Individual Model BackTest.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": [
    "## Individual Model Test on Historical Data of Stock1:PG   Stock2:BBY\n",
    "### Conducted by Zicheng He   zh1345\n"
   ]
  },
  {
   "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": [
    "### Pricing Option Value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 3,
   "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 historical data on specific stock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read data, change path here to load  data\n",
    "path1 = 'PG.csv'\n",
    "path2 = 'BBY.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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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",
       "    </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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.610912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>11.155852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>11.127076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>11.050546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>11.367423</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 First  firlogret     Second  seclogret       tao  OptionPrice\n",
       "Date                                                                          \n",
       "2019-05-15  106.699997        NaN  67.860001        NaN  1.000000    10.610912\n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032    11.155852\n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063    11.127076\n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095    11.050546\n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127    11.367423"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "# Monte Carlo Pricing\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(10000):\n",
    "        stockprice1,stockprice2 = SimulateSP(sigma1,sigma2,T,s1,s2,r,252,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",
    "df_mc = df.copy()\n",
    "df_mc['MCprice'] = 0\n",
    "count = 0\n",
    "for index, row in df_mc.iterrows():\n",
    "    count +=1\n",
    "    S1 = row.First\n",
    "    S2 = row.Second\n",
    "    tao = row.tao    \n",
    "    df_mc.loc[index,'MCprice'] = PricingByMc (K1, K2, r, tao, S1, S2, sigma1, sigma2, rho)\n",
    "    if count == 6:  ### just show some cases here, otherwise it may take too much time\n",
    "        break\n",
    "    print (count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>MCprice</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.610912</td>\n",
       "      <td>10.475882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>11.155852</td>\n",
       "      <td>11.562861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>11.127076</td>\n",
       "      <td>11.113263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>11.050546</td>\n",
       "      <td>11.349464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>11.367423</td>\n",
       "      <td>11.653102</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 First  firlogret     Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "            OptionPrice    MCprice  \n",
       "Date                                \n",
       "2019-05-15    10.610912  10.475882  \n",
       "2019-05-16    11.155852  11.562861  \n",
       "2019-05-17    11.127076  11.113263  \n",
       "2019-05-20    11.050546  11.349464  \n",
       "2019-05-21    11.367423  11.653102  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_mc.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 9,
   "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",
       "      <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>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.610912</td>\n",
       "      <td>0.158523</td>\n",
       "      <td>0.420789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>11.155852</td>\n",
       "      <td>0.158300</td>\n",
       "      <td>0.434901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>11.127076</td>\n",
       "      <td>0.163223</td>\n",
       "      <td>0.431378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>11.050546</td>\n",
       "      <td>0.163141</td>\n",
       "      <td>0.429932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>11.367423</td>\n",
       "      <td>0.177416</td>\n",
       "      <td>0.428924</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 First  firlogret     Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  \n",
       "Date                                         \n",
       "2019-05-15    10.610912  0.158523  0.420789  \n",
       "2019-05-16    11.155852  0.158300  0.434901  \n",
       "2019-05-17    11.127076  0.163223  0.431378  \n",
       "2019-05-20    11.050546  0.163141  0.429932  \n",
       "2019-05-21    11.367423  0.177416  0.428924  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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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",
       "      <th>NumDelta1</th>\n",
       "      <th>NumDelta2</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>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.610912</td>\n",
       "      <td>0.158523</td>\n",
       "      <td>0.420789</td>\n",
       "      <td>0.134419</td>\n",
       "      <td>0.420789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>11.155852</td>\n",
       "      <td>0.158300</td>\n",
       "      <td>0.434901</td>\n",
       "      <td>0.134230</td>\n",
       "      <td>0.434901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>11.127076</td>\n",
       "      <td>0.163223</td>\n",
       "      <td>0.431378</td>\n",
       "      <td>0.138404</td>\n",
       "      <td>0.431378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>11.050546</td>\n",
       "      <td>0.163141</td>\n",
       "      <td>0.429932</td>\n",
       "      <td>0.138335</td>\n",
       "      <td>0.429932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>11.367423</td>\n",
       "      <td>0.177416</td>\n",
       "      <td>0.428924</td>\n",
       "      <td>0.150439</td>\n",
       "      <td>0.428924</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 First  firlogret     Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  NumDelta1  NumDelta2  \n",
       "Date                                                               \n",
       "2019-05-15    10.610912  0.158523  0.420789   0.134419   0.420789  \n",
       "2019-05-16    11.155852  0.158300  0.434901   0.134230   0.434901  \n",
       "2019-05-17    11.127076  0.163223  0.431378   0.138404   0.431378  \n",
       "2019-05-20    11.050546  0.163141  0.429932   0.138335   0.429932  \n",
       "2019-05-21    11.367423  0.177416  0.428924   0.150439   0.428924  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_num.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing the Deltas from numerics and analytics, I found that the Analytical Delta1 is little bit larger than Numerical Delta1 and Delta2 are exactly same for both."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Test the stock on extreme cases\n",
    "### Case 1. Zero correlation, correlation = 0\n",
    "### Case 2. Perfect correlation, correlation = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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",
      "D:\\Coding\\Anaconda\\lib\\site-packages\\scipy\\integrate\\quadpack.py:865: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n",
      "  If increasing the limit yields no improvement it is advised to analyze \n",
      "  the integrand in order to determine the difficulties.  If the position of a \n",
      "  local difficulty can be determined (singularity, discontinuity) one will \n",
      "  probably gain from splitting up the interval and calling the integrator \n",
      "  on the subranges.  Perhaps a special-purpose integrator should be used.\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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <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",
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       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <td>2019-05-15</td>\n",
       "      <td>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.177821</td>\n",
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       "      <td>0.270054</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>6.635761</td>\n",
       "      <td>0.161758</td>\n",
       "      <td>0.284155</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>6.571296</td>\n",
       "      <td>0.163769</td>\n",
       "      <td>0.280507</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>6.515765</td>\n",
       "      <td>0.163277</td>\n",
       "      <td>0.279217</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>6.653214</td>\n",
       "      <td>0.172064</td>\n",
       "      <td>0.277766</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  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  rho  \n",
       "Date                                              \n",
       "2019-05-15     6.177821  0.157013  0.270054    0  \n",
       "2019-05-16     6.635761  0.161758  0.284155    0  \n",
       "2019-05-17     6.571296  0.163769  0.280507    0  \n",
       "2019-05-20     6.515765  0.163277  0.279217    0  \n",
       "2019-05-21     6.653214  0.172064  0.277766    0  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case1, when correlation equals 0, delta1 is not moving much but delta2 bacomes much smaller than in the original setting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "      <td>2019-05-15</td>\n",
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       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>14.461860</td>\n",
       "      <td>0.062246</td>\n",
       "      <td>0.609369</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>14.378344</td>\n",
       "      <td>0.063063</td>\n",
       "      <td>0.608083</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>15.015848</td>\n",
       "      <td>0.120554</td>\n",
       "      <td>0.612061</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  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2   rho  \n",
       "Date                                               \n",
       "2019-05-15    13.864211  0.055471  0.598878  0.99  \n",
       "2019-05-16    14.378648  0.046075  0.609748  0.99  \n",
       "2019-05-17    14.461860  0.062246  0.609369  0.99  \n",
       "2019-05-20    14.378344  0.063063  0.608083  0.99  \n",
       "2019-05-21    15.015848  0.120554  0.612061  0.99  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case2, when correlation is close to 1, I found delta1 tends to be close to zero and delta2 becomes larger than in the original rho"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case3. S1 << K1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\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>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.840463e-10</td>\n",
       "      <td>1.345148e-10</td>\n",
       "      <td>1.015571e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>7.079840e-10</td>\n",
       "      <td>1.606462e-10</td>\n",
       "      <td>1.214917e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>5.681261e-10</td>\n",
       "      <td>1.305778e-10</td>\n",
       "      <td>9.709950e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>5.032917e-10</td>\n",
       "      <td>1.163272e-10</td>\n",
       "      <td>8.614141e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>3.842114e-10</td>\n",
       "      <td>9.032021e-11</td>\n",
       "      <td>6.446333e-12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 First  firlogret     Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "             OptionPrice        Delta1        Delta2  \n",
       "Date                                                  \n",
       "2019-05-15  5.840463e-10  1.345148e-10  1.015571e-11  \n",
       "2019-05-16  7.079840e-10  1.606462e-10  1.214917e-11  \n",
       "2019-05-17  5.681261e-10  1.305778e-10  9.709950e-12  \n",
       "2019-05-20  5.032917e-10  1.163272e-10  8.614141e-12  \n",
       "2019-05-21  3.842114e-10  9.032021e-11  6.446333e-12  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test3.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When S1<<K1, our option is hard to be activated, and it will be nearly worthless. The result confirms our hypothesis, and I can see that Delta 1, Delta 2, and option price are all tend to 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case4. S1 >> K1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": 18,
   "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",
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       "    }\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>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>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>13.883722</td>\n",
       "      <td>2.003736e-29</td>\n",
       "      <td>0.606905</td>\n",
       "      <td>13.883722</td>\n",
       "      <td>0.606905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>14.394566</td>\n",
       "      <td>1.099686e-29</td>\n",
       "      <td>0.616400</td>\n",
       "      <td>14.394566</td>\n",
       "      <td>0.616400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>14.484283</td>\n",
       "      <td>1.152425e-29</td>\n",
       "      <td>0.618286</td>\n",
       "      <td>14.484283</td>\n",
       "      <td>0.618286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>14.401041</td>\n",
       "      <td>9.225453e-30</td>\n",
       "      <td>0.617121</td>\n",
       "      <td>14.401041</td>\n",
       "      <td>0.617121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>15.064838</td>\n",
       "      <td>1.323493e-29</td>\n",
       "      <td>0.628945</td>\n",
       "      <td>15.064838</td>\n",
       "      <td>0.628945</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 First  firlogret     Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "            OptionPrice        Delta1    Delta2  VanillaOptionPrice  \\\n",
       "Date                                                                  \n",
       "2019-05-15    13.883722  2.003736e-29  0.606905           13.883722   \n",
       "2019-05-16    14.394566  1.099686e-29  0.616400           14.394566   \n",
       "2019-05-17    14.484283  1.152425e-29  0.618286           14.484283   \n",
       "2019-05-20    14.401041  9.225453e-30  0.617121           14.401041   \n",
       "2019-05-21    15.064838  1.323493e-29  0.628945           15.064838   \n",
       "\n",
       "            VanillaOptionDelta2  \n",
       "Date                             \n",
       "2019-05-15             0.606905  \n",
       "2019-05-16             0.616400  \n",
       "2019-05-17             0.618286  \n",
       "2019-05-20             0.617121  \n",
       "2019-05-21             0.628945  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test4.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the last case, when the strike price K1 is extremely small, we assume that the barrier will become useless, and our option will become a vanilla option based on S2. The result confirms our hypothesis, and I see that Delta 2 of our option is pretty close to Delta 2 of a vanilla call option.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Values vs Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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",
    "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": [
    "Option value is monotonic increasing as correlation increase"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BackTest model on specific stocks with PnL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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",
       "    </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>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.610912</td>\n",
       "      <td>0.158523</td>\n",
       "      <td>0.420789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-16</td>\n",
       "      <td>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>11.155852</td>\n",
       "      <td>0.158300</td>\n",
       "      <td>0.434901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>11.127076</td>\n",
       "      <td>0.163223</td>\n",
       "      <td>0.431378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>11.050546</td>\n",
       "      <td>0.163141</td>\n",
       "      <td>0.429932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>11.367423</td>\n",
       "      <td>0.177416</td>\n",
       "      <td>0.428924</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 First  firlogret     Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2  \n",
       "Date                                         \n",
       "2019-05-15    10.610912  0.158523  0.420789  \n",
       "2019-05-16    11.155852  0.158300  0.434901  \n",
       "2019-05-17    11.127076  0.163223  0.431378  \n",
       "2019-05-20    11.050546  0.163141  0.429932  \n",
       "2019-05-21    11.367423  0.177416  0.428924  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# BackTest : Pnl calculation\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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": 22,
   "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>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>106.699997</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67.860001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.610912</td>\n",
       "      <td>0.158523</td>\n",
       "      <td>0.420789</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>108.110001</td>\n",
       "      <td>0.013128</td>\n",
       "      <td>68.739998</td>\n",
       "      <td>0.012884</td>\n",
       "      <td>0.996032</td>\n",
       "      <td>11.155852</td>\n",
       "      <td>0.158300</td>\n",
       "      <td>0.434901</td>\n",
       "      <td>-0.048871</td>\n",
       "      <td>0.544940</td>\n",
       "      <td>1.410004</td>\n",
       "      <td>0.879997</td>\n",
       "      <td>0.593811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-17</td>\n",
       "      <td>107.449997</td>\n",
       "      <td>-0.006124</td>\n",
       "      <td>68.930000</td>\n",
       "      <td>0.002760</td>\n",
       "      <td>0.992063</td>\n",
       "      <td>11.127076</td>\n",
       "      <td>0.163223</td>\n",
       "      <td>0.431378</td>\n",
       "      <td>-0.006930</td>\n",
       "      <td>-0.028777</td>\n",
       "      <td>-0.660004</td>\n",
       "      <td>0.190002</td>\n",
       "      <td>-0.021846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-20</td>\n",
       "      <td>107.330002</td>\n",
       "      <td>-0.001117</td>\n",
       "      <td>68.839996</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.988095</td>\n",
       "      <td>11.050546</td>\n",
       "      <td>0.163141</td>\n",
       "      <td>0.429932</td>\n",
       "      <td>-0.018118</td>\n",
       "      <td>-0.076530</td>\n",
       "      <td>-0.119995</td>\n",
       "      <td>-0.090004</td>\n",
       "      <td>-0.058412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2019-05-21</td>\n",
       "      <td>106.370003</td>\n",
       "      <td>-0.008985</td>\n",
       "      <td>69.949997</td>\n",
       "      <td>0.015996</td>\n",
       "      <td>0.984127</td>\n",
       "      <td>11.367423</td>\n",
       "      <td>0.177416</td>\n",
       "      <td>0.428924</td>\n",
       "      <td>-0.003733</td>\n",
       "      <td>0.316877</td>\n",
       "      <td>-0.959999</td>\n",
       "      <td>1.110001</td>\n",
       "      <td>0.320610</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 First  firlogret     Second  seclogret       tao  \\\n",
       "Date                                                                \n",
       "2019-05-15  106.699997        NaN  67.860001        NaN  1.000000   \n",
       "2019-05-16  108.110001   0.013128  68.739998   0.012884  0.996032   \n",
       "2019-05-17  107.449997  -0.006124  68.930000   0.002760  0.992063   \n",
       "2019-05-20  107.330002  -0.001117  68.839996  -0.001307  0.988095   \n",
       "2019-05-21  106.370003  -0.008985  69.949997   0.015996  0.984127   \n",
       "\n",
       "            OptionPrice    Delta1    Delta2       PNL  PNL_Option  \\\n",
       "Date                                                                \n",
       "2019-05-15    10.610912  0.158523  0.420789       NaN         NaN   \n",
       "2019-05-16    11.155852  0.158300  0.434901 -0.048871    0.544940   \n",
       "2019-05-17    11.127076  0.163223  0.431378 -0.006930   -0.028777   \n",
       "2019-05-20    11.050546  0.163141  0.429932 -0.018118   -0.076530   \n",
       "2019-05-21    11.367423  0.177416  0.428924 -0.003733    0.316877   \n",
       "\n",
       "            Price_diff1  Price_diff2  PNL_Hedge  \n",
       "Date                                             \n",
       "2019-05-15          NaN          NaN        NaN  \n",
       "2019-05-16     1.410004     0.879997   0.593811  \n",
       "2019-05-17    -0.660004     0.190002  -0.021846  \n",
       "2019-05-20    -0.119995    -0.090004  -0.058412  \n",
       "2019-05-21    -0.959999     1.110001   0.320610  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'PnL from Option and Hedge Part')"
      ]
     },
     "execution_count": 23,
     "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": [
    "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": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Total PnL from Hedged Portfolio')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SJnjIPwz4iIiIAswK+HR9nAdC44oBHxERUYBpOjN8xICPiIgo0OySrj58wDcZ5/VPJBP558eAj4iIKMCsQE8fJuCrqKhAR0fHhA5aJjKlFDo6OlBRUTHeQ/HEZVmIiIgCTDPn7unDBHJz5sxBc3Mz2trajsKogqmiogJz5swZ72F48iXgE5F7AHwCQKtSapHH9ecDeBzAHvPQo0qpm8zrLgLwAwBhAD9TSt3ix5iIiIgoW2Ycbg5fNBrFwoULj8aQaBz4VdL9JYCLhrnNSqXUEvPDCvbCAO4A8DEApwG4UkRO82lMREREZU9jly7Bp4BPKfUKgM4R3HUZgCal1G6lVArAAwAu8WNMRERExC5dMhzNpo33i8hGEXlaRKxdmWcD2O+4TbN5jIiIiHyQXYePAV85O1pNG+sAzFdK9YnInwH4PYCTAHht6uf5jBSRawFcCwDz5s0bq3ESEREFip3hY8BX1o5Khk8p1aOU6jO/fgpAVETqYWT05jpuOgfAwTznuFsptVQptbShoWHMx0xERBQEVpcuS7rl7agEfCIyS0TE/HqZ+bgdAFYDOElEFopIDMAVAJ44GmMiIiIqB4olXYJ/y7LcD+B8APUi0gzgRgBRAFBK3QXg0wC+LCIZAAMArlDGMzAjItcBeBbGsiz3KKW2+DEmIiIiymb2mOErb74EfEqpK4e5/kcAfpTnuqcAPOXHOIiIiCgX5/ARwK3ViIiIAk3nOnwEBnxERESBxnX4CGDAR0REFGhWZo8l3fLGgI+IiCjA7JIuM3xljQEfERFRgNlduszwlTUGfERERAFmrb/HDF95Y8BHREQUYBq7dAkM+IiIiAKNW6sRwICPiIgo0OySLufwlTUGfERERAHGpg0CGPAREREFms69dAkM+IiIiAKNJV0CGPAREREFmsYMH4EBHxERUaBxazUCGPAREREFmsaFlwkM+IiIiAIt26U7zgOhccWAj4iIKMCUYtMGMeAjIiIKNKuky6aN8saAj4iIKMDsgI8ZvrLGgI+IiCjArDiPTRvljQEfERFRgGlceJnAgI+IiCjQsgsvj/NAaFwx4CMiIgowdukSwICPiIgo0NilSwADPiIiosBSStlNG+zSLW8M+IiIiALKGeOxpFveGPAREREFlDOrx5JueWPAR0REFFDOtfeY4StvDPiIiIgCyhnwMcNX3hjwERERBVROSVcfx4HQuGPAR0REFFC6I8jj1mrlzZeAT0TuEZFWEdmc5/rPisjb5sfrInKG47q9IrJJRDaIyBo/xkNERES5ZVwuy1Le/Mrw/RLARQWu3wPgPKXUYgDfAXC36/oPKaWWKKWW+jQeIiKispdb0mXAV84ifpxEKfWKiCwocP3rjotvApjjx+MSERFRfjlduizplrXxmMP3RQBPOy4rAM+JyFoRuXYcxkNERBRIOku6ZPIlw1csEfkQjIDvA47D5yilDorITADPi8h2pdQrHve9FsC1ADBv3ryjMl4iIqLJzBnkMd4rb0ctwyciiwH8DMAlSqkO67hS6qD5uRXAYwCWed1fKXW3UmqpUmppQ0PD0RgyERHRpJbTpcuIr6wdlYBPROYBeBTA55RSOxzHq0Wk1voawIUAPDt9iYiIqDQaF14mky8lXRG5H8D5AOpFpBnAjQCiAKCUugvAtwDMAPBjEQGAjNmRewyAx8xjEQC/VUo948eYiIiIyl1OSZcZvrLmV5fulcNcfw2AazyO7wZwxtB7EBER0WhxazWycKcNIiKigGKXLlkY8BEREQVUbpcuA75yxoCPiIgooJxduszwlTcGfERERAGVu5fuOA6Exh0DPiIiooBiSZcsDPiIiIgCik0bZGHAR0REFFDM8JGFAR8REVFAMcNHFgZ8REREAWV16Yow4Ct3DPiIiIgCyurSjYZDLOmWOQZ8REREAWXtnxsLh8AEX3ljwEdERBRQVhk3GhaWdMscAz4iIqKAYkmXLAz4iIiIAko5Aj5m+MobAz4iIqKAsrZTY0mXGPAREREFFEu6ZGHAR0REFFC6zpIuGRjwERERBZTdpRvhsizljgEfERFRQFkl3Rjn8JU9BnxEREQBxS5dsjDgIyIiCiirSzfCpo2yx4CPiIgooFjSJQsDPiIiooCyunQjIWb4yh0DPiIiooBydukyw1feGPAREREFlG43bbCkW+4Y8BEREQWUbs/hC4EV3fLGgI+IiCigsl26YjdwUHliwEdERBRQOtfhIxMDPiIiooCygrwY1+Erewz4iIiIAsoK+CJs2ih7DPiIiIgCSlcKIkA4FIKuslutUfnxJeATkXtEpFVENue5XkTkhyLSJCJvi8iZjuv+SkR2mh9/5cd4iIiIyAj4wiIIi5iXx3lANG78yvD9EsBFBa7/GICTzI9rAdwJACIyHcCNAN4LYBmAG0Vkmk9jIiIiKmuaDoRCgnDIusyIr1z5EvAppV4B0FngJpcA+JUyvAlgqogcC+CjAJ5XSnUqpY4AeB6FA0ciIiIqkq4UQmIEfdZlKk9Haw7fbAD7HZebzWP5jg8hIteKyBoRWdPW1jZmAyUiIgoKTc8t6TLDV76OVsAnHsdUgeNDDyp1t1JqqVJqaUNDg6+DIyIiCiJNV2ZJ1wz4mOErW0cr4GsGMNdxeQ6AgwWOExER0SjpSiEcEoSspg1m+MrW0Qr4ngDwebNb930AupVShwA8C+BCEZlmNmtcaB4jIiKiUbK7dEMs6Za7iB8nEZH7AZwPoF5EmmF03kYBQCl1F4CnAPwZgCYA/QC+YF7XKSLfAbDaPNVNSqlCzR9ERERUJKtL14z3WNItY74EfEqpK4e5XgH4+zzX3QPgHj/GQURERFm6ntuly3ivfHGnDSIiooDSFLt0ycCAj4iIKKB0s0s3xDl8ZY8BHxERUUBpZpdudms1BnzligEfERFRQNkLLzPDV/YY8BEREQWUUsgp6TLDV74Y8BEREQWUZnbpZps2xnlANG4Y8BEREQWUphRCIgib/+1Z0i1fDPiIiIgCStddW6uxpFu2GPAREREFlN2ly6aNsseAj4iIKKCMOXyOdfiY4StbDPiIiIgCSinkrsPHDF/ZYsBHREQUUHaXLku6ZY8BHxERUUBZXbpW0wZLuuWLAR8REVFAZbt0rcvjOx4aPwz4iIiIAsrdpctlWcoXAz4iIqKA0tmlSyYGfERERAGls0uXTAz4iIiIAopdumRhwEdERBRQuqtLl3P4yhcDPiIiooDSdPfWauM8IBo3DPiIiIgCSlMKoZAgHMpepvLEgI+IiCigdF0h7Czpcg5f2WLAR0REFFB2ly6bNsoeAz4iIqKA0nQFEXBrNWLAR0REFFS6Mkq69k4bzPCVLQZ8REREATWkS5cZvrLFgI+IiCigdLNLl00bxICPiIgooDS7Szd7mcoTAz4iIqKAGtKly3ivbDHgIyIiCijd6tI1Az7FOXxly5eAT0QuEpFGEWkSkRs8rv8/EdlgfuwQkS7HdZrjuif8GA8REREZTRphEYSF6/CVu8hoTyAiYQB3APgIgGYAq0XkCaXUVus2SqmvOm7/DwDe4zjFgFJqyWjHQURERLnYpUsWPzJ8ywA0KaV2K6VSAB4AcEmB218J4H4fHpeIiIgKYJcuWfwI+GYD2O+43GweG0JE5gNYCGC543CFiKwRkTdF5FIfxkNERETIdulmt1Yb5wHRuBl1SReAeBzL9xbiCgCPKKU0x7F5SqmDInI8gOUiskkptWvIg4hcC+BaAJg3b95ox0xERBR4uoKZ4TMus6RbvvzI8DUDmOu4PAfAwTy3vQKucq5S6qD5eTeAFcid3+e83d1KqaVKqaUNDQ2jHTMREVGgWeXbkABirsXHkm758iPgWw3gJBFZKCIxGEHdkG5bETkZwDQAbziOTRORuPl1PYBzAGx135eIiIhKY2XzrA7dcEiY4Stjoy7pKqUyInIdgGcBhAHco5TaIiI3AVijlLKCvysBPKByFwE6FcBPRESHEXze4uzuJSIiopGxlmCx1uALiTDDV8b8mMMHpdRTAJ5yHfuW6/J/eNzvdQCn+zEGIiIiytKtDF/IkeFjwFe2uNMGERFRAFnBnV3SFZZ0yxkDPiIiogDSzSVY7JJuiCXdcsaAj4iIKIDskq65JAubNsobAz4iIqIAsoK7bNMGF14uZwz4iIiIAii7Dh+7dIkBHxERUSBpHl26Oku6ZYsBHxERUQC5u3RD7NItawz4iIiIAsjdpRtml25ZY8BHREQUQNmFl2F+FmiM98oWAz4iIqIAsrt0Jdulywxf+WLAR0REFEDuLl1urVbeGPAREREFkLtLl00b5Y0BHxERUQC8ubsjJ4OneWT4WNItXwz4iIiIJrmm1l5ccfebWLmzzT5mdek61+Fjhq98MeAjIiKa5HoGMwCAXvMzMLRLNyScw1fOGPARERFNcumMkc5LOzbLtbJ5ItxpgxjwERERTXopbWjAp7t22ggzw1fWGPARERFNclagl9KGNm3YXbqh7Lw+Kj8M+IiIiCa5VMYI7qzSLuC18DKbNsoZAz4iIqJJLmVn+JwlXeNzTpcuS7pliwEfERHRJGc3bTgyfF5duooZvrLFgI+IiGiSS3s0bXh16bKkW74Y8BEREU1yKY+mDXeXrrEO39EfG00MDPiIiIgmuZTXOnyuLt1wCNxarYwx4CMiIprk0mZmL2cdPjV0L12WdMsXAz4iIqJJzsrwpZzLsri6dEMizPCVMQZ8REREk1zaa1kWV5fuaDN821t6sOVg98gHSeOKAR8REdEkl+3SdTRtuLt0R7m12s1/3IZvP7l1FKOk8RQZ7wEQERHR6CQ91uHT3F26odGVdPtTWs4cQZpcGPARERFNcp7r8Lm7dEe5tVoqozPgm8RY0iUiIprkCs3hC4WyGb7RxGtpjQHfZOZLwCciF4lIo4g0icgNHtdfLSJtIrLB/LjGcd1fichO8+Ov/BgPERFROSnYpSuOdfhGneFjl+9kNeqSroiEAdwB4CMAmgGsFpEnlFLumZ0PKqWuc913OoAbASwFoACsNe97ZLTjIiIiKhde6/BpdobPuDzapo2Upo/q/mPl4TX7cfqcKThlVt14D2VC8yPDtwxAk1Jqt1IqBeABAJcUed+PAnheKdVpBnnPA7jIhzERERGVjZRHl65yLbwso1yHb6LO4fuPJ7bggbf2j/cwJjw/Ar7ZAJw/6WbzmNvlIvK2iDwiInNLvC8RERHlUXBrNZ922khrek7JeKJIcW5hUfwI+MTjmPsZ9SSABUqpxQBeAHBvCfc1bihyrYisEZE1bW1tIx4sERFR0Hg1bVgBXyiUDfiCNodPKYW0phjwFcGPgK8ZwFzH5TkADjpvoJTqUEolzYs/BXBWsfd1nONupdRSpdTShoYGH4ZNREQUDHbAl/HaacO5tdrIH2MiZtKycxcnViA6EfkR8K0GcJKILBSRGIArADzhvIGIHOu4+EkA28yvnwVwoYhME5FpAC40jxEREVGRvEu6xmdnl+5IS7pWJi2jqwm1H6/X+oPkbdRdukqpjIhcByNQCwO4Rym1RURuArBGKfUEgK+IyCcBZAB0ArjavG+niHwHRtAIADcppTpHOyYiIqJykvLIdOkldOmu2t2Bdzr68Rdnz/W83lkqTus64qGwH8MeNQZ8xfNlpw2l1FMAnnId+5bj628C+Gae+94D4B4/xkFERFSO7MDHWdLVc7t0rbl8uq7sry33v7UPq/Z05g34nIFkWlOIT5B9ury6k8kbd9ogIiKa5OyFlz3W4bNLuuZnr7JuMlO4A9d5XXoCdep6rT9I3hjwERERTXJepU3d1aVrffYq65YU8PkUXD2x8SAeXjO69fPSHjuMkDcGfERERJOcFYTpCsiYX2tK2R26QLZb12tplmRGQ7JAIOcM8lI+BXy/XfUOfvPmO6M6B+fwFY8BHxER0SSXzMnAGQGdpmfLuICjpOuV4UsbGT6Vp4vXeX6/smmpjG43m4z4HJzDVzQGfERERJNcWtMRMTN4KTvbp+wOXcDZtDH0/slM4cDJmUHzK7gyysjaqM7BOXzFY8BHREQ0yaUyOqpixlIpdnlXV3aHLgCEzS+9mja8mj68rnee348xj7Y87LXDCHljwEdERDSJabqCrlu++ogAACAASURBVIAac62UtHMOnwydw+fdtGFk2vKVa8diDt9wjSLFSHssOE3eGPARERFNYlawU20FfBkjoHOvtydSqGmjcOA0FsuypHwI+Ow5fBnO4RsOAz4iIqJJzArWqsyAL6UZ2bp8Xbr5lmUB8mf4kmMyh08bfYbPHEtmNJsElwkGfERERJOYlZWriRtz+FKZbJduqOguXSNITOYr6U70OXxch29YDPiIiIgmMSvoqYrlzuHTdYWwR5eu18orw2X4UmM0hy+tKXuB6JFIc1mWojHgIyIimsSsIK3a3aWrXF265n98d5duRtORMYOufMFc7rIsow/4NF0N+5jFSLFpo2gM+IiIiCYxd9NGytGl6wz4QnlKujnZu3wZPp9Lus7zjSbgy87hG12msBww4CMiIprErDl71rIsVjBllHSH31otmS4x4POhIzYn4Cth/p2mK+zr6M+OxZl5ZONGQQz4iIiIJrHUkDl8ZtOGQm7AlyfDl7Ntmua984VzCzQ/5vAlHTtslBLwPbulBRfctgKdiRSAsdkBJKgY8BEREU1i2ZKu104b2duF8izLUkzw5XdJd6R787b3JZHRFboH0sZ9nQEfO3ULYsBHREQ0iVmBTrV7pw1XSTdq7q3mDticAVfeZVl8btpIjnAOn1V+tps1HOVlNm4UxoCPiIhoEku6mzasOXyupo1pVTEAQFd/Ovf+RWTbcjN84zeHzwoOrazkWGz5FlQM+IiIiCYxK8NXY5d0za3VXAFffU0cANDWl8y5f05JN9/WapqOWMQIGfxY5Nj5mPmyit7303M+cw5f8SLjPQAiIiIaOSvQsZo2UmYw5S7pzqgxMnwdfamc+xfbpRuPhKCUGtc5fNZt7dKuYywZZvgKYsBHREQ0iVmdtdUeXbohR8BXFYugMhpGx5AMXxEBn2YEfJruT8A30nX4rMwgS7qlY8BHREQ0iVmNC1aXbsrRpRuW3NvW18bQXqikW2Av3Wg4hGhY+VI6HW2Gz7tpgyXdQhjwERERTWJD1+Hz7tIFgBnVcXQkXCXdIpZcsebwpTXlSyZtxE0bBefwMcNXCJs2iIiIJjErCKqIhhAOiR34JDMa4pFwzm3ra2JoLzCHL5knaEprRoYvFhZf1rvLbRTxXuzZi7tLl+vwFY8BHxER0SRmBXixSAixcMgOAPuSGbvMa6mviY+opJvK6IiFQ4hGQv7P4SulSzedP8PHOXyFMeAjIiKaxKygx5hjJ/ZctkRSQ008mnPbGTUxdCZS0B27bVjBUywSyht8JTNGSTcaDo3vHD7NNYdPU7BWnuEcvsIY8NGE8vNX9+DlHW3jPQwioknDCn4iITGCNi2b4atxZfhmVMehObYmA7LBV11FJH/ThmZm+MIh3+fwlbIOn9ccvqpo7pZy5I0BH00od67YhUfXNY/3MIiIJo2UphCLhCAiRgYuo0MpZZZ0c3sz62uNxZedZd1kRoeIsVNH3oWXzQxfzKeSbjGLPecbBwAk05p9ucq1pRx5Y8BHE0oimUF/qvgJvERE5c7KvgEwS646khkdmq5QU+EK+KqNxZedjRvJjIZYOHf+39DHUIiGxWjaGM85fPY6fNkMX3UsXPJ5yhEDPpowNF1hIK1hgAEfEVHRUhkdUXPBPWvplL5kBgBQ48rwzTC3V+tIODJ8aWNR5UJz+FKOOXz+bK1mPGYkJCUGfO6SrnIsR8M5fIUw4KMJI5HK5HwmIqLhpR373EbDISQzOvoGjddRa/cNS725vVp7b25JNx4N58z/c0tp1sLLIaR8atqIDRNk5huHdX/AzPCZ8xQzOjN8hfgS8InIRSLSKCJNInKDx/XXi8hWEXlbRF4UkfmO6zQR2WB+POHHeGhySpjvSJnhIyIqnhWMAbBLrnaGz1XSnVoVQ0iQs/iysV5fyA4WPR/D2aXrW4avcJDpeT97WZbsOnzZPYQZ8BUy6p02RCQM4A4AHwHQDGC1iDyhlNrquNl6AEuVUv0i8mUAtwL4jHndgFJqyWjHQZOfFfBxDh8RUfGsNfKA7By+RJ6SbjgkmF4dc83hM8qr8UgIvYPeFRZrL91YxL85fPFICCFtZMuyeGX4WNItzI8M3zIATUqp3UqpFIAHAFzivIFS6iWlVL958U0Ac3x4XAqYvqQR6PWzpEsB89j6Zlz/4IbxHgYFlLuk68zwubt0gaGLLxtz+MLDNG1kS7p+dekON2/QS7ZLN7uXrntLOfLmR8A3G8B+x+Vm81g+XwTwtONyhYisEZE3ReTSfHcSkWvN261pa+M6bUFkzTlhho+C5rWmDjyzpWW8h0EBZXTQmgFfxJhjl69pAzAWX+7IWZZFQzwaKjyHL5Ndh8+PTJpzmZd827nlux+QzfSlNR2V0TBCwoBvOKMu6QIQj2OezwYRuQrAUgDnOQ7PU0odFJHjASwXkU1KqV1DTqjU3QDuBoClS5cybxtAfY6Srq4rhEJeTy2iycdabshrM3ui0crp0jXn2CXMiolnwFcdx8YjXfZlq6RbKNuW1nREI/4tvGw9pjX+4u9nLsuSzs7hi4ZDiPg0riDzI8PXDGCu4/IcAAfdNxKRDwP4fwA+qZSy31oopQ6an3cDWAHgPT6MiSYha84JAAxmmOWj4LDezLADncZCylHSjUUEKU1HX9LYScPdtAFYGb7sHL5UpnBJV9cV0poy1+rzcw5fGPESSroZTYe1I5xzDl80Imagy1xQIX4EfKsBnCQiC0UkBuAKADndtiLyHgA/gRHstTqOTxORuPl1PYBzADibPaiMOP8ZsqxLQWIFfH15JsQTAUBbbxJtjuVSipV2dOlm5/AZr6HWtmNO9TVx9CUzGExnFzGOF9hFw8qc+dulq5W8LIszg+dchy9m7yHMDF8how74lFIZANcBeBbANgAPKaW2iMhNIvJJ82b/DaAGwMOu5VdOBbBGRDYCeAnALa7uXiojfY4MX3+SAR8Fh5W9dj7Hidy+9shGfO2RjSXfb0iXbsbo0q2OhT2nxthr8Znz+IYLvqxAKhYOIRrxZw5fThm5yEAtd3cOY4qEpitfm0mCzI85fFBKPQXgKdexbzm+/nCe+70O4HQ/xkCTn7Ok25/mP0YKDms+FQM+KqSlexBqBLGUu0s3pSn0DWY8y7mAMYcPADr6UpgzrSrbpZungcIKtGKOOXxKKYiMfD6q1bShKYWegeL+LpxrBCYzuh3gZReEZsBXCHfaoAkj4cjqsaRLQcKSLhWjdzCD7oF0yfdzdunaCy+nMp5LsgBAfa0R8GUzfDri0RDi5hw+5Yo6rYxe1JzDBwAZfXRZPjvDV8JWbdbtomFxBXxibynnpztX7MItT2/39ZzjiQEfTRjOBT9Z0qWgUErZ2esEM3xlry+Zwas72z2v6xlMo2ew9IDP6NK1mjaMACqRzHh26ALAjOqhJV2rvAoMXcDYneEzbjO6bJpzWZZiz2Vl+OoqokimNXucxrgEGZ8zfCsaW/HCtsO+nnM8MeCjCSOnpMtuRgqIZEa3syG9DPjK3mPrmnHVz1fhYNdAznFdN9bO609pJQdTRpeukXmzmzYGCwR85hy+zoQRXDq3ObPOl3t+zTy3ZAO+UXbEGkGmWUYuMcNXWxHxLOn6PYevdzCDnhFkXCcqBnw0YSRSGUytigIABtLM8FEwON/IsKRLbeZyKI0tvTnH+1IZe/5eqWVdd9NGxgwe85V0K6PGcihd/SkopextzqxzuEusKTO4i0eMpg1gaFBYKivDFy+hacNag6+mIoKUpjtKvCF77qKf+pIjK7FPVAz4aMLoS2bQUGPMLUmwpEsB4WzUYEmXrIzRjsO9nseB0gM+57IsVpbuSH8qb4ZPRDCtKobORMrOrhk7bRhLuAwJ+BzLslhz+EabTRvNHL7aeBRKZed6R8NiLzjtp97BNJIZ3V6+ZrJjwEcTRiKZwcw6I+BjSZeCwhnwsUuXrGCu0RXwOecwjyjgs7t0jYDsSCKdN+ADgGnVMRzpdwR8zpKuK3Byl06dx0ZC0xUyuhrxOnx1lcb3ZS0ubSwX4+86fEplt6cbybzKiYgBH00YiaRmZ/jYpUtB4cxWcw4fWcHczsN9OcdHGvA5d8EAkC3Lanreki4ATKuK4kh/2i6TOps2rDl7Frtpw6eAL+UKMktdh6+2wpj6Y/3MxmIOnzFH0CgRB2UeHwM+mjD6khlMqYwiFg4x4KPASLCkSw52wNfaC92xtIkzqCglwEjr2XIrADvTBxjNDflMq47hSCLlCL6yc/jcTRT2XDlHl25qFE0bzq7fWDhsL6A8nKSjaQPIvpmKRkKIhPydw+fM6gVlHh8DPpoQrKUrquMRVMXDGGBJlwLCKgvFIiE2bRC6+lMQAQbTOvYf6beP9yZHFmBk18jLdulaqmNDt1WzGBm+bEnXaqAACszhC4fsbuDRZNM8s4pFlHWzc/hyS7rGOnz+lnT7RlFin6gY8NGEYC1dUR2PoCoaRoIZPgoIK6t3TF2cc/gI3QMZnHxMLQBgh6Osm1PS7S8+wHCWW52fARQs6U6viqFrII2BlBV85Z/D58wC+lHSTTqziiMI+Ooqc0u6sTEo6Tp/H8XuBDLRMeCjCcH6R1gTj6AqHrFfhIgmO+u5PauuggFfmVNKoWcgjbPmTwOQ26lrlXFj4VCJGb5suRXIzfANV9JVCmjrNRZfNrp0vZdc8WraGM2yLM6sovWYSW3413xr2zfr+7L+nuw5fD526Tr/VpnhI/JRwhnwxcLs0qXAsOYZzWTAV/YG0zpSmo7Z0ypx3JQK7HQEfL2DGcQjIUyvjpUUYDjXojM+Z/e3Ldy0YSy+fKh7EACGWYfPa6eN0c/hi0fCiOd5TC9Jc3kUq2kj4Qr4/JzD18s5fERjw/pHWB2PoHISlXR1XdnbExF56UumURENYUpllE0bZc4KHKZWxvCuWbVodJR0ewbTqKuMYkpltLSAT8uWR4Fs8wYwTMBnbq/W0mMFfGHH1mr5M3xWUDiabNqI5/CZ46iJ52b4YhFBLCzI6P5l+HpySroM+Ih8Y2VBauIRVE+iku6Tbx/EB/5reWDeAZL/+pIaauJR1MYjOfOCqPxYrxNTKqN41zG12NXWZ3en9gxmUFsRKTngcwZjQO4cvtphlmUBgJZuY4s35/w8d5euswQb9aFpI+U1h6+I86VcXbpDlmXxs6RrnrsyGg7M6zsDPpoQEnaGL4zKSVTS3dWWwGBaH7IvJpHF2MQ+jOp47v6fVH7cAV8qo+OdjgQAI3iprYiirtSAL2N16Q5dlqWYkm5Lj1GhqIgO36XrDAp9m8NXSkk3oyMaFlSa3cc5c/gioVGVmd2sYPK4qRUM+Ij8lNO0EQ1PmnX4rHKuNfGZyM1absgqQ7GsW766+o19dKdURnHSzBoAQFOrUdbtGUijzszwlVJCtBZJjnk0bRRV0rUzfOH8TRuOoDLm8xy+Urt0Y+EQ4uYWcH2D7jl8OpTyJ+jrS6ZRGQ1jenWMO20Q+SnhmMNXHY/4FvB9/ZGNuG/VO76cy0u7Gei1MuCjPPpcAR/LuuXLmeGbPa0SQLZponcwjbqKEczhy7jX4cs2bRTaWq06FkYsHEJLMU0bmoZwSBAOiWPhZX+7dIsO+Bz3sefwhbN7/GaKWMC5GL05JfZg/M0y4KMJIadpw6eSbltvEg+tacZL21tHfa58mOGj4SRSGdTEI6ixdgeYJNMVyH/OgG96VQyxcAgHzQxbz2AGdZVGgJFIaUWX/tOORZGBbPNGZTSMcEjy3k9EMLUqajcnuLNtAykN//LwRhzuGURaU0MCSr8XXk4WOYcvHgnb36Nd0o2IL+sDOlkBX12JGdeJjAEfTQjukm5aU6P+w125sw3A2AZj7X2pMX8MmtwSSS0nw8fdNspXz0AaIkbTQSgkmDWlAoe6shm+2oooplRG7NsWw7lkCpAt6RYq51qmm2Vd6/7OgG/zwW48srYZy7e32qVU5+P40bRR+hw+LWdHEOccvojdPexThi+ZQY2ZcWXAR+SjRDJjvyOtMl+oRlvWfXmHEfCNZbnVyvC19g6O2WPQ5NY7mG3aAMC1+MpY90AatXEj2AOAWVMq0NI9iFRGx2BaR208gilm92yxZV13l671udCiyxarcQMwgq9ISCBizOFrNZs59rYnkDRLqc7zD9e0seNwLx5d1+y5R65zp418jSJeUppuBny5c/giIbFLuqNpJnEySuwR1FVE0ZvMFLXX70THgI8mhD4zCwIAVWYHVn8qg75kBq/ubC/5fJqu8IoZ8LX3JXM2KfdLfypjB6XM8FE+iWQG1bHIkN0BqPx0D6Qx1RFkHTelAge7B+xFfq11+KzbWjRd4ZuPvp2zM4cllSfgq47n30fXMq06at7HmJ8nIoiFQ0hldPtN7N6OBNJaNsMXLTKTdueKXbj+oY34i5+8gd1tfTnXeS3kXErTRtQxXy8WDkHE/5Ju36AxFcP6fQQhy8eAz6WxpRe3PdfoW6cPFcdaugJwBnwa7l+1D1f9fFXJAdXmA9040p/GGXOnIq2pMWmrb+81yrkiwQj4BtMafv3G3kC8k50oNF1hIK2hpoIlXTKCOCuAAIBjp1bicM+g/fpkNQlYt7Uc7BrA/W/txwvbDg85p3NNOyA7l69Qw4bFyvBZGTPACMKSGd1+TXuno99ulgBgN28MF1gd6U9henUMOw/34pI7XsvpdM3O4cvfGewlmdERjxoBXtzOOFpzC8dmDp/X72OyYsDn8tj6A7h9eZM9N4uODmvpCgCoihmfB1IadpnvDPd1Jko638s72iACXH7mbABA2xjshmGdc8GM6kAEfC9sO4x/f3wLVu3uGO+hBIbVoGEtKA4ww1fOutwB35QKpDWFveZafLUV3hk+a+qI9SbT0plI4e3mbgDOdfiMAKi0gC8bCsQjxvIm1lSYvR0JpDJ6znIv0fDwAV/3QBrvPq4Ot376DPQOZrC7LfsansroEDHOU0qXbtIxl9AO+FyffcvwJTOoiRvrIgIIxNIsDPhcrAV0m4/0j/NIyktfTsBnvNtMJDP2C+G+ztJ+Hy/vaMPiOVPxrmNqAcCej+In60X4tGPr0JvMTJrdQfLZ1TqynzXl51xuyL0dFJWfIRm+KcbSLI0txhvbOrMrFMgtIXYmzOYwxxvXn63cjaXffR6/fvMdHF9fjanm3L9YCU0b1lp8zoAvW9I1HmswraO5qz9nyzZrzbuC32u/sVXcgvoqALn/U63ATaS0gM+ZaYxHw/ZYjHFb3cOlVSi6B9L49Rt77TUSASMz35cceYZPKWPLze0tPROqWsiAz8UK+PYf4c4JR5O1dAXgKOmmNbzTYbxI7Oso/vfRM5jG+n1HcN5J9WiojQMA2vpKb6ro7k/j1me22+UHNyvgO/VYI6ic7Fm+bDaVAZ9fnAFfOCTGPtEM+MpWz0DaDugAI8MHwJ6bly/D12FWnNodrzGvNbVj9rRKPHHdOXjxn89DhRkAhc3Gi+IyfMZjWcETYJR0UxkdrT2D9mtxU2tfToYvFg4VleGbUhnF7KlGUNvs+J+azOhDStBWAFloSknKcT/3/Uda0r3r5V3498e34IO3voQ7V+yygz0gf4m9kHX7jmDxt5/D0u++gIu+vxK/eXPs1oEtFQM+F2b4xoc1QRbIlnSPJFL2oqT7S/h9bGruhq6AsxdOx0wr4BtBMPbU5kP48YpdWLv3iOf1VnnllFl1xmOMIKicSBjw+a/P3iPa+MdZUxFhhq9MKaU8MnxGwNfYYgR8dZURxCNhVERDuSXdhFnSdWT4Dvck8a6ZtVg8ZypEsuvtiQimVcUws7Zi2DF5ZvjMgK+9L4mz5k8DYGT53Bm+Qk0b1vc6tTKK2oooplZFsb/TleEz5w1aAVsyo2PzgW6c+q1nsKfdewpPStPt+YYxH+bwabrCo+uacdb8aThr/jT81zPb8fTmQ54BX0+Riy9vO9SD3sEMvvbRk3HGnCm446VdeZMGRxsDPoeMpqOlx/in3cwM31Hl1aW7vSXbkVZKELLpgDGn5fTZU1ATj6AiGhpRwGe9CO/K8+LT3pfElMoojjPfwY5F2fho0XVlB3z7GfD5xmrQqDbfxNTGI9xpYxx9+8kt+N5T28blsQfSGtKaygn4plfHEIuE0GT+7dVWGNe5d9votDJ8joCvtXcQM+u8g7rH/u5PcM25C4cdk9ccvlgkhP60ho5ECmfMmWoHVM7bRCOF5/AlUhoyevZ7nTOtMud/qjNTFwoJomEx1v470I1URseG/d5vsq11+Izx5JZ0s92+xZdQX21qx+GeJK75wEL85HNLEQ4Jth/qtbumjb2Njb/dYjN81tSez71/Pr720VPQ0jOIh9c0Fz2mscSAz+FwbxJWNpkB39Hl1aW79WAPAODEmTUlBSGbmrsxd3olplbFICJoqI2PaC2+7S3G47uXFLC09yVRXxNzlI0nb8B3sHsAg2kdFdEQM3w+cu4gY31mSXf8PLflMP646dC4PLZzlw2LiODYKRX2/DWryuEO+DrMOXxH+tNIazrSmo72vhSOqYt7Ptb8GdXFLbzs1aUbDuFQ1wCUMtYJnDvNmIOX27RReA6f+3udO63KNYdP85w3aP3fdTZ4OKW8mjbsBaFL3wHkkbXNmFoVxQWnzkQsEsK86VXY3d5nv1GriUdQGQ0jGpaSA77KaBjnnDgDZ86bijtX7Cp6TGOJAZ+DVc6trYigmf/0jhpr6Qp3l+7WQ0bAde5J9WjpGSw6Lb7pQDcWz55qX26oiZec4VNK2Rm+fOUFI+CLY3p1DCGZ3Bm+XeYL7Dkn1ONIfzoQHWlH24GuAVx8+6s5/9gSjh1krM8s6Y6PVEbHoe4BNB8ZGJffgRUwWM0VFqusW2vO8wSGBnzOzF5nImW/gT0mT4avWNY6fDFXhu+A+b9wZm0cC+qrjeMlzOHr7s/9Xq0Mn9XA4Gy+sB4zpWn24xYM+Fxz+KKRkc3h6x5I49ktLbjkjOPsgPf4+mrsak3YWfjaighExNhtI89r4mA6dxu8/rSGaNhYF1BE8JU/Pcn+vsZbWQZ8rT2DOPvmF+yttyxWwLdswXQ0dw2MyWK9NJRz6QoAqIiGIGK8sE2rimLRcVOgFHCgiKxrV38K+zr7sWj2FPvYzNqKkgO+tt4kjvQb2yDle/Fp70uhvjaOcEhQP4KgciLZ1WpkMc8/ZSYAlnVH4rWmdmw60J2zd7P93DYXXa6pYEl3vDQf6bcrOI0tQxcwdtN0VVTnaLG6+odm+IBsp65zZwwj4Ms+TzoTKVjb4rb1JnHYnHqUL8NXrJp4BJGQuEq6YXtB+YbaOObPMDN87jl8BbphuwaMjGSdXdKtMtb2MwNXZ9OG8ZhWhs943dmVp6riLAXH7KYN4wcTCZUW8D2x8SBSGR2fPmuufeyEmTXY05HIWRcRAOoqonkzfF/4xWrc+MQW+/JASrMbaADgvHc14P3HzyhqTGOtLAO+Z7ceRltvEve+vjfnuBWFL1s43Z60SmPPnudkBnwigirzD2b+jGrMnW684BTTOb35gJEVXDwnG/CNpKTbaHbNnT1/OpqP9HtmF9t7k2ioiduPMZlLurva+jClMor3zDUyowz4SrfDDCLW7euyj/V5ZPisIHCyy2g6Hl3XbM93muisjn8gO12jkH9/fDM++aNXfVuI3KukC2QzfM7u3TrX/q0dfSk709bel0SrHfCNLsMnIphWHUM8mpu9s8ysq8CCGUMzfMOtw9fjLulOz+3UNQK3oZ3B1pv6Pe0JO+Hy4xVNeHzDAQDI2eLNPYfPKummiliW5UDXAG57rhFnzJ2KRbPr7OPH11cjldHt+ePWnEr378Np88HunNfLgZRmT0sCjJ/xb//mvcOO6WjwJeATkYtEpFFEmkTkBo/r4yLyoHn9KhFZ4Ljum+bxRhH5qB/j8eLM1r2w1VitfEVjW05Qd+DIAKZVRe2120rpDKWRc3ZEWSrNsu6CGVWYZwZ8xcwte/uA8c920XG5AV/3QLqkTikrA3DRolnQFbCvI/exB9MaepMZ1NcYc2Bm1saL3k83ldFx4+ObsXpvZ9HjGWu72vpwQkM15s0o/LPe39mPW5/ZjozHi/2h7oEhgaL1j6kc7DCzpGvfyU44TyQzCDsyKDXxSGB22nhu62Fc/9BG/O2v106YLkQnTVd4fMMBO0v3jrmmZzQsw2b4NF3h6U2HsL2lF89sbin6MTc1d+O9//nCkNcLYPiAb2iGz7i9UgqdiRROmWX8X2rvS+Fwjz8lXQC4ePFxOPekBvuyM/PWUJPN8FkBFWDO4SuQ/cyWr43XxznmPEDr9cHZfAEYwWQipaGlZxAza+NIZnQc6BpAKqPjBy/sxCNrm6HrythKzV6HL7eUm93yrXCGL63p+IffrkNGU/j+Z5bkdDgf31ADANi43/g/4pxT6RXwdQ+k0TuYydn3fSCtoTKau62d8zHG06gDPhEJA7gDwMcAnAbgShE5zXWzLwI4opQ6EcD/Afgv876nAbgCwLsBXATgx+b5fPU/zzbiw//7MpIZDYlkBm/s6sAH39WAjK7w+IaD9u0Odg3guKmVmDNt6LpBVBylFLr6UyUtNunsiLJY+0DOn1GNmbVxxCKhorJOm5q7MX9Glb0BOQB7aZZSdk/Z3tKLhto4li4wliXY5SrrWm8U6p0ZviKziCsaW3HvG+/gr3+xGtsODZ9pOBp2tSVwQkMN6sx1wPIFfLc+24gfr9iF1a6lapRS+PzP38LHf7jSLsvc9fIuvPd7L+KtPRMnsB1LO1p6EQ4J9nX228+FRFJDdSxsv+DXVESQSE684KgY7hLnyp1tiIVDeH1XB7764IajuiVfWtPxv881FnxNeHRdM/7xgQ14erPRpLG3ox/VsTBOnz0lZwUALxubu3CkP41ISHDHS005r2dd/Sn8bOVu7PWY27uyqQ2He5J4ZO3+IddZAUNd3pJu9vgxdRXoS2bQM5hGuOSy0gAAIABJREFUbzKDlKbbiYj2PqOkGwmJ3XQxGt+6+DRcuWyefdkKqKZVRRGLhDwzfLFI4Tl87vK1ey0+Y3mV3DLyvg6j5P7BdxnB5+72BDYd6EIyo6O1J2k3iQyZw1fiOnz/9/wOrNvXhe9ddjoWmllTywkNxuVNB7oRkmwDoXtOpcV6rXM2YvWnNDthMdH4keFbBqBJKbVbKZUC8ACAS1y3uQTAvebXjwD4UzFeAS8B8IBSKqmU2gOgyTzfqPQOpu0/0Iym44HV+7C7PYEHV+/Hyp1tSGk6vnTe8Vg8Zwp+tzbbLn2waxDHTa3E7KMU8B1JpIru/DmSSGHV7g7sPNw7ognH73QkcrKct7+4E//80MaSzzOcn7+6B0tueh5nfPs5XPWzVTjUPfzPsGfQI8NnvkNaUF+FUEgwZ1pl3hf3x9Y347Ifv4Z3OhLYdKA7Z/4egGwXbQll3caWXpwyq9Z+QXA3bljBozPga+9LFfVP79F1BzCjOobqeARX/+KtcZ/Q2z2QRltvEifMNN7dzptehX2dQ8e0v7MfT5kdjq+45r++2tSOna196E1m8JX712Plzjbc+sx2KGX8foLoR8t34sbHNwMwfoYtPYO4wJwDuW6fERD3OtaXBIyMQUrTxyUj1tI9iG8/uQUdI5x68M1H38an73odSikopfDKjnacf3ID/u3jp+KpTS24c0WTfduVO9vwv881+jX0IZ7YcBA/XN6Em//ovcSKUgr3vLYXALBxv7FM077OfsybUY1Tjq1DY0tvThCn6woPr9lv72ixYnsrQgJ8/aKTsfVQD17e0YbugTRuf3Enzr31JXz3j9vwS9eUIADYfsgIJB/bcGDIm97uAWNOcK2re3aWVdJ1vP5ZQdbe9oS96PK86VWojIbR3pu0M2GhkP+ZIyuws14350yrRCwcyglihpvD1z2QRjgkqDYDpup4BDOqY/b/1GR6aNPGHjMDe+5J9QCM1RFWmW8WD/cOImnvGRw2P+eWcosN+B5bfwAfPvUYXHzGcUOum14dw5TKqLmtWsR+o1ZXGckT8Bnfz0A6+/c8mNZQGZ2Ys+X8GNVsAM63M83mMc/bKKUyALoBzCjyvgAAEblWRNaIyJq2tuw/m52He/Hfz263g6CXd7ThrO++gNuXGy8+r+3qQHtfClMqo7jjpSb8cVML6ioiOHvBdFx+5hxsPdRjL/9xsGsAs6dWoioWQX1NbEwXX956sAcfum0F/v6+dUOuG0hp+KcH1qOpNfsu9PqHNuAzd7+Jj/zfK3j/917MuQ4wXrCe3nTITkU7tXQP4oLbXsZv39pn3/beN97Bo+ubRzxPMZnRhryg9acy+PGKXVg8ZwouPuM4rN7bie8/v3PYc1mT2J0veNY7q/nmC58RhHj/Pu59/R2s29eFT/34dTQfGcDiPAFfvvKiVYpMO1Z633G4FycfU4vaiihm1saHLM1irXhfb557Zm0FNF3hSP/QLOL+zn78bm2znf18cfthXPqe2fjlX5+NRFLDf+b5p3W0WN/bCQ3ZgM8ruL7ntT0QACfNrMHLjbkB3y9f24v6mhj+59NnYN2+Llz9i9U4vqEGHzntGDy9ucW3/S0nkofWNOP+t/ajP5XBTnPO5+VnzkY0LFhnlnWde0QD2RLR0S7rJpIZ/PUvV+MXr+3Fz17dM+T6vmQGTa3eE+UBI4Bavr0Vbzd3Y8P+LuxpT+BA1wDOfVcDrjn3eFz07lm4c8UutPUm0TOYxlcf3IgfLm8qeE7L3vYEbn9xZ8GqwN72BJ7bYpRWdV3hzpd3ISTAM1tasNlcd9Ppzd2d2HaoB5GQYGOz8Zq4tyOBBTOqcMqsWjtAt9z7xl587ZG38S0zgF/e2Ioz503D1X+yEMdOqcC/ProJf/K9F3Hb8zvwvuNnYN70Ks/u/W2HelARDWF/50BOaR8wgqC6iuiQIM1ax9OZ4Tu+IftGs9NcdHl6dQz1tTFzDl8y7xp8o2XtxWst3BwJh/CLL5yNq/9kQfY2w8zhsxZddpYyjU5dq6Sbm+GLO0rES+ZORW1FBLvbElhtBnxd/Wk7Q5p3Dp8d8OV/Hg2mNRzqHsyZ4+0kIvbP3vn7MLp0M0MaOa05h86sfX8qY680MdH4EfB5vcVw/8Tz3aaY+xoHlbpbKbVUKbW0oSE73+D7L+7EHS/twqV3vIaHVu/Htb9ag4ym4ycv78KRRAqPbziA2ooIfnDFEhzuSeLJjQfxoVNmIhoO4ZNnHIdoWPDw2v126vy4qcaTfPa0Kuz3yHJ4SSQzuG2Y8oJTY0svrvr5KnQPpPHarna748ry7JYW/H7DQfsdZM9gGq82tePSJcfhB1csQSwcwt/ftx6D5ruK9fuO4LI7X8eX71uHrz/y9tDHO9wLTVd4YqNRvn77QDfa+5JQCli+rXXI7Yfz9KZDWPwfz+Gs776Av/31GryxqwMAcN+b+9CZSOHGi0/DzZ86HVcum4ffrWse9udilXRr4s6SrjWHz/jjmzvNO+Br601iY3MXLj9zjp0VPD1fhs8juD3QNYA/ve1lnHvrSzj5357GNfeuxpaD3UhmdJxszplZWF+N3UMyfFZJN5bzGF5Ls/zrY5vwzw9vxG9W7cOTGw8irSlcduZsnDKrDhefcSxe2dGW98WztXcQT286NKYdwFa52ipnzJ1urJnlzFZ296fx4Or9+OQZx+HS98zG1kM99pje6UhgeWMr/nLZPFx+1hx87n3zURUL466rzsRnls5FV7/x/AWAV3a02W+wxtNo97ds70tiX2c/UpqOVbs77SafRbOnYNHsKXaGL5HKDfisEpe1R3Qxmo/04wu/eAsv78gG2V39qZxARymF1Xs7PedWarrCPz6wAdtbevCuY2pw/1v7huz7/JX71+NjP3gl79y2XW0JO6v90Jr99u/zg2Y25usXnYzBjI4fvrgT339+JzoSSYTEO7u7qbk7J/N/+/Im3Pb8jpymCqetB3tw2Z2v49pfr8VvV+3Dc1sPo6m1Dzddsgh1FRF8/4WhbyrveW0PplfH8Jmz52LzgW4kMxqaOwcwb0YVTjZLo1ZZd19HP259phG18Qj+8PYhvLjtMDYf6MGHTjHWZrvughPR2pvEhe+ehT9+5QP46eeX4vQ5U+w5gZbBtIbd7QlcuWweKqIhPLb+QM71e9oTmFE9tAQ7rcrYfsz6+wOMN10iwN72/pxqQn1N3JzDNzjqDt18YmHjddSaCgMA55xYb2cigew6fC3dg7j+wQ1DGnfcO4oAxjy+Qk0bACBilLiPb6jBjsO9WLP3iJ0Rte4bz7MOX9SxDt+m5m6zwpD7d279D7HmJXqx3vg6K04nzqyBpitscb122Rk+RyPWQFrP6dKdSPwI+JoBzHVcngPgYL7biEgEwBQAnUXeN6+BlIbl21rx3oXT0ZlI4eu/exsLZlTj/r95H/rTGn64fCee3dyCjy2ahfNPnmm3Rv/pqccAMLaVuWjRsXhkbbP9TtR6t+V8N1KIpit85f71uH15E667f/2wmYxnNh/ClT99E5GQ4GefXwqlgD++nbsQqPVC8czmFmi6worGNqQ1haveNx+XLJmN2/7iDDQe7sW/PLwR19y7Bp/68es40DWAD596DBoP9w4pEVpzTVbv7URr7yBe3HYYITFeQJ4zG1g0XWH59sN2EJnP79cfwHX3r8cpx9bhQyfPxIb9Xfjcz1fhN2++g5+8shvnnDgDZ82fDgD42/OOR0gEd71ceNHJvjwl3dqKiL3X47zpVegdzNjrO1lWNLZCKeAL5yzAY3/3J7j5U4vwPlcLvFV29Qqabv7jVuhK4TuXLsIXP7AQKxrb8NmfrQKQ3TLt+IaaIe/mrYVQrXNbL477OnNvt/NwL1bubEddRQQ3PbkFd6/cjVNm1eK0Y41zn/euBvQmM1i/Lzcz29GXxCU/ehXLbn4RX75vHW7+49b8P8ACWnsG8dSmQzkvfI+sbcZDa/ajpXsQv19/ALc8vQ11FRG7G3re9CqkNTUkA9Kf0nDNucfjPHOOjbWs0a/eeAdhEXz2ffMB/P/2zjy8iupu/J9z78292fc9IQkhC0mAALKDgiKbCLiLUsWtttattdLa6q8ufW2rvq11KW19VdzqUjcUi1JBEFkE2XcIO4RAEkJCyL7M74+ZO7lJbhZIJMn1+3me+9zJzDkzJ3PunPme73bgiRlZrP3tpaREBnBhWjgB3jY+25zHipxCbpm3ljte/67N35kr76w9zIDHFvHUF7taNEcu31PA3W9v4NcfbOH5JTmtmtb/ve4IQ59czAJjArR8TwHTX1zBT95cx6Lt7rWR24+V8OyXe8zrb3Lpr6/3FLDneCl+ditxwT4MTghh89ESKmvqKCitamTSvSQjkhBfL/7y5Z52CZ1bj5Zw5dxVLN1dwBMLtlNXr5tT73prA9NfXGGOHc8s2s21/1jNqysbtHenyqqZu2wvk/66nMU7T/DotCz+54r+FJfXNBJGNh8p5qtd+dTUacz5YDO1RmLfxTsaxgOnH+aQxBAWbM5j0fbjJIT6mhr45Ah/bhyWwNtrD/P66oPMHNqLC1MjmL/xWCOtSG1dPTe+/C0PvKe7k1TW1JmaO1d/1j0nSlm2O5//bMlj1svfYrdaGJ0SxiPzt/L7z3aQGObLzKG9uPOiZBbvPNHIsnHoZBmLd55g1vAEhieHUVVbz7LduitPUpif+Vw7zbq//nALNovio5+NItTPzn3vbATg4nTdPD9reCLbn5jEs9cPJMsIBksK04UX19/K3vwz1NVrDEkMZVJWNJ9tyTO1Vnvz9XHAnRlRKcWyOeOY7aJB8/ayEhvkw4HCM6aZOdTPbqZ/0gW+70fD5xS+IgJaFiidefhe/mY/H23MZd1BN9rMpgJfqA+5p/R0Z82CNoztqABv7DYLfSL8WHfoFKVVtUzI0t/XziDK9vjw/XvdEeYu29dMSeAcx5v67rnSoOFreG6dQS1f72msIHHKCOU1DRaviuraRlG63YnOEPi+A1KVUr2VUnb0IIxPm5T5FJhtbF8DfKXpd+dTYKYRxdsbSAXWtvfCS3fnU1FTx/3jU/n0ntH8bFwf3rpjOMOTw7h8QCzzVh6krLqOKwbqVuKHp2ZwSd9I088GYPbIREora5m7VBdKXAW+3DZy8WmaxhMLtrNkVz7TsmPZfKSYF77aS2llDf+7aDcP/HsTn2/N4+ipcv67/Th3v72Bn761gZggb969cwTjM6LoGx3QKPN7fmkl3+QU0Dc6gMIz1aw5cJIvd5wg3N/OoAQ9gGBceiQ/GZvMZ1vyWHPgJA9MSGPpg+N4aEpfAL7a1fhHeaCwDKtFoWmwaNtxFu/MZ0hiKFP7R7NibwEV1XXMW3mA215bx1VzV7mNMNM0jX98vY9f/HsTQ5NCePuO4fz5umwWPzCWEclhPDJ/G4VnqrjvklSzTkyQD9cOief9dUdb9eUrrdQjGV0fkkszo7hxeIJpEujVQqTukp35RAd6kxUbSGSgN7OGJzYzmXhZLYT62SkoraLwTBXzN+ZypqqWlXsLWbj1OHePS+GmEYk8PDWTebcORdP0BchTo/SZXnK4H0Vl1RS7mGsLSqsIcNjMmVxWbBCxQd7873/3NPLPmrfqIA6bhfl3jyYq0JsjRRVcNTjO/L9GpYRjsyiW7W7cZ6+tOsiW3BLmTEpnUlYUi7afMB2DP1h/lMl/Xc7HG4+agk15dW0zAWJFTiFTnvuGn/1rA4u264L9hsOnePD9zfzqgy2M+OMSfv7eJuJCfHnnzhHmgGlGRRu/g735Z3hx6V4mZ0WTGRtIZkwg4f52vt5TwLbcEt5ec5jL+seYLyClFD52p5+NlclZ0Szafpx73tlAZIA3x0oq3fo/tcT7645Qr+lBIKOf+orff7ajmVb8j5/vYtmufJbsyucvX+5hyc4T5rHnFuewytBIAXyw7iiFZ6q5952NTHthBTe/upaSihrWHzrFT95cz28/2mqWzSup4Np/rGLq8yt4bkkOr6/WF0LfeOQUNotieO9QlucUsOfEGdKiA1BKcUFiCNW19Ux7YQW7jpcysk/DBCTQ24v7xqeycu9Jluc0tMkde/NLuf6l1ditFh6YkMa+gjK+2Hacr/cUsHr/SUL97Nz/7kZ+8d4m5i7bh5dVmVp8gLvf3sDTX+wmxNeLZ6/PZvaoJIYmhZAVG8i8lQfM38tzS3II9vXiT1f1Z8vREh79dDszXlzJHW+sY+5S3TVmzYGTRAQ4+NXkvsazc5IxhnbPyX3jU/G2WQjwtjFnUl+uGhxHbnEFa12i0TcfLaG0spbV+0+y6/hplu3Op9T4XTsTrZdX1zLthRXcMu877n57Az5eVt77yQheumkIWbFB5BZX8NOxfbBZLdwyujehfnYe+mgrZVW11NTV89CHW7FbLfxoRCID4/U0Q877khiqB3TFBHmz+Ugxcz7Ywur9J/nt1AxSowK495IUyqrriAp0kBETYLbbVRsFuqtJbb3WKDeos/0ZMQFcMSiOkooa87qvrDiI3WbhppGJbvvamaTXlaRwXw6cLDcnGU6BL7e4gtOVtV0q8HlZLZRV1fHBBl2D23RcLqmoaZZgOj7El+q6ev7+9b5mx53mWGfAZJ8If3NsmzZAF5KdiyE4zChd51q8zjx8DWlZ9hga96YBY06tbGJoKwJfuFPD19C+cH8H/eOCGmnZoUHDp2n6esPgPkq3u9BhQ7OmabVKqXuARYAVeFXTtO1KqSeAdZqmfQq8AryplNqLrtmbadTdrpT6N7ADqAXu1jSt3VP//2zNI8zPzrDeodisFn41ua957P7xqfxnyzHC/R0MNzQ+/eKCePWWoY3OcUFiCJkxgSw2XhDOaKJeIbqW49v9J0HBoF4h5kusuLya11Yd5Ittx9l1vJQfX9ibh6dm4mVVvPhVDm+vOWT6DX60oWEmbbfpA/dd4/qYL9dp2bE8s2i3GSG8YHMe9Ro8c0021/1zNfM35rJsVz6X9Y8xs7ADzJmYzqBeIYzsE2aqzvtE+JEY5svSXfncNKJhYNlfWEZGTACVNfW8vvoQe/PP8JspfcmKDTJ9+f66OId+cYEcKarg8he+4cK0COxWC+H+dtKiAli88wSLtp9gav8Y/nxdtinoBHh78eotQ3nis+1U1tSb99rJXeP68O53R3h7zWF+OTHdbT+WVtY0cpAFuG5Ir0ZlMmMCsSj4YP0R+hv+F1W1dXyTU8CMQXFthr1H+DvYcrSEK+eu5EhRBQHe+pI5CaG+/PiiZLPchakRzL97NEdOlZv/o3PGt7+wjMEJdvJPV/LFtuPmfgAfu5Unr+zPra99x9+X7ePnl6ZRXF7NRxuOcsXAOJIj/HnppiH8bdneRok+A729GJwYwtd7Cszfb0V1HW99e4hLM6K4++IU1h4oYtH2E3y54wRT+kfzzKJdFJVV84v3NvO/i/ZQUVNHUVk1GTGB/GhEAj5eVpbtLmDBlmOkRPgT5OPF01/sYnxGJE99votwfzv/d/MQvjtYRKifgysHxTX6bTkFvv/uOM6ghGB++f5mfO1WnrgiC9DXvrwoNYIlu/JZubeQUD87D0/NaPHeX54dy/vrjxLobePdO0fw+ILtzF26l5lDe5lpG1oiv7SSjUeK+cWlaUwdEMPcpft4bdVB3lx9iBdvHMTErGi2HythZ95pnpiRxY3DEhj91Ff8a81hJmZFs+5gEc8u3kN2r2A+SQmnqKyadYeK+Nk4XWB4+Zv93H1xH+69JBWbRfGrD7fw2ZY8npjRDx+7lZe/OcCmI8VGYEIeX2zL44EJaWw8XExGTCATs6L5/Wc7yD1VYU4snQvOHyuu4M/XZnPV4MZuybOGJzJv5UH+uHAnY1LCzXv/7trDlFfXcdsYfQ3UFw0/5A/vGkVEgIP5m3J50RDAEkJ9mX/3aGa/upaPN+ZyxcBYsmKDeHLhTvYXnKG6rp5V+07y68l9uWtcH/PaSiluG92bX76/mbnL9pEZE8hXu/KZMymd64f24us9BfxrzWEiAxz0jQ7g3e+OcO/4VNbsL2JY71CGJoXQO9yPA4VlpjnXSUSAg9duG4bdmGBNzIzGz27l4w25ptZ9RU4hSukv+NdXHaSkooZwfzuBPl6mqX/TYT0y8/HpWfSLCyQ1KoBA4+U779ahfL7tONdcEA/oPpHPXj+QW+et5f53NxEf4sPq/Sf587XZRAV6o2kaIb5e5gTAmXYoPTqAz410K/eNT2Xm0F5m37yz9jAXpka0OqY4NUQHT5aZ+fF25p3Gx8tKYpgfCaG+DOwVzCPztxLmb+ejDUe5enCcaRFoD0lhfny2JY/CM9Xm5DLC3276q39fAp9ToGrNR9DLpkzNI9DMHF9SUdNMi+YU5p5ZtJtRfcK4bXTDWr9OIdMZMJkc7nQv8WGgkRvUKVQ2JFxurNlTSpmaR6fFbu2BIq51eZccPFlOiK9XoywOTXGa1v2bBNeMTYswhVXnOze3uAKbRVFbr1FWXYuP3WpE6XqowAegadpCYGGTfb9z2a4Erm2h7pPAk2d7Tac596rBcdiszRWVKZH+/GZKBhHGSggtoZRi9qhEfv3hVrysykyk63zp3WiY9+65OIUHJ+kCy+MLdjB/Uy5DE0N5YkYWPxquC1ePTc9i85FiQnztvDJ7KFmxgaw9UERO/hmyYgPpFxfUzLZ/+YAYnlm0m/9syePHFyUzf2Mu/eIC6R8fxCUZkXr+IQ0mZEY1qmezWpjcL7rZ/3JxeiTvfneYypqGbN8HCs8wsFcIvcN8ed54iYzPiCIh1JcAh41HP9mORSlevGEwVovi4fnb2HnsNDX19Zw4XUV1bT1Wi+KRqRncPqZ3s4HQbrPwP1f0d3t/40N8GRAfxKp9J/llC31QWlnbSH3ujoQwX24emcTrqw9y9QXxDIgPZu2BIsqq6xjvorFtichAB9/kFBLmZ+ev1w9kya58/rv9OE9dM6BZn6RE+pNiRKxCQ26mN1YdJD7Eh5++tZ6Sippmk4eL+0YyY2Asf1u6Fx8vKzvzTlNZU8+tY5IAyIwN5G83Dm7WtnHpETz9xW59MfQAbz7ccJRT5TX8+EJdEB2SGEJcsA8fb8ylqraOE6ereO3WoZRW1jJ/Yy6RgQ4iA7z5744TPPyx7nQe5mdn9sgkfjU5nVV7T3LHG+u4/92NrDlQxOPTsxiUEGJqjJsSH+LDxMwo5q08yKebjnGyrJoXbhhkOnGDnjrho425BPt68e5tw1p9+YzqE8aNwxO4fEAMSeF+PDQlgynPLee5JTk8Oi2rxXqga3A14/ffJ8KfP1+Xzf3jU7nzzXU88dkOxqZH8OH6XOxWC9MGxGKzWpg5NIHnv8rhSFG5KSBtPlLM3vxSNh8poV7T8ysOiA/m5+NTG2mErxkcz0cbcvl6Tz4TM6P5bMsxxqZFcseFydgsiscW7GDPiVI2Hynm6gviGZsWzu/RndDTDJ/PqEBvXpk9hJRIf9Pk6YrdZmHOpHTufWcjv/pgC0/MyOLNbw/xp893AZARE0hcsA+fbj7G7WN6m75TPxuXwoPv66bQ528YRKifnTdvH8aSnfnMGBhL4Zlq/vD5ThZsziO/tBKHzWIKMq5cnh3D66sP8swiPYo22NeLm0cmopTij1f1Z0RyGFcMimPdwSJuf30dr6w4wPHTlYzoHYpSiptGJPLsl3sY2Se82bmHJoWa2z52K5P7xbBwax6Pz8jC28vKyr2F9IsNol9coDkZnjm0FyUVNaY25ruDp1AKrhwcZwp6TsL9HY0ms6C/iB+bnsXvPtFXO7htdG+uNgRCpRTZvYJZtltPIeNMgTK6TzjrD53iL9cNbDS22m0WFt53YavvDGjwAXMVdHbmnSY9OsCoq/i/m4dw5dyV3DrvOwBuH5Ps7lQt0jvcj5KKGvYVnCG0ia8wdHyVjZZwClKRbWj4QL8PDpulmStLcXlzH74swzJw9eB45kxKb/TedgpxTqHQOeYOSwoj2NcLu9ViJt5vloev0QogihMllabLTdNcpwcLGwT0lkgI88VqUc3eSWPTI3hx6V5W7S1kSv8YTlfWUFJRQ2qkPzn5Z0y/2MoaDxf4ugKnOXdq/5gWy7hqblpjenYcf1i4i0Afmzn4j+oTxtNXD8DbbmXeygN8vi2PByelU12r+7Zcd0EvnrpmQKPzBHp7sfiBsY0EolEp4YxKaT4wOkkM86N/XBAvr9jP5qPFbM0t4RFDWzK1fwz/2ZKHj5e1mfmkJS7pG8lrqw6yet9JLu4bSVVtHbmnKrhyUDyX9Y/m+a/2khjmS58IP5RSjOsbyYLNx7jvkj7mg/DGbQ2ZcWrr6jlUVI7dajHNqmfLyOQwXlq+v1nEopPTTVJXtMQDE9NYuDWP3368lbk3XsA7aw/jsFkY5ebF05QB8UEcK67g1VuGkhjmxxWD4tA0rV0JMZPCfLllVBJvrD7Igi151NVr/O3GwWTGBjYr+7vLM1l38BR/NF7eF6dHmD5DLTE2TRf4lu8p5KpBcby64gAD4oMYauQAtFgUMwbG8s/l+9lrTB7GpukaCFefoJ9fmsq23NMoZWhEjd/y+IxIhvUOZeFW3e/KNeeWOywWxT9vuoD/7jjBHxfuZGxaBJcPaPycXZIRybTsWG4ZldRIOHaHl9XCH65smBCkRwdw/dAE5q08SEl5DY/PyGpkPnllxQGyYgMZkRzGlztOEB/iYyadBX1A/u1lGdz86lreWHWITzblMj4jkhDDIX7msF688FUOj366nWW7C7hlVBJvfnuID9bncriojKhAh5mYu6n5f1jvUEJ8vfh823FCfO2cOF3Fw1P1ezy5XwyPLdjB80tyKKuuY1BCMH0i/IkN0s3UzmAA/Z43nqA15fIBMew+Xsrflu1leU4BBaVVXD4ghq25Jfzmoy0MTgzBZrGYQj/AjIGxPL8khyAfLy43xr1gX7sp3EQHeTMsKZQPN+jR99MC+i1HAAActElEQVSyY8174orDZuWTu0ez63gpS3aeICsuyLz/wb5205dsXHokccE+/OXLPca90bV0t45O4toh8Y36rCWuGxLPhxt0n9GrB8ez4fApfnxRMjMGxvLOWj1Bw7TsWNYfOsX8Tcc4ZWhg0120eu3h5pFJFJ6p5vDJMn57Wd9Gx7LjdYEvPtTHFORuH9Ob28b0divYuVMgNCXC34Gf3Wr6hGmaxq7jpUxxmYRHBDiYd8tQrvr7KkYkh7X5nDTFGbC26XCx6V7iqiHsah8+gBuHJbDu0KlGOQnr6zVOV+pRuq5EBnqz7pEJrV4zLlh/x/QO92NoUghXDIpFKUVkoMMM/mualsXLpb+8bJZGa7B/k1PYyN/x0MlyhvVumJS4w2Gz8ui0TFOz6GSQET389Z4CpvSPMc35aVEB5OSfoaxadymoqdPMlaK6Gz1W4PvPlgZzbkfxsVt5bHpmo1QJNquF64zZ8amyah79dDt7889wrLiC0qpaJma5H9DPJaP23Ren8OLSHLYcLSE5wo8Zhmno4vRIfO1WLkqNaHfUz/DkUHztVpbsOsHFfSM5UqQns0wO9yM9KoALU8MZnRJutnP2yETq6zXuGpfi9nw2q8WMWjpXRiSHMXfZPtYfOmUm1XTlTFVNuwb3QG8vfjctk3ve3shFzywFdO1Ae2ZTcyb15cGJ6Y36p719pZTiselZzBzWi79+mcPgxGCmDnA/0Qjzd7D0wXGUV9eiaD5LdEdmTCARAQ5eWXGATzcfY39hGc/fMKhR+64YFMfcZfvILa7gN5f1ddt2pZRp7m66/+HLMvjRy2v4zZS+jZylW/ufJ2VFMykr2q1gHOjtxQs3DGrzPC3x+xlZRAU6eH5JDhsOn2LBvWMI8Pbi8Mlyfv/ZDvzsVt65cwQr9hYyy8WX08mFqeGMTA7jT1/soq5eM018oPuOjs+I4ssdJwjwtvHAxDQOF5Xz8cajnKmsZfrAuBbzl9msFj2VzNbjOGwWfLysXJqha5Cjg7wZnBDMZ0agxKBeISiluCgtgne/O0JaVPufE6UUD05KZ0xqOHM+2MxVg+N4+uoBrD1QxI0vr+HgyXJmDU9oZFbzslr48K5ReFlVi+2fPjDW1PLe3IK/mPP6GTGBZMS0PBmxWhSzRiSYfoCphsCilGqXsAeYZuC/L9tHZIA3tfUaY1LC6RsdyJiUcA4XlTM4IcTMY7btWAkbDxdzxaDmwQ1t8cCENLf7nS/uJBdta0fz1ymlSAzzM33Cjp+upLi8ptn9TI0KYPmci89J4+OcgJdW1RLqpwtf4a4avoDvR+AbnRLOdUPiTSuXO4J97Xh7WbjmgngKSqtYvqeA+noNi0VRWlWLpjVPMN0aTX347DYL7/90lHk8KtDbTHPTNC2L04cP9PV0cwxz7qzhiXyTU8jaA0VMy46lsqaOYyUVrUboOrl5ZFKzfTarhTEp4Xy9pwBN00z/vdQof9iqJ1x2/o5Fw9fJXNY/hpF9wto1G2sPVw6Kb/HYxKwoHv10O//dcZxjxRX42q2MbkVrd7ZM7hfdzDwL+o/mvTtHEnkWqnuHTW/b0l36j3J/QUNUklKKN29vvKbfkKRQhiR1XGhujSFJIdgsitX7T7oV+Eora4lu52x1av8Y8i6rxGpRjEkNN19C7aGjy9v0jQ7kHzdd0GY5u82C3db+DPhKKS7rF80b3x6iutaPW0cnNdIUgD6L7BcXSFlVHVP6tazVbonsXsGs/38T2iXsuWtfZ2OzWvj5pWlk9wrm1nnf8cmmY/xoRCILtuhO7nabhRte+pbq2nomZjZ/NpRS/HpKX67420rC/e3Nflezhifw5Y4T3DIqiUBvL64eHG8GM03IbN0FYEq/GP697ijvrz/K1P4xjXJqTekXw4bDxYT4epkvjp+O7UN6dMA55UUbkRzG8jkXNwrimTm0Fx9tzOUnF/VpVr41rYuzfY9+sp2suCAGxAe3WrY9XDekF89+uYehSaHnJCQppbj3klRufnUtjy/YjsNmMX0c/zZrMFU1dVgsyhSUPt6gB1QNSey8McmZc601AeZc6B3uZ2qTdpoBG80FaHda1vaQEOqLRUG91pD+yanhc9gsBPp8P6/vlEh/nr4mu9Uyt45O4vIBMYQZS69V1dZTcKaKqEBvM5NCU5NuazT14WuKq/naKRza3Wj47FZFXb1GgMPG+AxdYfLdQV3gO1JUjqY1FvzPlrFpEXy+7Tg78k6Ta0ToOldAKa+qM826IvB1Mi1pWL4PYoJ8yI4PYtG24xw/XcnYtPZr3DqKO41NW0zM1LUbW46WmCaHtvwWvk987TayewXrATDo5g99aR39HpZW1pIa2b6folKq3ab6nsSj07J4aEpGqwPFK7MbIojPhXMR9r5vxqVFkBkTyNtrDjNreAKfbjrGkMQQHpyUzqyX1xDs62WatpsysFcw941PJS7Yu9GgD/rA/M+bLjBTyIzPiCTQ20ZNndamC8ColDACHDZKq2qZ3iSNxuR+0Ty5cCeDEkJMIS0p3I9bw3u7O1W7aCpQ/+HK/vxiQto5mexC/ew8e/3ARgFFHSHc38Ers4eeszsH6NrYgb2C2XSkmAtTw82xM8jHCwyhINzfQWSAw9SeOoXCziDM38EfruzP8OTOndgmhvmyaPtxauvq2ZarC3zpLq4HHcVusxAX4sORogrCTIFP/44K9O7S9Vm9vawNaZwMAerQyXJd4Guyjm578LPbsFqUGTTZFFf/4ZbSskCDP19KlD9eVn1y4fQNPWj4W3bkXTgxK5rHF+zglRUHCDW0nL2MdYLLq2sbBL5uatLtfm+AbsrErGg2Hy3hxOmqFs253YUJmVHYLIqFW/M4UFhGuL/9rGZb3wcjkkPZcrSEM1W1/PL9zUx8drl5rLSypt0mIk/FYlFtzgqjAr0bJT/1BJRS3DA8gR15p3l//VF2nyhlWnYsI5LDeG7mQB6fntWqFv+BCWlcP7S5T6LTJO0ULry9rMyZ3FdPHdLGYOywWZmQFUWwrxdj0xtrDnuF+nLvJSmNcqZ1NhaL6pB/1rTsWDNfXGdwUVpEq3nL2kIpxf3j9XRNrVlGMmMDqa6rJzrQ2zTtdRY3Dk/osGtKU5KM1CyHi8p5f/0RLkgMOSu/w/ZeAzBNuv4OGw6bpd0WkfNBYqgzgEVXLjgFvrN559w4PIHXbx3W4rPp+jw4mph0Gwdt6NtOy8+wpFB2nyiluLzabF9SO0y6LRHqZ+eGYQl8sukYaw8WER/ii6+x7nt5dR3lhsDnyXn4fhBMMoQ8q0VxSXr3FviCfe2MTgln4bY89heWdUiF3VmMTA43k1R/tCGXQyfLqTSSVZZW1uLfDl83wTOZMTAWHy+rES2uu2sAXD4g1vRn7QxuGpHYKEVJazw2PYsF94xpln8N4JcT003NodA+xqVH8H83D2kWYeuKMxn5BUkhXaq9ai9OTdE/v97PkaKKRgE2nYVT0HZq9pRSxIX4EB/auQJxR4gN9sGiGtKmFFfoEbJnI/BFBDhaDUx0Nek6mkTpuvrwOQU+p5n1wrQINA3mrTzIgcIygny8zkrz6I4fX9Qbi4ItR0uIC/bBz3D5cPXh8+SVNn4QpEQGkB4VwOiU8FZz+HQXpvaP4UhRBRsOnerQ7LyzuCAxBC+r4qtd+ebgVVBaRVVtPbX1WruCGwTPJNDbi2nZMVTU1DE6JbxNP7Xz1aaOmDGFxiilmJAZ5TZK34kz6n1oJ5pzv0+cmqL31h0hKcy3WeqszrmGU8PXIKS8fPMQfjOl5byX5xu7zUJssI+ZoqbBpNt570lXDV9rJl2n8OeMiB7YK5jp2bH8fdk+Vu072SmuTTFBPlw9WPf5jw/xMS0zriZdT15L9wfDW3cM5/mZA7u6Ge1iQmYUViMhZO9O8ufpCD52KyP7hNMvLpDHp/cD9LVtTxtrMP7QTbo/dGYNT0QpmiUpFn44jEkJZ0JmFJPPISipK4gIcJimu9svTD5n39rWGJoUSoC3rVle0O4wKXIlMaxhrfNzMem2RaOgDUPQc957V21aUw0fwP+7PBMfI4VOR8y5rvxkbB9sFkVKpL/ZjkZRut1Uw9c9xdBuSnd7yFojxM/OqD5hfJNTaGYt72pevnkIgLlAe2FplTkoBIqG7wdNdq9glj04rtMjKYWeQ7CvvgJMT8GZmuV4SQXXDG45y0NH6B8fxNbHJn0v5+5MEkL9WGSsiVxSUYPdZulUs6ZrBLwzSrdPhD9/uS670VKpXlYL/g4bMS6+zhEBDh6+LINffbjFbSL0c6F3uB9f/XIcUUEOvKwW7FYLZdW1lFfrqd0kSlc470zPjuWbnMJGs52upGlCz4IzVeaDLCZdobMGY0E4XzwyNQNN674v+PNFYpgvRWXVlFbWUFLePOlyRwlw6EthVtfVm0FcSimuaiJoRwU6sFmDm/mAXjsknqraujYTop8NCS7aQl+HlYrqOiolD5/QVVxjLEGW3MnRaR3FmWKgsFQfIAD8HWLSFQShZ9GZ+Vh7Mg2RuuWN1prtLJRSRAd5c7ykstVyf7p6AHX1mtv6N7lJptxZ+NltlFW5ROl2U5Ou+PB5MEqpTs0L1Vl4WS2E+HpRcKbSXN1ENHyCIAg9E2eA06YjxW7X0e0MIgMcbeYS9faythoY9H3hY7dSUVPb7VfaEIFP6BLC/R0UlFZRKgKfIAhCj6Z3uB/+DhuPzN/G6v0nOzVC10lUoLcZmdvd8LNbKTNW2lCKbttOecsKXUJEgIPCM9USpSsIgtDD8XPY+HrOOBbvPMHinflM7d/5kdZ3XpTsdgnS7oCPXffhq6iuw8fL2m3zSIrAJ3QJEQEONh4uNjV8/l2ghhcEQRA6hzB/B9cPTXC78k1n0C8uiH5xnbeCTGfiZ7dx/HQl5TV13XaVDRCTrtBFhPs7KDyjm3T97NbvJYeVIAiCIHzfODV8ldV13XaVDRCBT+giIgIclFfXcaK0Usy5giAIQo/Fz24z8vCJhk8QmhHur+fiO1BQJgEbgiAIQo/Fx241V9rorqtsgAh8QhfhTL58oFAEPkEQBKHn4ucwBL7qum6bkgVE4BO6iHAj+XJFTZ2YdAVBEIQei6/dRl29RklFjWj4BKEprusS+4uGTxAEQeihOP32TpZV4Wvvvu8zEfiELiHU144zVVGgCHyCIAhCD8Up8BWVVUuUriA0xWa1EOanm3XFpCsIgiD0VJxavXoNidIVBHc4I3UDJOmyIAiC0ENxFfIkaEMQ3OD045MoXUEQBKGn4uq3J0EbguCGCEPD5y8mXUEQBKGH4ucQDZ8gtEq4aPgEQRCEHo6rSVd8+ATBDU4Nnwh8giAIQk/F1aQrUbqC4AanD1+gmHQFQRCEHopo+AShDSZkRvHotEwyYwK7uimCIAiCcE78III2lFKhSqkvlVI5xneImzIDlVKrlVLblVJblFLXuxx7TSl1QCm1yfgM7Eh7hJ6Fn8PGraN7Y7Gorm6KIAiCIJwTdpsFm/Ee8+SgjYeAJZqmpQJLjL+bUg7crGlaFjAZ+KtSKtjl+BxN0wYan00dbI8gCIIgCMJ5xWnK9VgNHzADeN3Yfh24omkBTdP2aJqWY2wfA/KBiA5eVxAEQRAEoVvgNOt68lq6UZqm5QEY35GtFVZKDQPswD6X3U8apt5nlVKODrZHEARBEAThvOLr6P4avjZFUaXUYiDazaGHz+ZCSqkY4E1gtqZp9cbu3wDH0YXAl4BfA0+0UP9O4E6AhISEs7m0IAiCIAjC94Zp0u3GPnxtCnyapl3a0jGl1AmlVIymaXmGQJffQrlA4D/AI5qmfety7jxjs0opNQ94sJV2vIQuFDJkyBCtrXYLgiAIgiCcD5ym3O4s8HXUpPspMNvYng180rSAUsoOfAy8oWna+02OxRjfCt3/b1sH2yMIgiAIgnBe+SEEbfwJmKCUygEmGH+jlBqilHrZKHMdcBFwi5v0K/9SSm0FtgLhwP90sD2CIAiCIAjnFT+7DbvNgrUbpxnrUDiJpmkngfFu9q8D7jC23wLeaqH+JR25viAIgiAIQlfjY7d261U2oIMCnyAIgiAIwg+dqwbHkRbl39XNaBUR+ARBEARBEDrAqD7hjOoT3tXNaBVZS1cQBEEQBMHDEYFPEARBEATBwxGBTxAEQRAEwcMRgU8QBEEQBMHDEYFPEARBEATBwxGBTxAEQRAEwcMRgU8QBEEQBMHDEYFPEARBEATBwxGBTxAEQRAEwcMRgU8QBEEQBMHDEYFPEARBEATBwxGBTxAEQRAEwcMRgU8QBEEQBMHDUZqmdXUbzhqlVCmwu6vbIZwT4UBhVzdCOCek73ou0nc9F+m7no2z/xI1TYvoyobYuvLiHWC3pmlDuroRwtmjlFonfdczkb7ruUjf9Vyk73o23an/xKQrCIIgCILg4YjAJwiCIAiC4OH0VIHvpa5ugHDOSN/1XKTvei7Sdz0X6bueTbfpvx4ZtCEIgiAIgiC0n56q4RMEQRAEQRDaSacIfEqpXkqppUqpnUqp7Uqp+439oUqpL5VSOcZ3iLG/r1JqtVKqSin1YJNz3a+U2mac5+etXHOyUmq3UmqvUuohl/2vKaUOKKU2GZ+BLdS/x6irKaXCXfaPU0qVuNT/XUfvT3emm/XdNy73/ZhSan4L9f9l1N+mlHpVKeXlcmycUX+7Uurrjt6f7kwX9d2rSql8pdS2JvvdXtNN/d5KqTVGufeUUnZj/7Mufb9HKVXc0fvTnelmffeMUmqXUmqLUupjpVRwC/WvNa5Rr5Qa4rJ/lkvfbTKOux13PYFz6LtZxr3dopRapZTKdjmX27HQzTVnG+fNUUrNdtn/hVJqs9GOfyilrC3Ub2nMbXEs9US6Wd8tM+o7n5vIFuo/qZQ6opQ602T/A0qpHUbbliilEtu8AZqmdfgDxACDje0AYA+QCTwNPGTsfwh4ytiOBIYCTwIPupynH7AN8EVPGbMYSHVzPSuwD0gG7MBmINM49hpwTTvaPAhIAg4C4S77xwGfdcZ96Qmf7tR3Tcp9CNzcQpsvA5TxeQe4y9gfDOwAEpxt7er760l9Z5S9CBgMbGuy3+013dT/NzDT2P6Hs++alLkXeLWr7+8PqO8mAjZj+6lW+i4DSAeWAUNaKNMf2N/V97eb9d0oIMTYngKsMbbbOxaGAvuN7xBj23m+QONboY+ZM93Ub+196XYs9dRPN+u7Fp+jJucYYbT7TJP9FwO+xvZdwHttnatTNHyapuVpmrbB2C4FdgJxwAzgdaPY68AVRpl8TdO+A2qanCoD+FbTtHJN02qBr4Er3VxyGLBX07T9mqZVA+8a1zqbNm/UNO3g2dTxRLpj3ymlAoBLALcaPk3TFmoGwFog3jh0I/CRpmmHnW1t523okXRB36Fp2nKgyM0ht9d0RSml0Pv1g9bKATegv3w8lu7Ud5qm/deoC/AtDc9T03I7NU1rK+G99J2Oa9+t0jTtlLHf9f629z02CfhS07Qi4zxfApONc582ytjQBQ93TvktXqeVsdQj6U59dxZt/lbTtDw3+5dqmlbupm0t0uk+fEqpJHTt2RogytlQ49utytKFbcBFSqkwpZQv+uyjl5tyccARl7+PGvucPGmoOZ9VSjnO4d8YaajJP1dKZZ1D/R5JN+k70F9YS1wGs5ba6wXcBHxh7EoDQgxV+Xql1M1ttNljOE991xrtuWYYUOwiXDTre8Ms0Rv46iyv32PpBn3nym3A5x2ofz0eLvC5cg59dzsN97c9Y2Gb5ZRSi4B8oJSGyVS76xvnaDqWejzdoe+AeYY59/8ZE+JzxbVtLdKpK20opfzR1co/1zTt9Nm2X9O0nUqpp9Cl4DPoatJaN0Xdndg5s/kNcBx9tvMS8GvgibNoxgb0JVDOKKUuQ9cypZ5F/R5JN+k7JzcAL7fjsnOB5ZqmfWP8bQMuAMYDPsBqpdS3mqbtace5eiznse86Snv6fibwgaZpdd/D9bsd3anvlFIPG3X/dY71hwPlmqZta7OwB3C2faeUuhj9xTzGuctNMXcaulbLaZo2SSnljd5vl6D/Ftpd36DpWOrRdJO+m6VpWq5h0foQXeB+ox3Nb9q2HwFDgLFtle00DZ8xQ/gQ+JemaR8Zu08opWKM4zHos5BW0TTtFU3TBmuadhG6+SHHcLR0Ojb+FF1Kdp3FxgPHjPp5hoa6CpiHrnpFKbXIqN+qIKFp2mlN084Y2wsBL+US1OGJdJe+M64Vht5n/3HZ16zvlFKPAhHAAy7nOgp8oWlamaZphcByIBsP5jz3XWu4vWaTvisEgpVSzolmo743mMkPREPUjfoOw5n8cvSXkGbsc2ofFrbzX5K+a6HvlFID0CexMzRNO2nsdjsWKqWGu/Td9JbKubZH07RK4FNgxjmMue7GUo+lu/Sdpmm5xncp8DYwTClldanfpqJKKXUp8DAw3ZB5WkfrHEdIhS6Z/rXJ/mdo7Aj5dJPjj+HigGzsizS+E4BdGA6OTcrY0J0fe9PgMJllHItxadNfgT+10faDNA7aiKYhP+Ew4LDzb0/8dKe+M47/FHi9jTbfAawCfJrszwCWGNfwRTd39evqe+wpfedSNonmjv+tXtOl3Ps0Dtr4mcuxdON59NjnrZv23WT0YKeIdrZ9GU2czdGVB0eB5K6+t92t74x+2QuMalK+1bHQpVwocADd6T/E2A4F/Gl439mA94B73NRv7X3pdiz11E836jsbhtwBeKGb4n/aRtubBm0MQg8ccRuk5fYcnXQTx6CrKbcAm4zPZeg+O0uAHOM71CgfbQwOp4FiY9sZbfSNMfhsBsa3cs3L0CNs9gEPu+z/CtiK/rJ/C/Bvof59xnVr0SXul4399wDbjet/27SjPe3TnfrOOLYMmNxGm2uNus72/s7l2ByjDdvQ1fVdfo89rO/eAfLQgweOArcb+91e0039ZHTn8L3owp/D5dhjtDFB85RPN+u7veh+Rs52/KOF+lca9aqAE8Ail2Pj0INHuvzedsO+exk45VJ2ncu5WhwLm1zzNqOf9gK3GvuigO+MdmwHXsCItnZTv6X3ZYtjqSd+ulHf+QHrXfruOcDaQv2njeeu3vh+zNi/2HgOnW37tK3/X1baEARBEARB8HBkpQ1BEARBEAQPRwQ+QRAEQRAED0cEPkEQBEEQBA9HBD5BEARBEAQPRwQ+QRAEQRAED0cEPkEQPBqlVJ2RyHS7sWTiA0qpVsc+pVSSUurG89VGQRCE7xsR+ARB8HQqNE0bqGlaFjABPX/Wo23USQJE4BMEwWOQPHyCIHg0Sqkzmqb5u/ydjJ6wNhxIBN5ET4QK+koFq5RS36Kv3HIAeB14HvgTeoJhB/A3TdP+ed7+CUEQhA4iAp8gCB5NU4HP2HcK6AuUAvWaplUqpVKBdzRNG6KUGoe+hNnlRvk70Zcw+x+llANYCVyradqB8/rPCIIgnCO2tosIgiB4HMr49gJeVEoNBOqAtBbKTwQGKKWuMf4OAlLRNYCCIAjdHhH4BEH4QWGYdOuAfHRfvhNANrpPc2VL1YB7NU1bdF4aKQiC0MlI0IYgCD8YlFIRwD+AFzXdnyUIyNM0rR64CbAaRUuBAJeqi4C7lFJexnnSlFJ+CIIg9BBEwycIgqfjo5TahG6+rUUP0viLcWwu8KFS6lpgKVBm7N8C1CqlNgOvAc+hR+5uUEopoAC44nz9A4IgCB1FgjYEQRAEQRA8HDHpCoIgCIIgeDgi8AmCIAiCIHg4IvAJgiAIgiB4OCLwCYIgCIIgeDgi8AmCIAiCIHg4IvAJgiAIgiB4OCLwCYIgCIIgeDgi8AmCIAiCIHg4/x/lN283xg4IPQAAAABJRU5ErkJggg==\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": "markdown",
   "metadata": {},
   "source": [
    "In the first graph, I plot the different side of position into red (Two-Asset Option) and blue (Two Stocks). In the second graph, we draw out the curve of the difference, which refers to the Total PnL. It is apparent that, although from march, the PnL becomes volatile(because the market is volatile due to the COVID-19), before that time, the PnL is close to zero. The PnL refers to the difference between Long and Short Position. If we Long Two-Asset options and Short with Stocks, we should use simulated delta to hedge it. To test the comparative accuracy of Delta and Two-Asset Option simulation results, we use PnL to find the difference of opposite positions. The conclusion is our Pricing Model is proved to be accurate in this stock."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}