvxtW9o/iWpA4Pa7apZcCxMQefG3cy2TVApRjJHEBPRViLoWprIVqgwn07YtLYUl6+8+iwwTQ4878YDuRaZQEAwOu4Dy2Llpd0AxI5UcLkuVscRH88rAdBadPu2hB0y8fKJ1LOUpEv6U5bWsPOKqk7uFHBgVxaiY5x3bd+UYwp7nTFGkkrQBZ05TaxQLugqddyYD/bvh7/9W8ri9KSEdLaJjqUhBBIrPdXSNjGSo7OzmIDiBfznctAc8tGzMoKVrF7qIjFu094uCq7CeP8EIAm0NBMI+7BM1ds14HMQvto/PoGwD9N0Y/ImCTp/0AeOQ96uLgyyaYdwRNDsd8iZ1deLPrUbZ8fOGUt5DB0x6UWJmGqCbvilJBhZei9erI7BfSDxYu5++P0cd/+gsrgsZAKXWDEDAWb9IFHJQid6uomQmfJgVA/RYxkwsixb7X7nVKltePz5KCs4jrj/Pt4Q3szbFj1VuP71FBYeH4edT03wkwcdVZgc6DxvEQhBdzeMD5c/pJw4AdbwBGevaWPFChg8kqvJMhSbkHT1NNHaE4ScRWqiulU1HlddZNawG0ZHOHq08nobNsD3vqfC+SZjuCVfXtoyv/1oayE+rlqxjR6YqtZ++bhJ1wsbucq3BexiZYJKbH/WwXnpIL+5+hAhDEb3lx9obCBFEJPLr19NYPAId/63ySc/Cf/wD+gkCc2CYEEKOi/ebb4EXQhTmeVcIq1NZLJTkwvSCYeWtuIpWfKGSwhgcWxvuaALBinEV/Rcvpo2ksQHi7b8nGs5al+qJsBEXBIgp2Y0bwxhFeBfilcNvzSI2RN0wfbgFAvdxo0qe+vR74+xSI7Sed2rpxxTeJFbSHkkiZHOEwq6E2uN/TgrURoUX9p9Yj7Zv36Q8QfWk4iW9D/N5HGsHC09YQI+B7OC2zg2nqerpwl/i5uR6RXztZsIhH0sOrcD8vlCqYrJxOPQ1ukrWOhih9WXerDFTzDiw8w1YaZtgoH6zl8w4sNye8t6VkNPIPlCyuo0XUuvbNoh3NKEzyemdbmOj+XByZMYmOq68zBN1U2jL6AEXbWkiJEdKs5uyatXACBaIjS7BZItC4y7HuDwD56pGDdVEHQ9xQepQFCohJpJHDs284TofTZKLXQ0NxMJ5Ocm6F5QVpjla9SDWaVSOFLC8ZcyrGyZgOuugx/+EP7+7xH+qRa673+/cm9nj9TRcbj3Hl644zle3K28B+3nq4z67l4/45P00JH9JkxMsOq1S1hxURu5sThjY2pM1YL8bRuSSUnnkiAtbiZwpRJJHkPH8xCL8drQTkgmOfJ8ZTPWoBt2OTnTNp8H25K0kyDan2C8ehL5vFPaEWNs14my12IxeOFH+7nKfILuG/5ALSvpnTt5Oxt/cJS+1Iss//sbWMwYo4fLxV98KEunSBB477u52nkKa38/7S15hgdyHDlyEg5Oo6mTBSnovLgbYx4EnZnJE2x2oKl4qOE2XyGDsZRUGlo7imURmi65mD7/MM7YOE04+Ntdl2tQkE8qIdNx0TI6IzliJ4pP9l7cVvvy1sJ2A82y4MoFJSrTk7LPvAm91LpSCMBvCxYsdJ614s6/3cW+7z/LWcc384c8AFdeOeWYvFpZ2dEURsYhFHID9M15EnTjJydmJvrEc7BvH+ahYhC414aqpSdEoFliZabW/4vFBZ2LmwsWulzawsnlcRxJc9hP9/k9avtVigsnk9CxqLnQIs7LFgy2NRcEnZXNEwzUFwgfiPixcm4Gt5cl6z4geFYn7/rv28eUZJNMVhBpbcLvh3yu8rWzLEi6fWgTh6tbSoaHgXicvlVKHFVLshjeM0YbSUKXnK8WBIM0Y2Nl8yQm8jARgwP7eeaXUwWhkbDwY+PrbCueg5CY8iAxMaFK9WyfoeuWXUnQoUr9peMzx/RVI7p/nFZStF2qssMrPUSOjoI5EmfFha3qM/z7vw833kiTT32eSwXdhg3KzVeN1OFRdRPs3s225wO0kcTXtwyArhURjGS5e/TIxgFCMkPvNRey4tVLIJ1i4IUEP/853HprUWSVEo9JSGfoXB6htVfdx6kT1RNHhnYMgZPnvD+8hB6iHNlQWSme2NwPD9xPcrT8HBnpPNg5ZeEbHubAi6fOXGVkJTnXszG6t/whbeszDnLnLl77Guj4098Dig9ok9m5E45uPMp1wU3wR3/E4i6b0ePlDwqxUYuOdglXX80fd/2cLzxzLR+8dTnceSf7d+tqw5rGszAFnTvRWVUyzqpRqXikskqVL4y0N2OZsswqICWkM020dpVbAM46xw9Igr584Yk8GBaFHXVcsISOriZiYyVuUtcC076ywx2EMTm0jZb2JjLp8snNm1iNbDF7tLQosTfx24ZN3pbYG57huqc/zV9t+GMuf0UGurunnBOvtEJmLIOZdQiGVfkNL+NyNpQWlq3FQvfss7B5c337GDuqBHKpxcTrrNGyOKIE3ST3XXRMkk8ZLO4L0txWtNB522gO+4mct1yN+1jxSd1xlIBSbb/ytPeGCpZNz/IabAsSiPhxHEkm5RAI1NZVwCMQ8ePYyq1qZXLKBd8+SdBlLaJR+JePD/KrreUiK2sIwm1+mv2yag/giZEcpJUaSBypPHFB0ZW64hUqDbuay3XkYIIlYhTOcUvhCEGg2cHK2iT6xwFJyEqw5a7DUz53ZtJSGeBtRUEXDIopdd6Gh10hPkMpOTtbWdC1tAkyNdRZq0b0cIIeogQufQVQ2UJ3/IgN4+P0vbq3bLn3feCVLZHS/R6Z5iPhJTydb+6CPXvoDFsF70HXWW2QyRTKIQH0bx/jLI4iLr+M5VetRiB54fFBHvphCp7ZTHSwQi3G/hg4eTpXttG6TJ3/1FB1V+PQjiFCGLT/+ds4Wxyj/7mp946UcGL7cRgdJXWw/GHI+w445wI/oVySl9YPVD8B80x8IFl4+hk9VG6F3HrPEValdtH70XfgX9VHG0liA1OFrePAj36QZcnBzVz5tuXQ2sriZX7GRmSZezsWdejsEuD3w0c/CitW0Pabr2WZeZj9j1fxU2s0p5CFKehcN021EgKVkBI+ef0+fnlfeZaWmXUITiroH+4IgGWRzUgee0y5LbNZcEyLlq7yhusr1yqLTqlFJhhykyQwCa5aRuciP/GJ4iffE3SRvm6aUMsDzVNF5eRAZc+thGEUXvO2FewMF9oe5Y2c2z7KIfDW31NpjVVSGyNL3M4Y41kMQxKKCALBpkKA/mwozXKs1HFjMo/fNcr6u+urZ+BlopZOsIVOHr0tFd3G/c+OgpPn7F9rIeDWTMtl7UK3iEBLM4FFSsSY8aJF9X++J/nS/y9bIQAAIABJREFUFx1VesbJ07a0pSDoPMtroC1Y6OyQTDgEZ+j6NZlgazNIiZWyMFM2AXKIkLoxvVIctmGT2nsMHvoJEz/+ZeG9uRzYlkO4I4C/WWBXsdCpDhjquk7nch3acQKBZMUVywv7rcTwsRy9i2VZqIAS0sX4r9fxNNHnjnLgQPl7VaiDAa0lLtewb0qdt6hrSJwuaB8gb6kxeu5pj0ibn0xq9tbm6HGDnnCW4Gp1LiqVZBnYOojI2yz/jVVly70YOs9C54na6Y7FE1ZvWfwMWCadncXXOs5Wf3hdHqRU2bVntYzD2WcTuOwSFjPKL5+0sX7+NOzcSWLrVP+uV16jc1Vn1ZqXpQy9GGMpQ4jXXMGqsxzGjqSmiNJoFKxRdU+VZuEDmGPqcxm56tWcx0sc2Di7TNnZ4FUX8GMzerT4XXHiBBzbeJTXhHbBW98Ky5fTSYzY4NSL8+yzMPjEXt5i3UPTzR8HYPHZEfKJdCFesNT6D6jAuW3b4Hvf40L289LW6Kzi6L7yJZOnnzzFtZ80L1sWpKBramvBj42Rqv1Gd/KS8Qee4sT3nyhbbmQloUmTb7gzCNIhE82y4b5htj1wjG2bVD251kXlK6+8+mxAVfr3CISVsOoIGIj2NjqXhkgmi09zXkxSYHEH4SbXZVquE2npbCad9ZVZNgqWkrxdaELvlcgIdITLkiK8bLzAyiXw3vfC1VdXPC/BJapESmbcwDAEIS9bcw4NzXMlnQVKixVXI3rvk+Qf+EnN23ccmIiqk1lmoXM7a7QsbSMYnBpg3//kYfzYrHjDRYWMzFym3EJXyfo79q0HOPK1h/jJXa4bfUVroedvfMwtUdIeJNDiCTpVhqQevPdasYwKAwgUXfDFGDqL7JCyQpYKsmzaAcsqEXSVxXj0xaLVMXGiukVm+IVxeogSWqvaklUSdIYBiTGT3rPLa+0FmtV59zL+XrdmguCR/TzzZHkygZm2CTZL8BVDGCoJurGRPGzdSvb49IFXXv9af2SSoGv3z1iKohpSQnTEpntpoBDmUekhcmD7EEsYpvny8pJABUHnli3xPv/TWuhGMvixOf/Wd/M6nuZVK4tuws5zlIU9fkip3GQS7JEJ1YZQCFi2jBUtcdi5kzcc+2+17vGp19mrxdh1Xg/BpV34sUmNVq+9OHQ4y9JOEzo6OPuyRTAyytEj5ffY4CAwoa5RctK95YVdBH/tXM7pnODE/uS0HTfmk3i/GtPZ4hijQ8Xvgy1Pm4hDB7niD/uUXz4YpLPVJjYp6cRx4Mf3Wqzc8zMu+72lhbJPved3QCbN6DH13ZHJqASrzqWTJpPOTi64AMxjo1WTSaphZCV7//F+Dnzlp3UetUZTmQUp6ArFe+vo+5hLGiDllA4QhgGhSPlhhjuVZWToYJrhh56Fxx7lx99z3Xm95bXFVvz2GppwCJVY+YIRV9C5HtWOFa1IwyQx6nYl8ARde4hwyLXQBctddJHuEI6dL5tASifW1HE1HrPEQlcaa1XoNtA6SSlOQnR1EiZLNmZimIJQi09NrHOo2VyaXTpTnKNlQTKWL1hYamF8NI/jVkMtjdfzrAyRpe1ugP0kC932KCubBvFdtrYo6LJ2MVO4pZnmTrd1W4mV0RyMwtAJnv3uC4Bylft7OmjCIT6hJolgR6gQl5dMNxEM1elyda+TOZHBypQnVRQFnV2YHEvjlFQzeEmkK+gKusr7GD84QRMOncRIDFe/LuP9CXoYx/9rFwCQM6aaFkaHHYjHWXJBR/lxBCBnOiSOJxBIem6+kV/L7+TAIy+VrWek7SkPUsFwE2au/LxFdw7CjudIb9pRdbxQ7I7hD5ff7y1dATJZMasOBbEY5GIZes8O0dTeih+78HkrZWBvkj7fUKEvr8fkpAgpgXR62t6pqdEsraQRN/w577xsH7/xW0ULZsd5Kps4flR99ieiDoyP07VmhbtDwSUXmKxMvcBbzttLhAyJwamCLnYsiR+byLnLED3dtJAmFa2ssEwTJkYslq5SF+usa89BmFkObS4v2XHipTSkVJZnanhShxu3hVyoK8zyy5bB0BBDtZXLm3NnCa+6wHnnOCQm8pim2ubWuw7xitzztN/w9sK6nT1+YtHye318HMY2vMjrsj9D/P0nC8sXX6zc617pkviICaZBx4pWJnP+dStheJj9e+r7Uh16YRwSiUKbNo1mrixMQQeEAqobQ614pTQmd4AwDAiFJ4mpHjXZ73jGgJFhrsxvIPn0rwBoXVIu6Pznr2ZFeIJwqMRCF1HCqsOtM9dxlpr0YvuVq8ETPM1toYIQbJ4k6Fp61BdoaR/KgsuVYlaalbbxYyurpetytQ27KOhaJgXnTSYcJtxkkYlZmJYg1Op3BV19gqQUL4tXIDES03+JjUdVUFG+Dq/C2J7hgrmjVPCmx9Qxt6zoVG24SuYox4Gj+w1WrZIQCiH8PvxNDlY2X7g3mluDiFCQgMhhlTwsWKakjwGaDim/YdvZ3YjWFsIYxGLqPAXaQ4Xeq3ZOxSLWgyforHgWM5svi8ErzXI1JtQxJqLF4/ZaW4W7QtNb6I6k6CRGZyRXqH1YifiJDJ09Pvw96r6tZKEb3jkM+Ty9l/x/9t4zTI77vPL9VXdVdQ4zPRkzg0EOBEAwggmURUkUFShZOXhtreVrebWWvU4KtmxfZ1t6bD1XtmVJXoddS7Kyd5UTJSqTIsUkkQCRB8BkzEznUPl++FdV55lBIAiacz7oEQfV1dXV1fU/dd73nHew6e9KKICu2RTmKiQoEnjVK+jNBCg81hxIp1XsNtKrRmUss7l3dfG4uP47jeJrhEfogq2ELhPG0Q3RmH+emJ82oVRkcGsSYu5ospaHSE2DxbM1NkwobRmPAbm55GrbwGc/Q+X7D3d9z9KyTjxqiz6sBx+EP/1T/99CE8OEqfnRGtlji6IXbmufv82tzwvz+8G/IvTJfyNJ0R8r2Hi8jz8p08ci0sgwpFLEqFDOic/1+c/DiRMN52DOgWyOoZ2i3Bu97Vo2MM3Rbzc7RmcemiVNjgxLlBZbTBFu20W4JyLK0qUis0e6l/w9PPoovOMdXJSal58WQeJjNw5DqcTijM6pU7D0yGluzJyE5z7X3zY9qFLM202Go8U5E37yEwZu3NRkKkvvGRVlXNdo4WcGjtV7Qj0k77yJYessR7+5htliDZh/UEh6+aX1kus6Lg0uC6GTJOkuSZKOSJJ0XJKkd63lNaEQ55Uqb5bETaU1MLimC1WqEZ6D8bFvLhI1C7wh8w0Spx8HRDmv5eD5r79g85qX1e86HolKDQi2lt4kRhd4/RxG1UTCQU5EiERdQtBSovPcp5W5+o2vcUanT+gqpphdGo3WF36tgdAlWhoEWyFJRMIOuawDpkEoobqOywtTNbxjAohTplpc+Wa0dKoAloV5HuttowO1saepvFxDwUAZ6GkrG89NW2gLOSauqRtDFNnBqFm+iUOJKiBJhFomFtQ0GJ8I8nz5O0SpkNjcD4EAEdXy+wVD6YhP6KBedl8rvDFfeqGK3tLX6ZEUs2ZSdQN5i9n68XlZf9G+qCB0Dae88Ttcnq2RiWkk+1QK2c7fi+OIaJfUUIRg1M3q6zAbduExsaAPXNucbehFj+TnNZJhcV0m92+mdq7UtDDXKnbbg1QoJoNhNpVdl84KdaeSW/nBwI8tiTYTumhfBHB8B7RhwHvfC5OTK+4OgLlHZsG2GbpmWIwmC5ht95xc1oGlJTK7Btpe7+fQeaYI24FajfJipetvq5QziSfc8yK1PFRlMqQDRXJz4redPS5Krz3b++vbvPvdwhJ87bUk43ZTrI/jwEc+ArOzDq9Nfg3CYQgGiUcsSjmTxUX40scLfPcb9S9q7rF5MA1xDgD27mV76AwnHi02XWezh7KMMENcKlNcbv6u/BDpTIz+GzcRxGLmwdVHlN37dYPCk9Mdc+3Wivx8lbRSof/aMcDh3E/neOS7RQJnTnP1z+1pKvmnh6NQLlNo4JpLh+ahUqbvDS9o2m9g2xYyLHHuhNjYzwzc3G484+BBtnGM4z9aOq/pEXM/EQLAaoagdaxjrXjKCZ0kSUHgA8CLgN3AGyRJ2r3a67oRulqtPQcJ6s7LxsBg2wZDdxeSBngN76VjM2zjGKF/+SAv5suE0Hy1rRGjH/p9Rv/2HfVjc/eXHhZKX2qbuNl7lnijKlQ1KRrxF7W2kmu/OIbGfCirYQKAV9bQKhaqZIKi1E0RmlF3vyZX786PRiG7KPYdTgpCZ1tO1/iL1eAR1mhMWrXP0ct7Oy+F7mi9BNFYdi9nDWKqCbLc1o81+Z3TYBhsvH2j/zdFFuVEP/fNJWSqStPoM10DdWKEV/7lDfz5pn8mOCgUkUjYwWONajradK69svta4RFvPV9Dq4kxZB4aiXotJ96vcdHxJiFE+mIuoasrQr/7u/X0/qUFi97+AMlemXyXRaJSEQ8/6eGIUDEluyOhmz+8TJoc6p7tzZ8jJGFoDoUlg1RKXNPJoShUK01J/VrNaTtHakwBx/a/D8OA3Jz4vJXiyozfy97zSKiHuJezNi0+8OKiUKBaTRqdMP/YnPjNX7dVHF/LdQFQObsEtSqxqybaXi+SkKS6QucGDNsVravqVCrYTdFIrTtMpxwxBB7InsoiY5LYMVLfJp32+7xSaUnEx7j41rfgwa8u8fLj7+OqO+rKajzmUC5YPP6wDp/9DGf+vT4revahGQLY9N/gfj5ZZvt1CYypeT9bzXFg9mSVkfAy8f4opXxLFSRXD5EO7L2KQeaZ/enKs06Xl+HIpx6DL36R8mTnbLi1IH/OIJWC/n2CkJ57YoFHP3uCXc4TRH/h1U3bpseToNXIzde/nMVD8wSw6dm/sWlb+vroVwssuEYLb1a3VxZv3Xb7Zova2QUx83eNmDvittVUrTX1InvQ7nuY5b/6x/Zso3U86yGvvslF40bguOM4JwEkSfoE8HLg0EovCkXqsy8b8e//LhxM73538989QtfoMKvVAMNoV+jchndmZtkxUoKXvYw77ng/t37r7YSGT7AaPKUmNSrUvOSOYSQccmcF09SrFmrAgmDQf28l3HwMnhLoNfpDc+nLKy8WShJxVdzg67ElFqbt3kRTqxO6SCzAqWVxLsNJFd29Eei5CvJAe0/IatCrwqUZiQVWJXTLp8RNazUHmHdvkmVYmizQS5Ys6SZHbSWvE42KzyEIXf3fTn/vDGFqDL1gr/83VXEwtLpC5zlfVZWmSRmaIRGKBZF+57eJ/vZv+cpJJAIURGlZ7Yk1E7r4+f10/OknBQ1Nc0g3PDc0ErqqW8IulcVCKklQXWogdGrAP1e1GmSXbe6/T+LmmyVyWcjsVCGhUjoiCF+g5ZEtt2RBueJfu3LQ6Ujo5k5WGAjlYWio6e9KWBDpWs5muNdtORhLgl0mP5mlr7/XP7bwQPObC2W7KqYx9KsigLaQR0Vf1alqaSZBLCS1JbbE/R15DuhSzoQf/Iji/i3wgqG2/TRi/kiOQeaRdovIklCofdasRxSjo+3KjCSJ//EVOk+GrlYpl2nrIQQolSA+0r1NItUb4LhrCMqeESV0aXys47bJXplCg3n861/Q2PmdD3NX5kH4cL0nMZYIUCo5/PTLZ8EwmDtZEZNTFDj1WIENTCPvfY2//bY7N8EPsxz5UY4tW9LC4bpYYHhzFMNWKOab78v+vOy+OAxlGA5lOXtCPJA6jiCaExOwZUv9NT/6oYXz5BEAymeW4KYORGkNyC9bjPYEiF01QZQHeOzHBguPnePOoTm4tjloXVRSlkVrzC5xTheP5eghS3DH1uYdSxL9Q0GOzVs4DuSni8Qoo2wcoRN6bt4Jn5wXEznGVmmDcTF3WkPCwUEi/+Qs4QMTa3rdZ37hc3zv+DAv+sgf8pIv/yry+Ahksxhf/SZf+uc5csUAyQQEghKlskRNA0WyUIIWNgFsJ4DlBLAJ4LSqxOt4RuNyELoNQGNzwRRwoHEDSZLeArwFYHx8HBBZb+V8O6E79vEfU5yv4Pze7U0VC6+vq9rQ3qHVHDCMplIZQGQwKX5ItsXO29z+lL/+a0If/CAMD6/6gbx+KC9mINCTIilX/cwyo2ahKuKmHIkLItdaoosOixW9cQ6lp9CFqfl9Kgv5MKMhQYq8hd/ULHQ3hHbVkqt7DMasIDXhdBhNE/vW81WiA3Gq1aZBGqvCqFooCkSiErXKygvx0hlxTkxr5RvH+98vYvR+8RdFz1Jfj0k5ZzQRunLBJhYT+wlFg+hmfZ+Tj2YZD59D2lFXlBQF9Jrj70OJi3PV6JC1LQfTcOq9iA0XVdgrl6MjxaL+qC6A0Gq9iy1QU+4c1JKOrjmokfpPzyu5NhI6u6pTKVrEkkE/GiYymERRJQxTECW9YsJHP87xG65l5nW7sYtlesdimKEodlWjXLBIpJuvu9zJZXBsejaJa1eMEmv+Dg0DpqbgjlGzrSyohoWxoapLJDeL406Op4EyhZOLcIMgPpqGH/PinzP3d6jnKkCKxUUgX2CUKc5UOi+U/jHpDrJkNZXQQBhkoIHQPTkFTzxO6fsleOvKhG7uVJUtPfWsvFBIQmtxTnv9i22tGNQJnW+KaCF0mUzz9rYNlYpDPNPdyJTqV8kfEUQoO1ulRylDT0/HbZP9IWonTV8NzH3lhzxn6YdI3/4EDNRLxPFUkPK0xJEfiR64paUw01MO4xslTh3ROJBahr56n178hbcy8kdf4eg3JnnxG/cLh+vyMiO39rA8rVKZc5oeFrSCJoLXexIgSQxvVHl4RscwhDv2U58S2912G7zylaJicN8nTpMpn2aJzIqhx6shX4CrxlQYHqY/mOXYIQNp+ixXv3Vr27Wb2tIHLLsmBJfQnS7TpxTaHlwABsZCaE9UWV6G3GyNVKDY/qW6CN1yHXxsBu2J47Bv16rHbduwMO8wHs9yutRL/sgcg2shdIcPc+i4SmTTMF8+qvLoln/m+XyTzdZR/pVf5HRoOz0xg6KmYNtCDAjLJgYhDFsmINkEEaMoA46FJF2kK2UdVxQuB6HrtJI3XUWO4/wj8I8A119/vQMQigTR5psvtmIRlh8+BaUyxeLtJJP1f/NLrrWAr2zUCiKrLdxC6KR0ihAaMiYjL3QVnWuu6Zrl1oqxiSAjzLDh6hvdHUokkhLFRdflWrNR3DMbTiiA1ZXQeUoc1HuZUlKRck7MbFzMyVyXFNt4eWWWZqK7yphHFFZCJCH7pcNwOixiMBCEbmm6xu/f9SC/9vc72f2ctT0l61ULRXYIRwPkO5DuRnjBp6sRuuX/+VlOhQd44xsPsrRgsXtQZq7sNJXAykWbfrf/SPQBBnBsB8uWmDppcMc2pUmSUlQJQ7PrMTIu+RXByu45KApbXCv5AIi46qoasESZt0GhW9WM0gLve9KKwpzSaKpoJHR1xdOhMLlMbF8/1WwNCYdQfxI5FMR0ba7aUgmqFewnj/K9r4yBZZLZnKLqhIEshcllEvubv1Mvo0wsbkIRbR0ldmbSxlxYZsuLmw1CIB5MyrqCo2ukBsMN+5qmcEaoWZYljCPhFhXTN4a4ruOl6RpUyoxzhpO1a33VqBMswyIYbL+GWnPWilPi4cf7LXaDYYi5qbdMROvHF5Iot1QFGp3VrWgldLbRTOhaUSmYOJpOvK/7bzY9FMF8WKNSgeyCyaZMsL3XzkVyMAKVKsWCI6oRk5MM3H0j3H5703bxHgX7pI49vcCdfJ2P197A2UcWUdR+arNZNu9rUemvu44doQ/xg4fyWBbMHs6JebfXjXBat3GqNcrlemZ0rWgQDtRzFYd3JnG+nmN+Hn76iIn03e/zMzeU+c537+ThhxUOHID5+0/xGunbfNp5VVOV4nyg1RxqJUtch4EA/f1w+vgxttjHSL7xFW3bx7cNI3OInOsiBlicNdg71Pkc79sHn74/xz3fcMidM0gnnXbJ20Vo4xAwg7aQ7/jvrVg+W8YsVdnxnDinv1OPqlkN2Q9+gkVplNe+93b6glk++57j/Jt2F6gq4fEBfvX3Btl3TT0Oa12Auzz4M+ltT/chAJfHFDGF9zgkMAp0GFjTjFAsSE1rvhpPHyrDchZ0zS/lefAWbce2/fE9XlZbONnyRJxIkCbPLg4j3X7w/D4NMPTGO/h/P72XxMH9/t/iCYlSwSUJNdsPEo4kxQrVSuhCAykCbj6cB0+hSyahnDNYXAQ7V2Bgs7jh+rElmtk2D3QlRFP1VTKUjjQ5Lhe+cxj78UM89uH71/z5Dc1GVR3CsSC17vFWgOjrArBWadcz5xcxnjjGQz+okcs6ZMbap0GUKxBLinOgRmUcRD/Y9PEq5lKOiRuayYuiShi646u3XpRJKCyhuTNF/QytRLtqEom7AdJuxIiXVSa2P09C535PekkQOs8pDRAIq0g4WLrVVMIuToqbfCVvEKWClE6Jkqt7SoTSBSwscN/nBVHL7OjzJ5QUJtvjELyIBK/vUw62E7rj90yCrrHlrm3tnyMSxKlpYJl+hEN88wASDoVp0WekaYDerox7hNr7fS4eWiCIxXCsCDVtxUBeU7ORg+0PD7ExoQh6D0ZecO9Kw+gB5mdtnFzed3dC5zYPT0GPjqRpRZ3QifPnK3SmQXmpPTamdEac+1YnfSNSG+Kg6+RmKuSyDj0DK5RnN8TBtshPFTl3PA+6Tv/e9gpDvFcV02rmz3LLziwRqpy5b5qTjxUhn2fzwQ3NL1AUtl8bR5+a5/774XtfEMpe5NpdxAdioNWaollqZavJ5DOyfxBqVWYPZXn8i5NMPPlVXv+Rl/IH/+c6Np38Jvd+sYRy6ii3vnKQADalhQsbH5ifKjZdh30jKpgm12TOwk03tW0vjW4gRZ7clBuJpENh2aBvrPM9tG/PEDdb3+e7n88xvxQk3dt9ufR+32udPz73gHC47njhBOBO9+iCQ49oVMqi2nT0Yw/A+DjbD/Rw9Ss288f33ck7PnMjd//Bfn7v70fYd41YZyRpncw9G3E5CN2DwDZJkjZJkqQCrwc+v9qLQlEZTW8hdPccwxP3Wgcxe4s24Iezeot1ONVSlgwE+LX4v/KGwXubGzvWCkWBV7+66RcTTwYoubNZDc1GcWMpIim3Eb9F0ZHkILGQSTnbkEOn2wSwiadlykWLczMGFPL07xJqSmOvVWPg8GrwjgEg3ButE7qi5gfEHnlgbU+W4BFWCMdlaisIIaYJ+az4TLbVPPOy07aYBt/428NQrdC3OYEaau51q1brBNlT1PRchcUfHgXHYfCW5u9SVUUkiafyKV4PXSSIW3VGz3qjvToROtnfD4DaU1+I1fjqpe5G+MG1JQPdkJqNOqEQQSxRci3bxBGkpHBWfCfVgkEkaEA4jBwK+GqnlhMkJkUe7RHRktqza4jkRlGi8xSzRuSn3F6gTcK92kmhO3HvGQZYIHHXrW2vV6Oyb631iGNgwzAJin7LgVbQwLa6EjpfoTu6RC/LxPZsAq0mFq0usIzOhC7YmyKMRnlZXIgeOSjmV27anH9sDkyTwX1184AaCaBrLQrdskaYGsH+7j10jnv6PFME1HvvGlE6K0xT8aHufavpjeKcTj22hFms0ruhe4+sT9xPLfl5af1Xt5euY5kw6Do79J+i/uovM8ZZpn66zMl7TxOnRP9z97S9ZtudmyCb5d8+XEWbXebN/Avs2eMfu/dZQFzTjeMVBw5sIoDN0e/MMvmjefYoR+FrX2Pk2iF+/fPP5zc/eTNvtf+eyDt/XUSqNJDff/xHMYDBg66LnulOyB9baDpnG7cqKBhc87MbOytpiQTpcI3cnHv9LVhQKNK3uV19BeCVr+TFkW9jP/gQ1aJZnxLRAeE+cV46jY7rhLlHhKYx8fytqOEguQ4B0QCHPvU47z/wMf7j+r+A97+fY8sZIvu2sqEeTciWLfDSl8LgYMddrONZhKec0DmOYwJvA74GHAY+5TjOE6u9Lhx3ozUaSMDpH82RRtwol480O6M8hQ7qfS++nb6V0AF9o2Fiz7/5kj3GxNMypbLYVyOhC6fFDVmJtt8MohGHSkOOm6VbyJJNLC1TKsLCT+bAthncL566vTmWpm77JKWRZHRDtKf++cN9cb90qBdqFKbFuZo9rfnuutXgfb5IUqGmBbpGNGSz4JTL9LEIrgLVdZ9uP9zMvaJROrO9T4woa+h107R6KLRHkLVc1S9XpK6eaNqnEgpgGA5Gtbk8HYoGfIesP3GjQy+iTx5dXhKMqAQlV63rQABXQjARRcIRyoZlNRM6VRWETreoVWwG4oKoFWfcvrC8RdQNqJbVILYj4ZiWT+iu4yGYmSZBEXXrOMlNos+n0/iv3EyFVLDs90y15to5Dpx4tMjW3ixs3Nj2+kZlMTXh9nZFIiTDOgV3BmltUSxOrb87zxjiObQXJ4v0sUh0/3ZwHL/0ZpqiJNoIU7eR5Q4XWiBALGJRzrqEzp2I0MkJ34j5h4UdceDGifpni8hoLT+BynKNaEBrGmHWCEmi3RRBs3vdgxcWHh9tV/s8eLEYpx7JQbVKeqwL2aDew5s/k2fhyWVilInunmjbLjEoHib28Di85CWM9WucPaFz/MEsmzmFdMP17a954S3s4AjbznyTd8/8qrgehoZIjAryVDxbJ6y1it1kAJH37aafc9z3fRNn8jR7D6bhzjvh61+H++5j510TXPWqXXDDDcTClv9Qa5rw0MeP8tAX6wWcr30N/uiP4LOfpS0SxIsS8a7Daw6ovId3kvm5u7qes3TD3O3FQwtgW/Tt7Ou88dAQfb/589xy/H9DvkBqqPvDs5oR9WfPILIa5g5liVEhvm8z6TTk59qJoHFsko+9+R5QVH50qp/K2/+Qo9Fr2Pb8iW6V33U8y3FZLgvHcb7sOM52x3G2OI7z52t5TSih4rizLz2cPlRiR885IlRZOtH8BGxWGhS6hWZC11gq8/GVr8Df/u15f5ZuiGdCVKpliipeAAAgAElEQVQStpjS5Ks6HqHr1HMVjUmUG5QEUxcqRCytUq5IzP9knhAaif1CefJ7rXQTvWygBNpdf50Q6a3fiMKZWL30VdAozLrNPqbJkf+zovHYh645qKooZdum5ROmViwtAeUKA4gnaava/WZnmhLbpONQEIte356hpl63Wq4Gtl1XPP0YkCqF6aJQNre0h+AaujAPSFJd4VSjsk/ovDy/Tm5h7738cpIkEZLtrtuvBEkOEgqalFwlqWnCRyiEjImpWVRrkBlWRAnT/W5ms2EGY4Ls+OHSZc0nRtfshwA2vYpo2g5vHETGrH+3Dcgt6GJ+qPsgoyjCcOBhYd6hdDbLlus7N+I3PpgkN9cXwlRKIu+GGXskufUceaYSLyx6aVojE9eIbhEPLF4m4yc/CX/3d83vaxpOxx46gGhUouyWAL2JCLWyvWKqw9yhZXrIErq6Pv0hFA2itbR5lPMmsYjd9cFPkmjvoaNu0miE1/y/EqHzYjEmHxIPQT1bOuSeuYhv6ndL3UXOnSqJ39nmzW3bjW+WeS2f4paR0zAxwfjOKMa5PAunymweM+ojbxpx/fX8ZuTD/M537iZdmhLSmST5x+6RU+iQObhhA8PhHMbRUyRL04y//pb6v910E3zhC/CZzwAQi0t+6HExZ8F3vs3s/33A33zyk/cjf+x/8fV/Os373tecYpA/2xwlIv2XnyP2//0FPOc5Xc9Zul8hl7VxnHqVp2/fCoact7+dF6d+yLA9xeZt3aOKAqkECkbTZJuVMH+qzFDGgFCIVEZuf5g+dIgv3fE3LBppXvt3B9Ff9/N8+SX/wPyBl7Ft5/lFJq3j2YMrluf7JbVlsZDlsg656TIbbxwkE6mwfLZ5sWpS6BbFv/kKXU+HJ6uJCWGrvESIZ0L+DFZdc/zcuUhPd0IXS0hNcQ2mbhMMChecVTM4e1jcpKWdO4BGU4QlokM6KRYdEHFDjCUc1EyiyXFZOFcjo5aIUuXJr06uaX+G7qCEAn5vYu1cZzlkeU6HWpXBmOt0rXQmdI4DluWw4/qEiBDAIrVvI6FwfbyX9x6e6lNvsK+Sn6uSlEWPWSOEQlc3cUgBzyEr+yOovJ6XTgTNf6+GDEFVdWNT1pD/1wpVcSi4qfBNJgyv5Kpb1GoQ64+RCFQoLlSp1WA5KzGSEQuFdw0YJc0v76Tf8CJu5j72DiyAJCEl4qSUCoWF9gbH3LJNuq+usskKTQrd8XvPQq3Kludv6vwZ3OtYwSA8UXcGJntlClnxXS1Oucc10FJy9ZThki5Gwi1q9G0IEx10I3zmxQI9NWmyMN0s0ZmGg9zFwhVPQLkgyJTf21WtUlqh137+RImheLMVNRSTMYzmsOZKwSQa667iBySn3kPX0ChaOddOpr1sydh4Z6ckgLJxhCgVzh4R311TqHDrew8PkqBIYa7CuWmN/pTR0a4e6OvleXyL0MEbQZIYu34Q8nmYm2Pz9V3ugYqC9OEPwYc+BMePw6teBUB8ozh2r1cRoFZzmscruk5X5ubYwxNId7+062eIJQL+d5c/tQyOw/y06ZPxqQfnuK78Xd781ddy4mP38z8/bPtKXX7aHXG22b0OBwbgf/yPrsYFgPFx0IoGJ0/C4tElFAwS+zpf6wCk02Te/d/4I/6Y8V0rVEMUBTVorXlc5dy0zdBYPaA+l3VV3tk5Hn/hb/PvV/05X5/bx02/cRPPe/NGtu2NcM/of4Vt29i+fYUdr+NZjSuX0LnJ+tqyuAme/v5ZqNWYODhKpj/I0mwzOWhUibzcLs19Wuqo0F1ixN2yRulsVrj13Ny55JD4e6xDmGg0ITc9cYo+IYj1RcE0OH1MZyCpiTBRGiYK6DZ61fbJxWqIukHKITd+o76wauQXTdJ9MtvHqhx5aG3xAbouyJKnPnqTDFqxdDwr5n0Ou8pirfPNzqyZ4DgoO7dyx8aT7FOeJDDYLyIyXMXEI3Q+QfYb7DUK52okE3SM2NBNCaNq+q5jEKTEtCRsw6oTunT7Qui9V6MjNeSe807brwZVEeXTxuMX/+GWXA2LmhYgnFBIxB0KizqzMw4sLzGyRyy8HqEzK7roVQPUgwf4hY3f5e5rpvxdJhIS+XPN59u2oZB3fHcqgKwEmgjdia+fIEaZoZfd2PkzuEQ6GWwm0Mn+EIWimD4yc6KKhOPPB/Vfm673ES4tAYUCmYmE7yCtuI7S7KfvofLJ5jZby7AJyp2JVSwRpOz235UKNiE0MHTf6XrvvUL18+A4MDdtMjjWQjhjChhGUx9duWgTS3S/TUoB6j10jQrdYjuZLp2romKgDncndKRSpOUy5vwiAWySO1aIUertJRkosTyns3zOYmBDF7Xee3C97TYAhm7ZjIyBpNeY+JmJ7vv/+Z+HX/kVGh0P8sgAYWoU5+s3rk4h0sM7xbWxZw8dI0E8xFIy5ZI434WTwthjZ3PMTVuUy5CbqzF64wYOvGU//+XR3+bQRx/yY1Dys1WSSg0p2R4p0w3794NSyXP/1wssnizSF8whjY2u/KK3vQ3+8A/h7rtX3CysOmsaV1kpmBSyFoPbxHWf3hAjr4dxcnnu+X8+wd/ds4v7r38bV//VG3jtHwoF+Y47xHUbCglSuo51dMIVT+g8Y8Ppe08i4TD2or30joRZWnKanqSbCJ3rHK0VDD8U9qlGwnWulabz6Ibkqzojt2/lHXu+zK6Xbm17TTSlNBE6UVaC+IBY+IzZRQbG6jfTZkJn+WXd1eAFKYdVUTqqK3QGhZxFsifIzpt7WJzSWDq7uuPMMIQC6SmftaUOGQ2IsV8p8oQ3iAWsW8nVn7UakbnzH36W//Zno6K8GQmgu+XAqqu6euTcH6VV1MgvWaR62i9lJRzEMCQMzfJdx1BXmfRsGc1VuTq5hb1SdSOh82awrsWM0opQCIquccY7fu8fgljUquK7DScUEYOTNZl9ZA50nZEbR/3PBILQee0Iod4YfPWrTXXKVMotYTWgVLCxyxXSG+q/h9YeuhMPZdmcWETa3u5whYYMxqTTRKCTQ1HMska14jDzk0UGWEC5unkgjJyKISFyARdndCiV6NuRITIkFv/qUgXbhvxsGS1bbQqjNsWAkI6IphTKbv9qqeQwhDAIeI37Dz3U3GhfLDjUlisMbW8mAqIv0vGJMkCl7BBNdk93Egqdq640KHSl5fZrvbSkEQ+bbVl6TZAkUQGtVukh2zVUWLy5CJA9NRPCKRTp39TFbHH99WKkyBvfCEDw2qsZ4yyjTBG67Ybu+++EdJq4VGma51rTpLaImv0HE7yKz3L163a27qEJsbRC2b3l5Cddo4VlMfPAFNNHSlDIs+HGDfChD3Hrm3fy/Iffy73/a5IPfAAmZ1RSqfPLUQu/4RVcw8P8+GNHmJ8yRCvpag1pkQj88R9D/8qxTmpI6kjo7vmSxvv+tP7QO3PfabAthveI+2JqLIlGCO3IJI9+O8fYVUned9/N/Mpvx4m5P9X9+4WYvGPH6oe7jmcvrthLw0/Wd/txTj+4wIi6iHr1LjLjMWoFnWqpfsc3avX/70WBlHNu3EPi/KchnC/iI+JpqzhTxDCoj3bKZNjy088hbWsndJGUQlWrfwWWYSHLEBt0j7dUZGBbXQUJqkFAwtItl9CtzdARGfCCU8V/+xEaZYN8IUCyX2XH3dvBtjjyH6v6VQRhjQR9wtOV0J0pk2GJ4AbxhG5Wuyh05YZy4otfLCZ2A2o0iO46nb338Obw+qS0qFHIOyT72tmtGglimJJQMxsIXWPAre72c3VSccO9LnlsJHQuUb8Q1VcNQbHsRqE0lniDQYLYlIs22BaRdIhkT5BC3mHmR2eRMem7tbnsblZ0vxdN7YnBzp2ijcBFMqNQKDQvdrkTS2DbYgSSC1mtz4Y1TZg7WWXjvlTXnjFPWUymm28dfoTG6RwzR4uMJEptyowUi6Kio1cMzj44BzgM7RtAHsygolNeqlIogF0sg1aj2iBymYaD3EWAivWolKuivK5VLIaTrtPVzaRbPJmneHrZL9UtPL4Aus7Anuaey0ai76FclYilu/epNpoiPIVOwqGSb7/WS8t6N29FE1K9gvClIzr+it4FybREJVuDSoX+7Z37HlFV+Iu/qCt1ExO8KfZZfin0Mdi7t/NrukGSSMQdig2EtaYF2sYrhu58DneOHkZ+42tX3F0sE0ar2piGQ8H9vgLYgtD9YBKADbdOiBP9gQ/wqutO85LvvovJj36fubMGvb3naWrbvZsDN0LlsaPMzkki6uQSIRSWOo6rPPq+L3DkPZ+jmBcX4OmvPQnAxheJB57UZkHs5v/pC5ysDLLnRWNtDy+BALz97fCmN12yw13Hf0JcuYTOa6B2S2JTxyqMbVYhGCSzrQdsm6Un5vztjaqJHHBQAjbVvLjZ5HIIV+xa7qIXifgGQbxK82V0U0JZw/B2JSxjO/WFwDIcYYoYqZO4wT31p8JAUEIKSFiGLaJD1picERkWJVsvWsAjdNWCQbkCyYEIwy+/kahU49S9k6vuzyspe4THU1FbsTynCUI3KspG3UqunkLnuXg9qJF6r1t1Wazu4YxY4LyysVbUKRZFH0or5LCMRQCtYqE0ehBcQqdlKz4pCvW2L5zezN9GZ6dHii+E0IVCku/0berBkySCMpRdEhBOhUhkVIolmPnpEkPME9gnoiX8aSEVHa1kEMQimGq/vhP9YYolqckZmDsmnOGNA8YVNeA7jLVcFcoloju6q0LetI1UX/OKI6ZFwPKxJRamDDZs63B+VBVVMtHLJicezjPCDNGrNkFPD1EqVLOamLNZrYJlUVmqMzrLdJC7lFzjmRCOaXLuTBVqGkObxL2jOF3ANCH31ftxvvENP+w397goTaevas5f89s83IdIwxBj9qLp7ou+JEk4TrNCF6VCudCu1JTyFvHU6rdcr/ewJ7P6tqmMAufE9zqwd425FYEAw7dsYvjWzd2TnFdAIin5vYqmbmOZdnvW5969cPZsR5NGI+J9YbAsyucqFGbKxKgwJC0w8/gyUz+eI0aZ1K1urEo4TOA/PsPLxh/lPfc/h98o/gmvet75T7bf/Y6XkizNQC5L36a1l2tXQygSaMrN9JA7XYByiVNfFQ7+0/dNk44apK4XKnh6m7jHP/DRo9hyiJ1vuKbj/nt6LstSto5nMJ4RhM5xoLBs0bNZPIH27hQ3ruUn6gFFRk2oW5Gw4xO6bE6ih6yYNfMUwws4LcxVsEwHJbz6EA7FHf/kERrTcAjKUhOh67+mub9DDtpYuiVGK4XX9nQqZ1Kiid11oklyECVgszhdA8chNRxFSsQZ7NVZmFy95KqbAdRI0M9e8kZTNcJxIHfOpEcpI/eJxb5xVm0jPIVOiTSfMzWmYJgSjmVTy4rF3VMbPYVueaqCbVokR9rvdB4RqxSb1UyvbKjlqnWVq0PJNdrv9h42qA+hSAAJBzl5AQpduKEXr6UHLxjED6aO9IRJDoTRKjZnjmmMDFq+UuOdI7MqxqKFJINOtffUUARH033XJ9TT6L1QYcCdDSsIiadMrTROzlfoBpqP38u+O/JAHiebZWRfhz4xSSKk2GhVm5OPFdkinRJNVqpKVDWpZDWyT9aHk1Zm605K04Sg0vl2Fc2IY5n/8VnAYXBXr4iImS+zvAxONg/FIvmc+Jxe9mJ6+0DTfloJXXlZA9MQOW5dIBQ68f+9B7M4Jcolpy3Op1R0iKdWvy+kh8XnWSlU2EOyPwSmSQiN+FXtMTNd8YlPwKc/vfbtGxBPy/616kfUnGfQtofogLiuy1NZ8vM1kjGLkUGL6RM1pg8XGI1mkUYbiPf4ODz5JAHbZFf5ITIf+JPzfs/Ay+/mhswpAPq2XzpjXCgSoFZtLwHnlsR1ceqLT4DjMPlEhY07I74KntraD5LEA7W9KJs2sOWq8zdcrWMdcAUTOk/90Qoa5XMVbMMkMSR+/Jm9wma+dGTR397QhJMxEnGoFMUPKJeXSIdqK/esXCIog72E0MguGGBZTapO19d4/VClFkLnksMwNRLXNvcyBQNiO11zmgjCigiFiMhGU7SAqjgsTgsy4wWUDg4FmJ/vuAcflulgmzZKRPYJnUe2GlGrgVmqkugL1QORuyl07ti2NoXOK4Hlq3XHcr9L6FwCdu6kMEt4w+Yb4ZGfchk/FxAa3Jb5CnrZQJYhoLRfI5HBJL/Av3HT5oX6a8MBQkELKXj+P53G76u1By8oS5RcT0q4JyKywxyb4tkcI9vrZLWp5FoxRSm5Q3nU65PLHqv/RnJnCkg4TY32gtCJ13uTJ1bK2POMMB7p8OBFRzz5nXmwbUYOdO7cVlWHyaU4lallEQPhSg7RqESlYDYdb3W+nuVmmnQvubqkYN4Na03sHiNOieJClcUFG4oFsCw/qDk/5bojtzbHVTTmMwKUZ8T20RVGdTXGlngKXSJiYVWEk7dQgGPHxLalsiSmNqwCb/JBz+jqvb9eNtoAC0hbzyMkvbf3gl3+8V6VYkkYYLQll9Clzy9o29+XOyO3PJ2jsGSQSkuMbIuxOGswddpkdLPaufwvSeJB/UJyRGWZ57xlB5s52d3lewEIRYN+zJIHy7D91ofJ++eoHT7FfDHCxE31doR0JgixGAWSbL1t6EJE03WsA7iCCZ1XAtMKGoUToqTgjxraNYaC2ZRFZ2o2iuIQiUhUSyaWBcVlvS064SmDohAPGWTnOqtNneARGI/QiLISBPt7CVNjQG5vig4GxU1C11k7oQM2RRcY66k35qqqw+KiuNF4AaUD42GyWact1LUR3rEqEdlXy2qF9uylYhEoV0gMRusjy7q5XN04k9bw5cZpEJ7qGuprIXRT4r09hagRHiEsVySUhugRP+C2oKGVTUJKl8bqnh5uDT/sD7IH6Ou16Yt07hlcDWqjW7alZCsHwXTPT7gnQnKDS1B1jZH9DYqaFy5dNdArzSOXGtG3Qyhk5x6vM/TcVIlEoExwqF7Gl0NBf5SYF1TcZNhoQWZLml/iX7jhtuZtIpuGkDE580SBIBYDt3duhldVifl8GBYW2HKwTqiiMYlK0SJ7sj6BoDHLTZgiurhcXVIw/6Q7WmvXGPFAldJijcUnF/HcFZ6LMj9bIaVUkVLNob1+367b5uEphLGB7nWuQKBuivAmRSRSAahVKRdtPv95+Ju/djg7aVGtSaLEuAp6N4kHrMzG1etr3nXSHylf0himlRDvC2NWDHS93tsaPs9cRg/+LN7ZAvmsTTKjMLI3A6UixmKBDVd1z+y7GAz+7pt551/2kLy7e2bd+UKNKWLsXQMKR2ZxbAc1HGTypMXkR78PwMYXNuQfhtyHKFlh9ytWNpGsYx0r4YoldJ4zVSvqFE6JUpHXpyOpCpmU2eTINDQLRYFoXKJScsjnwSmUSI9evqaDeNRhecGdSrAWhc4lMH7J1XQIKhKoKplQiQ3DdpulSQ46gtAZosdsrfjvrznH3a9vGF2lQLEkFsjEJhEQO7A1CZrGwrHuY8A8FUeNysipGAEcaoUODeAloFwmPpyoq0pdTBHe2LY2hS5eNy/Uijoh2Sagin3JYZlAQBIKDPjTERrhnd+yLqOG2tUxLV9Dq1iEQl0IXSQCjz4Kb36z/6eX/MNLeMfnb+u8/SoINfRVtvbsBWUJquI6iPTFSIzVF7Lhm+qlNP8hoGqiVe2uTue+a4VCdu5wg0I3XyOVpOmakkNBX6HzCN2KGXvDw9z40AcJ/dyrm/4sxWMkVQ0nl2dQWSa4o90EBG4P4vw8MTPHwPPqDfnRpEylbJOdKqMirgfP2QziYUeYgtrhkYL5U+L44xszonE/a7B4+BwSzaXW3ILeMUvXN9p4Cp1LKKOD3e8hklSfZuNNioj3quA4lGfyHPnYgzif+CQf+WthAon3r+6O3rgvxVv5IPtuWF318tT1/pHLJ+skBkWsUnG+4hO68w3a9uC1l5TnSxQKkBwIMXLAfYi1LUYPbFjh1ReBRALe9a6O7QoXinBcbiN02UNCNd5zey8VO8yD//AghCOM/0y9t1CSIHXLHrj5ZnbtvzClcx3rgCuZ0KWjSIjMKm8mZXKi/gSaGQiI4FoXhua4hC5IteqIoMZigZ6JDnfupwjxhMRy1o216BAk3Aq/h84lNI2N37+25cu85jkLba8JBt2Sqy61ZT+tiH/6J/iN3/D/M9SQYZfcIhSbwd2CFC081mV4InWFTo0rSAGJSMii2oHQFQsOVMokRlNNM2g7wSN6crQlF8wjdPkq1YJJJNxczlBlm1xBXMKp7e0N4Yr7HdgE/PI2NDtktYrlj/bqiB07aJxrFNw0Tui5t6zwgu7wSH6nHrygLIEhroNwX5zERnGtKxj0Hdzlb+cROqtmoFctQl3W0fD2cRJSmcXjdRU7v2i2DRhXQgFMJ4Bj2T6RWXVxvvbajhkiSfentmEs0LXNQQ1JUC6zhRNIt9VnxUaSCpUy5GarjEjC7FRZrD+wmZaErHRR6FxSsDBjIuEQG8+I2co5i8VjWfo5h4ruuyjzyxapTPvx+fN2XcW54uYrxoa6j9+SJHxThKfQeaRt6ok8Cw+cZqhwhNP/+i3xbyvMcfX3efNN7P/NOwi85EWrbpvZ2kM/59ixzV5120sFf57rmWW/3cJrkTlfeO0lS2cr6FWL1FCU/oM7kRHf5fBznjkpumpcRTMDTfE1uaOiurT/5/eCLPOj/A4yEwkSyeZrOXXTLmLX72J0lUi8daxjJVyxhE4KSKiKQ61o+DMpPeIB0DsSEeGkLgzdRlYCRBIy1apE7nQeDIP01i5z+p4CxJMBv8leia3+5OcrdGVvlmF90er5xqeJ/d1ftb1GDjqYho1mCGPChcKL34gqJkpaqEUD+0UJbOHQYtO2p47ovPsVh8gt2/6oLMUlX+GQ+I5aUZorgWURH+upk5AuhM77/K3nrHG8V61kEm4xgagqOEAoaBEaaCfuSgNBbDIkNCzcetU6r9L1xcAj+apst/XgBRvISqQ/7o/VGooWCYzWS5PeOTKrhgh0DXXpIZJl+nstFs8IUuQ4YuJEawuCP32kovmlxgvJ2AP8LMCRHd0JkGfk2dqXh7F6O0EsrVCrOiIgdzhIEMuPHwJRNZXVLqaIUUEKilmDKFUCfb0kemSKRVg8U6ZPWiZJgcKMUJPyeYdUh5gb/7pwf8Nldy5sdKR72a/RFOH30Llh4o98dR6Wl3jTc8/SVzkL1N3wKyIchve9b00lVHV0gD/jD7jq2sun7HifoXg2Vy/TX2B4uzqQRsZi9sk84JAcTRKYGGc4tMxAYAl1745LddhPOUJxBZsAVr7e2pI9IdoAdr1glNCGfgwUNu5vbw+56y54wxsu2WjxdTxLccUSOhAqklYWMyllySIyXid0mY1xShXJLwEa7vzUSEqlUgv4brn0zu4p5Zca8R7FV1mUtSh03uJcqQ+n9tPwR0b8CRGNCMoSetXCRlqTCtgNqruwJhN1pS68c4IkBeaPNQ8W/9zvP8ji//0e01/5SV2hc987HJaoldut+t7w7vh4bz1qo5vL1VPoYs2Lkh9Nkq9RK1tNA8ABQopYQFOJzrM2G+elNip03uKjl11StEa38MXCO2edevaCsvgpBrCRe5Mog71EpBobNspNn80LlzaqJrpmr0jq+4dlzs25/WNzFcp5k+EtLb17oboxx5tDeaGELtknvr+Ra7v/5jzyvPlAc0hrpCeMo+ksZSV6NqWISjUq2Xr9yrSkroROTkYJBU3xABG1IRgk0atQKTucmzHpGwiQilkUzmkYmk2l5LSZOqDe5uEFNlcWKwSwCQ93yXdDPHi2znKNuyXgQ/fMEKXCxN//Dq9552aUgM3AtZe4hDgxATfcAHfeeWn3uwL6t7gl7uPFulkpc2Hh7ZIcJBqxmZkU33VqYxokiVfsO8mrdh++oFiVpwt+D+Zivfczd6aAHFVJDESYuE5UQDY+tz3KZc8e8TWuYx0Xg7U3YT0NCIdstIqFYWkkYs2qRqw/CuSpzORQ01EM3SEalYikVExb4twTC8iYxHZdvjkpid76zUddg0LnlRh9U4TlIHeJZvAQDELVnf96cYROvE8y3UBm0mkGI0UWztSVkclJOPw9odgVTy8TCrmlQDePLByRqFXayz2l6TwKBqHxQYJBbwZtndDlcnW+6k358PbpoXEaRK1iE2kJL/VUxmSqMyFr3F8j8fFHUBV1tJrTccrEUwHP5NGpbcdTZiOShhQJgyTxlgM/of+lB5q3c68Zs2aiaaxI6Pom4jzwpCjRT337OOAwdnNLDI5L6IxyPaj4QtWW1GAIMBi5tftszHBUIojFxPObe+yifVFwClAo0jMaJxIpU8nVWypMSyLYhdAhScTDFlpZJp4Q5zHeH8Gp1qhkQ/RtDFOcDzK3aJA/sQiOTWq0/WHJm2ThzeMsZ3XxfawwWiog1eNJPIVOKFh5jJkFdvflCOzawf6/2sn7/6BGMHaJIynCYXjggdW3u4RIXLOVJPcy/ZMlxoZcI88FEjqAWBTm3e4Srxf2qs/8MU2jQp4B8GNvlkp4ZyM7UyWdjiJJMPG6Axyxt7Lx4BrzAtexjvPEla3QhSS0qk1xSSfZUsVpnfVqGKIkE+0VN8zZJ5ZIk0PavMLg5UuMxobnRnWoGxrLZyBKrt0avz3IshhHtNb36AaP0KV6m0nSwKDE/GydoH3lI+cIz08CUJgp1V2u7rGHowGqFZuTXzrMD9/zXX9xK86WSFCEoaG6M1MTN+jJb0/yzvGPM/eo6JXqqtA19LpVqw7hWPO58QldpjOxbSR0ja5jWQ0gyUH0iiBFjZMgnkp431cnZ6qXsRYO1WNIdt/3z/S/+y1N2/nXTM1E11c+9r6taRzTZPnIOabuOwPA6B3NPUn+d9MweaJTyPJasP+ODM9NPkz/7bu6bvO8Tad4Kx9Euf3mpr9H+zwS6dCzKU00ht+baVsOtu0gr/DbiMZcIufOTOcq/aEAACAASURBVI4PiMZ9cjn6NidJ9SkUcjb5465jfmM7oZMUmVDQQq+IB4xKTicW6az++q8JSPVJEW4PnTrYg4o49h0HB/zXX3Iy93QhnWZDn87U4QK1gtv32X/hAb3xRP0cJre6ju7xcdh0+e7dlwKt041AGHC8PMEbbpbZcXBwtazldazjgnFlE7qwhFa1yGdtUj3NN3MvD8ubUmAYDkooQMQldDMna/RENDra2Z4ieDNYoV1t6gRvcTYq4uZvWXRt/PYQlCV/JNLFKHQhT6Hrbz7OgTGVwrJJrQYzM/Do58/yfO5BwaQwV/HLUV5/WyQW4PS0zHte+l3+97sOc+4hQRxKCxVB6IaH/TKhpYuFMv/YJBQL5H9yGqgTujaFLl0ndLUqbYTOI0apLtE0TQpdg+tYkoTLVysLUrQWR/KlgKfQdSR0bqk9El55NqWv0GkWmi6hxrofe7872urcI1OcfWyZnlCV6M5mxdrPQixr6GXxPVzo7OOxt72c12c/iBTrrvD1bYyxt3cG9u1r+rsX4gzQs62PaCzg50l6yu5KDzsxT5lLi/ORGHbNB6ZJ344MyaEI5aLN4jERi5La0rm3VlUc/zyUCybRVU5FJ4UuoMrEouKP219z9co7eIZibHuEmdMm1YJBMOC0PYydD7xZuQHJIT5x+XqeLzV897wrMmBZ5LL18v7YGPzWb3X+/a9jHZcCVzahi0hoNYdCARJ9nRd772nINIRjz5v1WZivke6/vP0XjQ62FaMfXHiEo5HQdUvD9xAMQqUmtlkp0X81eCQmOdjcSzS4JQGlIguzFp//nEPo+BPccZtBMmqKHqRyM6HbducmRjer3P48QTSWfips+sVFjXiwBqlGl6vV9Hm9ni1vDm+bQueVRkuGGADekkbvl42HOq+6jd9BW8adaguFTpfa5lA+VfDOWScThkdWWvsEWyHHxQZGzUI3AoRWIPXelJHFJ+aZOlZjbGOgTW1qDCrWyzpywPGjYS4Iq00Of9e74KGH2lyy0cG6wtOzc5BoIugr0VbFDZ4OrUToXGUuI86xN1sZoG/fCMmRBNSqTB12g6i3DbTvBLdv153HWSlYxOIrP2B1ChaWggFicYmoajL6yhtXfP0zFRuuHcQsVTkzaRNWVlYxV4NHwpOxdrPQMwme09czjjlT02SdFOmxSzdebB3rWAlX9K8nFAlSrUCpEmib1elPknBdVoYpoYSDRN35m+hax8bnpxKNi4iSWJ3QeQTGIzgrNX77r1Ekarbbi3VRhE4sgH6ArYuBnb1g2/zwS1ke+cYid+U+TuxNryaREEHNnnrhfb6f+fMX8AcnfpG7/lIEdC4fE9bjUtYgkQ6CJLWVXFsJnWeWaFXofEJX0KiaMpFUZ0LnBU63ovE7aFXhVFVCLxvoVuCilM7zgUcwO5VJPZdrJLrywuidy2rRBNtakYym9oyhSCYzT2SZn4fR3e3uU1/xqxpoZcs3mjxlSCREI38LosNCSQ9gk9g9RjSlUHErV55paEVClxbnxVPJE+PCyBCmRnT3BKkx8dnP/iRLEJv4ls59TKEQPqErlx2iiZXJbZMpwi25BuQAOw/2c8vdfUgrZuI8czF6UJRDTx3Ru0bnrBWxXnc+8FOTIXzZ4N2vvCiXypNnMJFJb+puqlnHOi4lrmxCFw2ynA9gI5EcaVZhvMZtz2VlmJJQ6AbqBCU93j0+4alAYyTBWgidr9C5pgDTXqHx20VQlnAQi/5Kif6rQXUVK2+h89C/T4yFuvdrOqmjD/A89fvw6leT7AlQyNp1ha5FgUxftQEJh8WTwiFbzNv+mKN6yVUslF6JtUmhkwK+WuQfYzIMSJTmSjhIhFs+r2cISHbohwJQknVC3xqJEgpBNadhIvul0KcaXo9NR4XOHT0Wjq38/QeCElIgQDnnlkdX6KOUVIW+tMVP7yti2w6j17eTGF+hK2voFRP1aSoHedEgPWoFKZ0iklap1sR4Kb/HciVC1yPOQ3xQ3Cfi48K808cS0pbNfoblmRM6yZiJpHQmampI8sc3VSoSsVVmr0oS2I74PfoKnRzkNZ95Ha/5zOtW/+DPUAw97yoC2GhVi/BFXjPerNxkzxXt0VsVXu+pl+eYPSx6hHt2dFaD17GOS40rm9DFZHTb7YlpyW/yXFVaXgyYNywJOSw3lW4u95ORF5IJayy5uqTPrJk4lo1ts2LjNzT32K3lPbrBU6VaJyyoOzbRQxZOnuRlT/wlod94K6TTJHoVCkX8hvFGsgQQjIZIx02WpyroOuhlnUS/OD5PBfIInUdgvX48s2YSDLZXbQJBCVmB/IIgfpF0F0I30WEQPF6ZVey0LeMuJFHIC2XlchE6r8emUyC0V2qPxFbPFpSDju8AXU2l7RuS/bzG0dvbZ302jhLTKhaqeuGls4tBaKgHCYd0j5uP2BPGNGyMiuErdN4IuU7wSIHX9hAcHiBKhUzagnDYz7AsL+ud0oDqx+G2eTgOVKoS0Z6VFTah0Aki5zX2B+Qr+rZ6SSBnUgz1ug7Xi1XoXFW1tZ/3mYZQRlx7mkvocseEASe9Y93Vuo7Lgyv6ztNYTmp1pXk/nlpBx6kJpUWNBIkM1Ynf5X4yCvRniFJBwiGYWD36obEfyptzuprLNdgwz/JC88JAnBtFkejd0zygnLExxqUpNhz6OrdkjsLv/R4Ayf4wpbJUL7km29+7L+OwNGeIOa6VComBSMNnkuolV4/QufsyNBtF7mwGUBWHwlJ9xmkjPGLUrR8qEJT889WqZIUikjhOLk7pPB+sSOi8Hrr4GkbGyTbloiARocTKhKN/XLynKtv039RO6BpdsyKoeNW3f0oghUNEZcN3BEZdglaZyfm/jRUVuj7xOX2VPB7nhcq3OLhF9HQmt3vZeE6bs7sRajiIrtlU8zqOaRLrXZmtiFmu7p7d0V/P5D6w88HYVnGxnNfEmg7wZuWmhi5vi8ylRigZAimA5jp/s6dyEI2RHnxmE9V1PHNwRWvcjU3wrUqSKLlKaEUds+hOL4jIhFJhpEAAx7ZJ7xq+nIcLqkpcNbD0oMgSWwVBJYAUCGBUzTX1CXmv8d/uIhS6a3/9Nra/6WZirWUOReGXNt6DMzlJ4E/e57uEk0MRbEsjN68hUS+jNqJ3UOX4UYvSkgaa5vcUBgIgBSVMXax8Xs+cR+jMmtl18LqqQD4nyF7reKHUwX2En5wnMdrdyazIDpbZoT8vHKRkuSXQi+hFPB94hK5Tz5743i0iydXVQjmIS+iCqyt0W1LAOTaMQEBpv7b82bBl3R0l9vTdEn52/yTDzxXDyUUv7Dmqszk/sHel38a2F2/jqo8cZuSgS1olibv2TMMdIkJFHuglGtSoWKEVF9hQNIBWs6hMCzdsNLMyyZAkCceLLfEUug7n+T8jNuzLwANLhKMXR2BjQ6KqkuzSC/tMQSgsgaKglcR6lDtbRErEL2fQwjqe5biiCV2j+uDnE7kIyhKyKqGVDH+4vRyWkSSIhG0qFUjtvXyhwh7iMZuK5azJ9SVJonxm1Cysqkvo1mCK8OA14V4IpIBEokvPSmjfDojJ8Mu/7P8tMZIEcixN18ToqkD758uMRnjwx1UR3gokNtT784IBsAxB6AyP0LnlW1O3keXOi2Ao5FA45xoGMs2f9zlv28u1b9pLcIWrWFVsajWpXaGLBtBwFYYLHCx+vggPJJFDst/f1QhB1C3CyTUEUjdkEa527P27+4FzjG7vfK20BhXHe58+den2B//G//8R19xUmSv45iHPLd0J/Qd38utTO5v/+IMf1N20kkQq4VDJQWq4++8mFAmi6SblWdELGhtYObckEADHzctudLk+GzB6yzj801JbnND5oufAdti8SP8L9lyiI3t6EAxCQA36eY652SqJAaXT2ON1rOMpwRV9qXmLsKwG/dy5RoRVh1rJxCgJQudFU0TCEJQcv6R5ORFPBMhWVs4Sa4QiOxia7Td+r9QnBC0K3QXmha2Kj34UbLtp7E5yVJCzxQUbtYsTsnciiW1XmfqByJdrJC5y0MFylRbDbTr33K6GZqN0UTVUVWLBEQtwaxq9LEPPKm2S3kdoVbLUhqDhy0XolKjCOx9+HYOb2gmF+N4NwqnV1UJZhkJRXAerHfvggQngMOM3jXT890ZCp2vOZQtZXg2ealNZKBHud/sgI+d5u4o0q2vJniCzuXYjUCPCmRjFislH/vt9AEQHVlaNJEn8VKDB5fpsUeju2AE8sqY2gZUwsCnGH33/BQxdvimNTwkkSZit9LIBuk522Sa97z9JmPQ6nhG4ogmdR+JSCbuj4BUKiXBYw22u9whdNB4gmnh6mruvH55mQ7G4+oYuFMXB1KzzL7kGgk9dIG6iPTcpuVEwp+WsRLf2wMy2XmCe0w+KObqNIaHBIJi6ILpeL51edV2vut31KVYNS3j0ONJ//iUZ1SV0rT1/jefOyzS8HBjf3fkzeD10rcaPTpBlqFni+FdTaQevH+Ntn3sBO1+4sfO+GmNLtHqczdMNrxe2cq5M9oz4PQ1e05mUrhXJPhVOOR2nRHh43l+/CDv3SR775hRB0vRvWoXQNcSWPNsUutR4iqtev48tL7/4XuXhy9wd81QhFHJnW09OknNSZEaf2WXkdTyzcEUTOq9ZPZHqfIMMh6FWsesKnfsEf+07nu/nel1uHLg5AMEja95ekVtMEasodF5JVpGdi8nyPG8kNguXoGF2n5ed2TUAHOb04SpBLCITdXdXUG4suTYTOkN3ULpUGtWQKEUChPrPP4bGK1G3xsg0Gm4uxlxyqeB9763Gj06QG87/Wsjo3pd1H6HkmyI0C90QJccrAV4uXWWxwszhHNGQRe/1FzczKTUYBqqkNnd2RQP0TKR47T1v4TWHDmPe822Ug3tX3KcUqMeWPNsUOkmCX//4zatv+CxCKCyJVpITJ1iml+2b1xvo1nH5cGUTOreclOrt0l/ljgYz3Ww0b3F68a8+jTMA3/teMM3Vt3OhKEKhWiuh8xQ6VVl7WfdSIDbWSwAHG6njcHmA3n1iMkF2tkaKMtJg/ck9GKwTOmGOCKC7xM40bOQuEzJCUZfQBYJEes6/fOEda6uBpLE/80KH0V9K+Apd7xoInXxp+iihwWldNdH0AKGLLJ9dKgiFTqK6XOXs4TKjGyMd+zbPB+mdg/DVadK7V1f6pN27UHZ3n0nrbyc1KHR2PYduHc9OqJEA2qJN9fAkVSL07uh/ug9pHc8iXBl37y7w1Idu+USh/7+9ew+S7CzvO/57Tp/TPTuzM3tf7Wp3dVlYCSGQhLIGRDASRmBCVMhEUAGDIYBLFi6IXRTEOHKAcoKLS5WxE+IiKoIhCcYkxiQucxESBkMFi1gmkrIyN4FkEAhYtJL2ptnty5s/zntO9852T8/0me73nJ7vp2p2Zk736fNOv9tvP/28tw2RFg931zPLuo+CSpLBKaw+4sTUPO1WtHiq1M3QDQqqxsXimubn2nrsRKxkQPYz2bJRCzNNHV2U5mfbZzwPcU9A1zyVBXRZgOeUDNghoT5Tk9RUXI9GGlycNCJJnbMydL0zTUfdjH4tZXuqLh0n2E+adUyDiPrWYl06+W4lxxbVVJwvOB1aXI9Ub5iOP3RMD/4k1nOeVTzT8Y/ffq3Oue6o5s9du62Yokj5Xq6d1vpZhw79NTbUdGrRpYsKx+dp6xPPngAFjEupW57sjXb+nP5ZiJm59MXTXJKhq5KknnY5ZhuQL90tYak8QxfgT82G1tUbgzMlW337tXHTmYFpHEst/4aXLV9yejH9vdkcPLs3G+s20xgtI1lvmKwWnfX4+SSJKFp2t4VJeer+E7pBn9Q5FwzP0OVxsp09e3e14nokWaSTR9JhC2V4LjKzG5weuOtRNV2sfVftKf548zVddvXaLjbedwwdGbp1qzGbvicdue+INL+grdvCDP3B+lTqDN3sE8+VnnSJtjy/fxdqYy7WqVPdvR7L9Ga0Ukliap503dXwl1maQep2zYVYAHZhcyT9ePmAbtvOmh74kc5aEqUWS600Cammnxxx+pQP8JpuYECXLVo66mr0SSNSHLfPGm+Yd7nGSZDgeKm5l7xAL/jht6WLLxp637ieZujqiQp3Q0ZRugBzuvPEzNCFiidpdla6/0dpALbveRcHLk1/Fpk6bsk6dGTo1q3GXKwjp6Qj9z8mLSzkH3CBSSh1y7NpW6xf/9Pn6Bk37Ot7+8zGWIunLF/+Ius+qpK4HqnZdPliu8MydFmX7HJB1bgsbE2DzbQbs79te/wWTNvPjMBqNeuOoWv6gC6NYf0+vAO6XP3khQ0jzltI9p6j+vazu+uyDF1ST4Oa4HbulH73d9PBhkNk28M1Biwfs1px7HTisfT/X5k+FG3YGKmjSPHGDdr11HKORUqXLTl7L1esT42NiU6prod/cFK1zSwqjMkqdYZOki6/fPBtjY2JTrlEzUdPSDp7N4AqSOqmVlN5l+tKM3T9Nngft4XtdUmP5+O9+tl2wbykhzW/88yALk6kts/M5Rk6n7FrtdzAPWyzMV3DNq0fZP+b/qlOP7/P42bbcJUnflmx2O+3Wl+j/+7dnScmtw3aSszOx5La2n1+vbSLs1pkcnmGbn3NcsXZ0oCuoSOdTdqya2aiKxEAJW0mV2ZmPlFLsRYPp+tULR34XgVJI1KzqRVn6EIGdPO75iQ9vuy1tz5hi6SHNb/7zMH6tThS62T6c9MHcqdPp61dmqEbMIbOZ4xWsml9P1dfnX4tlc2gbow4Ni+kbEbwWnW7x7F04rjfeaJMAd1CLOmUzntqedMcUaTuXq6+y5UM3frVmK+nAZ22aut54SdbYX0pQ2fTyLI3n+OH/V6uVczQ+YAunxSxYfkMXdblGmJF/4Vz0wZquRX7z/25PTI57bjozMEjtdjUziZF+FVdTndqUqulVssGzu7NxnQVXY3+rMf1S5XUl+k+Lqu17nZPYqcTJ33WrwRr8mVmN6d1v++ZxSdEjItFIkOHXH1hRi3F+pm2a+v+tZ2AAwxT7QydX1X/+MOnJNUrmaGLGzU1W5Zn6Pptet8rW6dubLtELGN+72ZJ/6D6MovPbn/2k/Tu245r03OvPON4nJhOtrqzWiXptOpyRx5RU/HAbtwsQzczv7bLaeRdrjPV6xPJJpA01ihLGyfSo530tVSmgG7DRfukjS3tveaJoYsyUBRZzxg6MnTrXbZ136O2RVsPDF7AGhiHSgd0Df/mc+yRphTVhm5sX0bJTE3Ntql9Ol1kd9gYujw7E2BF/2z7r2HB5OZrD551rBabWumfqGbLpCSRazbV+snDaike2NWcTV7YsLDGAZ1fkLcse5euRvf/wBoFdLHplNLneZLboA2z8/qrNPP4VdpXzgmukrIxdOnPzHJFvoD5xo3aurPSb6+ooEr/j8v2ej32aEcWRyuZIFg6yUykVifqLiw8pMs1z9DNTb7qFg7slCxSfcvqx4bE9UjtliTn1GpJtrEh12xq8cePyskGZ+h8A7mSTetXo7ExkaJaJQO6bLzhWpW9d8LBKHU7Ls98pnTFFaMvWTMJvZMi0lmuVngpGVRXvusMS5YggEoHdNmL5/gxp6Q22b1N10oyE6ulWK1j6TjAobNc8y7Xya/ov+n8LXrFLc/VFdftXfW5tSRSq21Ss6mmYm2YNZ08Lp186DFJgyeD1M9Js4IzuwZvqD6Kel3Srl2q71/9/rChdTN0a/PyzWbNSuXYBi1jNvpyNZPSu5era3cks3Isg4Mg8gw3AR0CqHRAN7PVB3SnYiUL1ZutKHUnGCw+dkrS8O3LssCnd+uqSbrmV0cbz1RLIrXbknt8US3F2jxnOinpxENHJQ2eaNF44j7phhs0c/Xato5xLEUvvk6NCu4tngX12aLLReVbuUW1NHOJFUv3ck1/7rSdZFbJD5ZYG40dC+mg1O3bCegwcZUO6LKtwY5pXiXZU3zVsgBt8VhTkg1dHDnP0JVoAdiViBNTuy21j6eZyLn5SD+TdPJwuobgoK7m7dulfVds1wX7175MmzZJC9VL0OXd02sV1Mc+oLOkVtr13soqqnXH0LmOkyICuvWssdCQXvFyzW2dCbKbD9a3SjffM9vTtc5aivM3parJM3THmpIa+Tpzg9T27pbqddWf0H/3jLKq1WtqtU3N42kmcnZTGoycOHxSUm3gPryzs9Lv/M54yvTWt0pz5RkytmLZh4C1yqZlk4nqiQhGVslMZ0yK4Plb3+p1SRtmtXV76JJgPap0QNeYi9NNQtut7oblFZP4sXCPn+jIasPH39T37JD+xWu14YoJFG4N1ZJIbUX5rh5zm9O/++TDj0vaOHQyyDhsq+iqAuMK6Br1ag5bCMlqUZqZUzqGLjIG0K1n2QQeulsRQqVbn3pdyiK5pFo9kLksoFs80VIcDX9D3bNHeu1rpUsvHXfJ1lZcj9RWTc0j6a4ec1vT/ogTR9KMXRJgkkdV5eMo59emTyfP0FX0NRRS1DMpggwdstcQAR1CqHRAZ9bduimpaJdrlpl6/IRb0bIrZulyDlUb61Sr19LZvI8elyTNbktng5189LSk4ZNB0LXWAV22DEq9gossh5buFJH+7DqOGa7r3IYNaZZu7+oXAgAKq1hYcLZGXTolDdwLtOyysWOLiysL6KoqW2rj1CPphq6z29MZyiePpjtkDBpDh7MlO9IlXBq71yYNsNY7T6wnFkVk6JBLEun3fq/8y+1gOlU+oJuZkY5KldwlQuoN6ExxBTeKX6lsssfikTSgm9s2I1mkk8fTNR/I0K1c7bJLpRt2qf60tRkEmO8PTIZu1SwyOUlyzmfopvc1jJWp4kQrTIdqRkE9stXy12qj8knLApnFU6Zp3gIyD+geSZctmd2USHFMQDeC88+XnvGibbrwwrV5vHgm3HZyVRfVTE4mdTo+Q1fNdghA9VU/QzebNqCDto4quyxD97hrqKJ/wopkWaBsAeW5zYmUxDpxMh0Hlmxk0aaVmp2VXve6tXu8OFuouILboIVmpjygI0MHIKTKt+ANn1WobJerD2SaSio30WE18gzdY4uSpMZ8XXFiOql0LN2wBZUxPvlWYgH2B666tMvVpHabDB2AoKoZBfWYmUvfjJKKdhcl892dx2vx9L4ZZHvULh5tSkoDuHoinVA64IQMXTj5rFmWjlk1q0XqKMozdCxDByCUsTY/ZvYyM7vXzDpmdnAc18gWV00aFQ3oegKZac7Q5V2uR9NlSpL5GSV1U1OJFNUqm2GdBvlCxWToVs0inTGGLprez2QASm7c76KHJP0zSV8e1wVm/CaugzZ3L7versaqbl+2EtketIvH/TIlGxvdiSy1WmV3+pgGWXa7Mc/ElNWKalHe5Zpm6Kb3NQyg3MYaBTnnviFprONKGgt+UH1FA7pkpuaXm+9MdZdrlgVaPNGWZIpn4jMCumnOTpZd7LvD6xsJ6FbrjAwdCwsDCKgUzY+Z3Whmd5rZnYcPH17VuTML6ZtQiL1A10IcK92PVlM+hq7RE9DFsZK65QGdxRFvhAFlrx0ydKt3RoaOhYUBBFT4bdTMbjezQ32+rl/pYzjnbnHOHXTOHdyxY8eqrl/1DJ2ZFMfpUgdxfXrfDfJJEY+7PCNX9zsTxDXxRhhQfOBCads21S95QuiiVI5Flk+K6HTEBxMAwRSOgpxz165FQUY1szmdJVqfq2aGTkoDmpakWjy97wZ5l+uipKSmWq27kC3j58KKd++QbnipGueFLkn15F2ujKEDEFg101o9Gpc/SbroMcVXPCV0UUaWJE6LmvJJEVmGrhkpmU27prKsakxAF9SMXzlndjZsOarIoogMHYBSGPeyJS8xswclXSXp02Z261pfo7F5g3TNNfmG5VWUZaimeemOPKDTjBL/MaI+6zN0lf9YUW3790u/9mvSgQOhS1I9+cLCnY5cp8M6dACCGfcs109J+tQ4r7FxY/p9w4ZxXmW8soCulkzvu0E28H5RM3lGLlvIdpozk1VgJl15ZehSVFMU9+4UQYYOQDiVb3727ZPe9Cbp4otDl2R06yFD1xvQZX9vttVUMsWTQTDdsjFzrt1hDB2AoCrf2WUmPaW6w+ckSbHPzNWmOKDLulzbqin2y7PU5/ySM2ToUFHmU3Ku1WYMHYCgaH5KIMtQxfVqbl+2ErUN3TXOsr83m5lMhg5VFdXI0AEoBwK6EsgCmqkeQzcTS8oC1/TvzHYmmOauZky33i5XMnQAQqL5KYHE75iQbWA/jWo1SbX0v1ueoZv3i0I3+G+IarJat8uVDB2AkHgnLYHEZ6hq0x7QRenfl2fofEAXE9ChorIArtN2PkNHQAcgDN5JSyCeyQKdKQ/osgydD+DqC+mKttP8d2O65WPoWm05R4YOQDgEdCWQ+MxctoH9NOrN0C0N6JIZAjpUU9bl2ml31OkYY+gABEPzUwJJtkn9FHe5mkm1mpPU/TvrOzZJ27YrvnBfyKIBI+tOinCMoQMQ1PSmhCok9pm5aQ7opDRL11Y3I5fMJtINNyg5GLZcwKh6J0V0Ot0uWACYNDJ0JZBtUp8tvjutYh+vZgFd3S9NF/OxAhV1xk4RjKEDEBABXQlkAc56yNBJ2Zp03YAume44FlOsd2FhxtABCInmpwS6GbrpTlVlAV3295KhQ9XlkyJafqcIulwBBEJAVwLZxvW1xnSnqrLALQvoZmelTZukc84JWCiggDxD13HqONahAxAOuZESSC7YI9W+q3jPdEc2tdjviOED2DiW3vvekCUCijlzpwgxhg5AMAR0JZA8+YD0+gOK94QuyXhlAV2WoQOqLuti7bSdOs6Y5QogGLpcSyCbFFCb7jkRiv3fGc/WwxYEWCPmX7Su3WEdOgBBEdCVwIUXSk97mrR7d+iSjFeeoZud7rGCWD96ly0hQwcgJPq+SmDzZummm0KXYvzibAwdAR2mRO+yJWToAIREhg4TU0vS/27JX97GDgAAE6JJREFUXCNwSYC10btsSUeWbVcMABNHQIeJyWe5MoYOUyKf5dpsyclkrCwMIBBaH0xMnPgxdHMEdJgOUdwN6DqKGEMHIBgCOkxM3uU6PxO4JMDayCdFnG76DB0BHYAwCOgwMbW637OWLldMid4uVzJ0AEJilismJn72M6WjR5TMMHIc0yGfFHHaj6Gr8RkZQBgEdJiYeO8u6ZJd+ULKQNXly5aQoQMQGB8nMTHZThgxHyMwJSxO/1N3M3QEdADCIKDDxGQBHRk6TIveSRFpho4mFUAYtD6YmCwzR0CHaZFPimi1meUKICgCOkwMXa6YNnlAl2XoYppUAGHw1oqJueoqacsWyUhiYEr0LixMhg5ASAR0mJidO9MvYFrky5Y00y5XMnQAQqH1AYARZQFc53RLksjQAQiGgA4ARpQtU9JudiSJDB2AYGh9AGBEVuuuQ5f+TpMKIAxaHwAYURbA5Rk6FhYGEAgBHQCMaGlAR4YOQCi0PgAwomzMXPt02/9Ohg5AGAR0ADCibC/Xdsulv0c0qQDCoPUBgBFly5R0M3Q0qQDCoPUBgBGlAZ2p02IMHYCwaH0AYERRJMlM7Rbr0AEIi9YHAEZklv7DLFcAodH6AMCIsoCuQ4YOQGC0PgAworzLtelnuZKhAxAIrQ8AjCjN0HWXLSFDByAUWh8AGFEa0EXddejI0AEIhNYHAEaUZehYtgRAaLQ+ADCipRk6ulwBhDLW1sfM3mdm3zSze8zsU2a2eZzXA4BJSidFiC5XAMGNu/W5TdJTnHOXSfq2pN8e8/UAYGLydejaZOgAhDXW1sc593nnXMv/eoekveO8HgBMUrZsSSfL0MW1sAUCsG5N8uPk6yR9doLXA4CxyjN0ziSRoQMQTlz0Aczsdkm7+tx0s3Puf/n73CypJeljAx7jRkk3StJ5551XtEgAMBF5QKc0M8cYOgChFA7onHPXLne7mb1G0nWSnueccwMe4xZJt0jSwYMH+94HAMpmaUAXJXS5AgijcEC3HDN7oaTfknS1c+7kOK8FAJNGhg5AWYy79fmApHlJt5nZXWb2wTFfDwAmJt/LNcvQMYYOQCBjzdA55544zscHgJDMJMnU8Z+NmeUKIBQ+TgLAiMwkRWToAIRH6wMAIyJDB6AsCOgAYERk6ACUBa0PAIzILP3KZ7mSoQMQCAEdABTQG9CRoQMQCq0PABRglo2hM1lkoYsDYJ0ioAOAAvIMnVm6Lh0ABEDzAwAFWNQN6IwEHYBACOgAoIAoy9BFBHQAwiGgA4AC6HIFUAY0PwBQgEVKJ0VYRIYOQDAEdABQABk6AGVA8wMABUR5ho4xdADCIaADgALMLJ8UQYYOQCg0PwBQQG+XKxk6AKEQ0AFAAVEkOZlkERk6AMHQ/ABAAXlWjgwdgIAI6ACggHz/Vma5AgiI5gcACsizcuwUASAgAjoAKIAMHYAyoPkBgALyII6dIgAEREAHAAX0ToogQwcgFJofACigm6FjDB2AcAjoAKCAfAwdO0UACIjmBwAKMDJ0AEqAgA4ACrAsimNSBICACOgAoIAsQ2cmAjoAwRDQAUABkR9Dl4+lA4AACOgAoIAsKxdFLmxBAKxrBHQAUECWmTP6WwEEREAHAAVkAR1LlgAIiSYIAArIAjmjNQUQEE0QABRAhg5AGdAEAUAB3WVLGEMHIBwCOgAoICJDB6AEaIIAoABjHToAJUBABwAFZF2uZOgAhEQTBAAFmI/kyNABCImADgAK6O4UEbYcANY3miAAKCCqMYYOQHgEdABQAOvQASgDmiAAKIAMHYAyIKADgAKY5QqgDGiCAKCAbIcIMnQAQiKgA4ACrJY2o1nXKwCEQEAHAAXke7mSoQMQEAEdABTApAgAZUBABwAFZGPomBQBICSaIAAoIMvMkaEDENJYAzoz+7dmdo+Z3WVmnzezc8d5PQCYtO6kiMAFAbCujTtD9z7n3GXOuSsk/aWkt4/5egAwUWToAJTBWAM659zRnl/nJLlxXg8AJi2bFBER0AEIKB73BczsXZJeLekxSc8d9/UAYJLyDB3r0AEIqHCGzsxuN7NDfb6ulyTn3M3OuX2SPibpjQMe40Yzu9PM7jx8+HDRIgHAxGRj58jQAQipcIbOOXftCu/6J5I+LekdfR7jFkm3SNLBgwfplgVQGebXKyFDByCkcc9yPdDz64slfXOc1wOAScu6XMnQAQhp3GPo3m1mF0vqSPoHSTeN+XoAMFHZsiXZdwAIYawBnXPuhnE+PgCElmfo6HIFEBAfKQGgAPZyBVAGBHQAUAAZOgBlQEAHAAXkGToCOgABEdABQAHdvVxpTgGEQwsEAAWwlyuAMiCgA4ACuhk6AjoA4RDQAUAB3b1caU4BhEMLBAAFRJsXJJls00LoogBYx8a9UwQATDXbc670ylcqOjAXuigA1jEydABQgJmkubn0OwAEQkAHAAVkgVxEawogIJogACggC+jI0AEIiYAOAArIMnNk6ACERBMEAAWQoQNQBgR0AFAAGToAZUATBAAFkKEDUAYEdABQALNcAZQBTRAAFECGDkAZENABQAFk6ACUAU0QABSQBXJk6ACEREAHAAWQoQNQBjRBAFAAY+gAlAEBHQAUwDp0AMqAJggACiBDB6AMCOgAoADG0AEoA5ogACiADB2AMiCgA4ACWLYEQBkQ0AFAAXS5AigDmiAAKIAuVwBlQEAHAAWQoQNQBjRBAFAAGToAZUBABwAFsLAwgDKgCQKAAsjQASgDAjoAKIAMHYAyoAkCgALI0AEoAwI6ACiAWa4AyoAmCAAKIEMHoAwI6ACgADJ0AMqAJggACmAvVwBlQEAHAAWQoQNQBjRBAFAAY+gAlAEBHQAUsHev9PM/Lz3hCaFLAmA9i0MXAACqLEmkV70qdCkArHdk6AAAACqOgA4AAKDiCOgAAAAqjoAOAACg4gjoAAAAKo6ADgAAoOII6AAAACpuIgGdmb3FzJyZbZ/E9QAAANaTsQd0ZrZP0vMlfX/c1wIAAFiPJpGhe7+kfyXJTeBaAAAA685YAzoze7GkHzrn7h5yvxvN7E4zu/Pw4cPjLBIAAMDUKbyXq5ndLmlXn5tulvSvJb1g2GM4526RdIskHTx4kEweAADAKhQO6Jxz1/Y7bmZPlXShpLvNTJL2Svq6mT3dOffjotcFAABAypybTELMzB6QdNA597Mh9zsm6VsTKRTW2nZJy9YvSo36qy7qrrqou+rK6u5859yO0IUpnKEbg2855w6GLgRWz8zupO6qi/qrLuquuqi76ipb3U0soHPOXTCpawEAAKwn7BQBAABQcWUM6G4JXQCMjLqrNuqvuqi76qLuqqtUdTexSREAAAAYjzJm6AAAALAKQwM6M9tnZl80s2+Y2b1m9hv++FYzu83MvuO/b/HHn2Rmf2Nmp8zsLUse6zfM7JB/nN9c5povNLNvmdl9Zva2nuMfMbP7zewu/3XFgPPf6M91Zra95/g1ZvZYz/lvH/4UVVfJ6u4rPc/7j8zsfw44/2P+/ENm9mEzS3puu8aff6+Z/XXR56fMAtXdh83sp2Z2aMnxvtfsc/6FZvY1f79PmFndH39/T91/28weLfr8lFnJ6u59ZvZNM7vHzD5lZpsHnP8yf42OmR3sOf7Knrq7y9/et92dFiPU3yv983uPmX3VzC7veay+7WGfa77GP+53zOw1Pcc/Z2Z3+3J80MxqA84f1O4ObE+nUcnq7kv+/Oy1s3PA+e8ysx+Y2fElx99sZn/vy/YFMzt/6BPgnFv2S9JuSVf6n+clfVvSkyW9V9Lb/PG3SXqP/3mnpJ+T9C5Jb+l5nKdIOiRpVuns2tslHehzvZqk70raL6ku6W5JT/a3fUTSS1dQ5qdJukDSA5K29xy/RtJfDjt/Wr7KVHdL7vdJSa8eUOYXSTL/9XFJb/DHN0v6e0nnZWUN/fxOU935+z5H0pWSDi053veafc7/75Je7n/+YFZ3S+7zJkkfDv38rqO6e4Gk2P/8nmXq7hJJF0v6ktL1Qvvd56mSvhf6+S1h/T1L0hb/8z+R9DX/80rbw62Svue/b/E/Z4+34L+b0nbz5X3OX+49s297Oq1fJau7ga+lJY/xTF/u40uOP1fSrP/5DZI+MeyxhmbonHMPOee+7n8+JukbkvZIul7SR/3dPirpl/x9fuqc+1tJzSUPdYmkO5xzJ51zLUl/LeklfS75dEn3Oee+55w7LelP/bVWzDn3f51zD6zmnGlUxrozs3lJvyCpb4bOOfcZ50n6P0p3GJGkX5b0586572dlXeHTUEkB6k7OuS9LOtLnpr7X7GVmprRe/2y5+0l6hdI3lqlVprpzzn3enytJd6j7elp6v28454Yt6D71dSeNVH9fdc494o/3PscrfS/7RUm3OeeO+Me5TdIL/WMf9feJlQYW/Qa9D7zOMu3pVCpT3a2izHc45x7qc/yLzrmTfco20KrG0JnZBUqzX1+TdE5WCP+9bzqxxyFJzzGzbWY2q/STw74+99sj6Qc9vz/oj2Xe5VOQ7zezxmrK713lU9ifNbNLRzi/kkpSd1L6hvSFnoZqUHkTSb8i6XP+0EWStvg09t+Z2auHlHlqTKjulrOSa26T9GhP8HBW3fsugwsl/dUqr19ZJai7Xq+T9NkC5/9zrYOArtcI9fd6dZ/jlbSHQ+9nZrdK+qmkY+p+YFrx+f4xlranU68MdSfpj31367/xH3pH1Vu2gVa8sLCZbVSa8v1N59zR1ZbNOfcNM3uP0gj2uNIUZqvPXfs9cPap5Lcl/VjpJ5VbJP2WpN9dRTG+rnSLjuNm9iKlWaIDqzi/kkpSd5lXSPrQCi77R5K+7Jz7iv89lvSPJD1P0gZJf2Nmdzjnvr2Cx6qsCdZdUSup+5dL+jPnXHsM1y+dMtWdmd3sz/3YiOc/Q9JJ59yhoXeeEqutPzN7rtI33mdnh/rcrV+Gbdn7Oed+0cxmlNbdLyj9/7Di872l7elUK0ndvdI590PfK/VJpQH1f1lB8ZeW7VWSDkq6eth9V5Sh89H9JyV9zDn35/7wT8xst799t9JPEMtyzv1n59yVzrnnKO0e+I4fxJgNGrxJaYTb+yl0r6Qf+fMf8tnjU5L+WGlaVGZ2qz9/2UDBOXfUOXfc//wZSYn1TJqYRmWpO3+tbUrr7NM9x86qOzN7h6Qdkt7c81gPSvqcc+6ES/cD/rKkyzXFJlx3y+l7zSV19zNJm80s+5B4Rt17L9c6yfCUqO7kB2pfp/QNxvljWebgMyv8k9ZN3Umrrz8zu0zpB9XrnXMP+8N920Mze0ZP/b140P16y+OcW5T0F5KuH6Hd7deeTq2y1J1z7of++zFJfyLp6WZW6zl/aDLKzK6VdLOkF/u4Z3lu+IA9UxpV/sGS4+/TmYMM37vk9neqZ4CvP7bTfz9P0jflBw8uuU+sdGDhheoORrzU37a7p0x/IOndQ8r+gM6cFLFL3bX3ni7p+9nv0/hVprrzt98k6aNDyvyrkr4qacOS45dI+oK/xqzS7qinhH6Op6Xueu57gc4eWL/sNXvu9z905qSIX++57WL/epza11tJ6+6FSicT7Vhh2b+kJQO5lX7wf1DS/tDPbRnrz9fNfZKeteT+y7aHPffbKul+pYPqt/ift0raqO57XizpE5Le2Of85d4z+7an0/pVorqL5WMPSYnSrvKbhpR96aSIpymdmNF3IlTfx1jBE/RspSnEeyTd5b9epHTMzBckfcd/3+rvv8u/+I9KetT/nM3U+YpvXO6W9LxlrvkipbNTvivp5p7jfyXp/yl9M/9vkjYOOP9f+uu2lEbLH/LH3yjpXn/9O5ZW4rR9lanu/G1fkvTCIWVu+XOz8r6957a3+jIcUppKD/4cT1ndfVzSQ0oH5z8o6fX+eN9r9jl/v9KB1/cpDe4aPbe9U0M+gE3LV8nq7j6lY3yycnxwwPkv8eedkvQTSbf23HaN0skZwZ/bktbfhyQ90nPfO3sea2B7uOSar/N1dZ+k1/pj50j6W1+OeyX9B/kZy33OH/SeObA9ncavEtXdnKS/66m7P5RUG3D+e/1rr+O/v9Mfv92/FrOy/cWwv5+dIgAAACqOnSIAAAAqjoAOAACg4gjoAAAAKo6ADgAAoOII6AAAACqOgA5AZZlZ2y/Sea/f0u/NZrZsu2ZmF5jZL0+qjAAwCQR0AKrscefcFc65SyU9X+naUe8Ycs4FkgjoAEwV1qEDUFlmdtw5t7Hn9/1KF2PdLul8Sf9V6SKfUrrK/lfN7A6lO4/cL+mjkv69pHcrXUC3Iek/Ouf+08T+CABYAwR0ACpraUDnjz0i6UmSjknqOOcWzeyApI875w6a2TVKt9i6zt//RqVbbP07M2tI+t+SXuacu3+ifwwAFBAPvwsAVIr574mkD5jZFZLaki4acP8XSLrMzF7qf98k6YDSDB4AVAIBHYCp4btc25J+qnQs3U8kXa50vPDioNMkvck5d+tECgkAY8CkCABTwcx2SPqgpA+4dCzJJkkPOec6kn5FUs3f9Zik+Z5Tb5X0BjNL/ONcZGZzAoAKIUMHoMo2mNldSrtXW0onQfy+v+2PJH3SzF4m6YuSTvjj90hqmdndkj4i6Q+Vznz9upmZpMOSfmlSfwAArAUmRQAAAFQcXa4AAAAVR0AHAABQcQR0AAAAFUdABwAAUHEEdAAAABVHQAcAAFBxBHQAAAAVR0AHAABQcf8fVDnSwum8TKsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(10,6))\n",
    "df['PNL_Option'].plot(c='r',label='PnL_Option')\n",
    "df['PNL_Hedge'].plot(c='b',alpha=0.6,label='PnL_Hedge')\n",
    "plt.legend()\n",
    "plt.title(\"PnL from Option and Hedge Part\",fontsize = 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Total PnL from Hedged Portfolio')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2 = plt.figure(figsize=(10,6))\n",
    "df['PNL'].plot(label='Total PnL')\n",
    "plt.legend()\n",
    "plt.title(\"Total PnL from Hedged Portfolio\",fontsize = 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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