LSMC.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# American Put numerical Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we implemente the Least Square Monte Carlo alagorithm described in Longstaff, Francis, Eduardo (2001).\n",
    "\n",
    "We provide examples in pricing American style put options, with an underlying whose price process follows a geometric brownian motion.\n",
    "\n",
    "We first show a sample optimal stopping decision making process. We then use the algorithm to compute the price for a made-up sample put option as discussed in Moreno, Manuel, Javier (2003). We get slightly different result due to the difference in availbale execution dates setting.\n",
    "\n",
    "We also try to use the algorithm to price March 2020 S&P 500 at the money American put option, which is most traded in the current market. Simulation result shows consistency with the market traded price of this option.\n",
    "\n",
    "We majorly focus on power polynomial with 1 and 2 terms, legendre polynomial with 2 terms. Our algorithm is easy to adapt to other basis functions and to including more terms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coding the algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.special import comb\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = 1\n",
    "n = 8\n",
    "r = 0.06\n",
    "sigma = 0.1\n",
    "T = 8\n",
    "r_daily = r / 365\n",
    "sigma_daily = sigma / 365**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set attributes for underlying price process simulation\n",
    "def initiate_path(npath = 8, s = 1, r = 0.06, sigma = 0.1, T = 8, strike = 1.1):\n",
    "    \n",
    "    # first day\n",
    "    path = pd.DataFrame(np.zeros(npath)+s)\n",
    "    r_daily = r / 365\n",
    "    sigma_daily = sigma / 365**0.5\n",
    "    \n",
    "    # generate data day by day\n",
    "    for i in range(T):\n",
    "        day_index = path.shape[1] - 1\n",
    "        this_day = path.iloc[:,day_index]\n",
    "        next_day = this_day * np.exp(r_daily - sigma_daily**2 /2 + sigma_daily * np.random.normal(size = npath))\n",
    "        path = pd.concat([path,next_day], axis = 1)\n",
    "\n",
    "    # clean dataframe\n",
    "    path.columns = list(range(T+1))\n",
    "    path['pay_off_at_maturity'] = strike - path[T]\n",
    "    path['pay_off_at_maturity'] = path['pay_off_at_maturity'].apply(lambda x: max(x,0))\n",
    "    path['option value at maturity'] = path['pay_off_at_maturity']\n",
    "    path['executed on'] = T\n",
    "    return path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>pay_off_at_maturity</th>\n",
       "      <th>option value at maturity</th>\n",
       "      <th>executed on</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.991354</td>\n",
       "      <td>0.987061</td>\n",
       "      <td>0.984422</td>\n",
       "      <td>0.987900</td>\n",
       "      <td>0.984065</td>\n",
       "      <td>0.992569</td>\n",
       "      <td>0.995158</td>\n",
       "      <td>0.996598</td>\n",
       "      <td>0.103402</td>\n",
       "      <td>0.103402</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.001648</td>\n",
       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
       "      <td>1.014421</td>\n",
       "      <td>1.026246</td>\n",
       "      <td>1.023345</td>\n",
       "      <td>1.014924</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.011235</td>\n",
       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
       "      <td>0.992844</td>\n",
       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003065</td>\n",
       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
       "1  1.0  1.001648  1.011402  1.015786  1.012167  1.014421  1.026246  1.023345   \n",
       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.103402            8  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.092171            8  \n",
       "4  1.003804             0.096196                  0.096196            8  \n",
       "5  0.978821             0.121179                  0.121179            8  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.072115            8  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = initiate_path()\n",
    "path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg = LinearRegression()\n",
    "\n",
    "# functions to generate polynomial series for different basis\n",
    "# here we did power polynomial and legendre polynomial\n",
    "def polynomial_power(n, data):\n",
    "    result = data\n",
    "    if n == 1:\n",
    "        return result.values.reshape(-1, 1)\n",
    "    for i in range(2,n+1):\n",
    "        result = pd.concat([result,data**i], axis = 1)\n",
    "    return result\n",
    "\n",
    "def polynomial_legendre(n, data):\n",
    "    def term(n, x):\n",
    "        big_n = n//2\n",
    "        dn = 2**(-n)\n",
    "        fn = 0\n",
    "        for m in range(big_n+1):\n",
    "            cm = (-1)**m * comb(n,m) * comb(2*n-2*m, n)\n",
    "            gm = x**(n-2*m)\n",
    "            fn += cm*gm\n",
    "        fn *= dn\n",
    "        return fn\n",
    "        \n",
    "    result = data.apply(lambda x: term(1, x))\n",
    "    if n == 1:\n",
    "        return result.values.reshape(-1, 1)\n",
    "    for i in range(2,n+1):\n",
    "        new_col = data.apply(lambda x: term(i, x))\n",
    "        result = pd.concat([result,new_col], axis = 1)\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to work out execution path based on LSMC method\n",
    "# expecting basis and the number of terms to be specified\n",
    "def process_day_i(i, path = path,  basis = polynomial_power, n = 1, display = True, strike = 1.1):\n",
    "    \n",
    "    # function to compound execution value into future value on maturity day, for future comparison\n",
    "    def update_fv(row):\n",
    "        if row['if execute']:\n",
    "            return row['execution value'] * (1+r_daily)**(T-i)\n",
    "        else:\n",
    "            return row['option value at maturity']\n",
    "        \n",
    "    # fit OLS to model conditional expectation function\n",
    "    day_i = path[[i,'option value at maturity']]\n",
    "    day_i = day_i[day_i[i] < strike]\n",
    "    if day_i.shape[0]==0:\n",
    "        return \n",
    "    x_transform = basis(n=n, data = day_i[i])\n",
    "    # print('original \\n',day_i[i].iloc[:5,])\n",
    "    # print('transform \\n', x_transform.iloc[:5,])\n",
    "    reg.fit(x_transform, day_i['option value at maturity'])\n",
    "    if display:\n",
    "        print('\\n day', i, 'ITM path: ', list(day_i.index))\n",
    "        print('\\n conditional expectation function: ', 'intercept: ', reg.intercept_, 'coef: ', reg.coef_)\n",
    "    \n",
    "    # generate conditional expectation, make decision on whether to execute or continuue\n",
    "    day_i['expected continuation value'] = reg.predict(x_transform) * (1/(1+r_daily))\n",
    "    day_i['execution value'] = day_i[i].apply(lambda x: max(0,strike-x))\n",
    "    day_i['if execute'] = day_i['execution value'] > day_i['expected continuation value']\n",
    "    if display:\n",
    "        print('\\n choose to execute on these paths', (day_i[day_i['if execute']==True].index))\n",
    "    \n",
    "    # update execution day, option value, into main dataframe\n",
    "    day_i['updated option value at maturity'] = day_i.apply(update_fv, axis = 1)\n",
    "    path.loc[day_i.index,'option value at maturity'] = day_i['updated option value at maturity']\n",
    "    path.loc[day_i[day_i['if execute']==True].index,'executed on'] = i\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backword optimal stopping decision making example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " day 7 ITM path:  [0, 1, 2, 3, 4, 5, 6, 7]\n",
      "\n",
      " conditional expectation function:  intercept:  1.0939393878695778 coef:  [-0.9889866]\n",
      "\n",
      " choose to execute on these paths Int64Index([], dtype='int64')\n"
     ]
    },
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>pay_off_at_maturity</th>\n",
       "      <th>option value at maturity</th>\n",
       "      <th>executed on</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.991354</td>\n",
       "      <td>0.987061</td>\n",
       "      <td>0.984422</td>\n",
       "      <td>0.987900</td>\n",
       "      <td>0.984065</td>\n",
       "      <td>0.992569</td>\n",
       "      <td>0.995158</td>\n",
       "      <td>0.996598</td>\n",
       "      <td>0.103402</td>\n",
       "      <td>0.103402</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.001648</td>\n",
       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
       "      <td>1.014421</td>\n",
       "      <td>1.026246</td>\n",
       "      <td>1.023345</td>\n",
       "      <td>1.014924</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.011235</td>\n",
       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
       "      <td>0.992844</td>\n",
       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003065</td>\n",
       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
       "1  1.0  1.001648  1.011402  1.015786  1.012167  1.014421  1.026246  1.023345   \n",
       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.103402            8  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.092171            8  \n",
       "4  1.003804             0.096196                  0.096196            8  \n",
       "5  0.978821             0.121179                  0.121179            8  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.072115            8  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " day 6 ITM path:  [0, 1, 2, 3, 4, 5, 6, 7]\n",
      "\n",
      " conditional expectation function:  intercept:  0.9101236612017741 coef:  [-0.80858583]\n",
      "\n",
      " choose to execute on these paths Int64Index([5], dtype='int64')\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>pay_off_at_maturity</th>\n",
       "      <th>option value at maturity</th>\n",
       "      <th>executed on</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.991354</td>\n",
       "      <td>0.987061</td>\n",
       "      <td>0.984422</td>\n",
       "      <td>0.987900</td>\n",
       "      <td>0.984065</td>\n",
       "      <td>0.992569</td>\n",
       "      <td>0.995158</td>\n",
       "      <td>0.996598</td>\n",
       "      <td>0.103402</td>\n",
       "      <td>0.103402</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.001648</td>\n",
       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
       "      <td>1.014421</td>\n",
       "      <td>1.026246</td>\n",
       "      <td>1.023345</td>\n",
       "      <td>1.014924</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.011235</td>\n",
       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
       "      <td>0.992844</td>\n",
       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.115946</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003065</td>\n",
       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
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       "</table>\n",
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      ],
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       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
       "1  1.0  1.001648  1.011402  1.015786  1.012167  1.014421  1.026246  1.023345   \n",
       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.103402            8  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.092171            8  \n",
       "4  1.003804             0.096196                  0.096196            8  \n",
       "5  0.978821             0.121179                  0.115946            6  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.072115            8  "
      ]
     },
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    {
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     "output_type": "stream",
     "text": [
      "\n",
      " day 5 ITM path:  [0, 1, 2, 3, 4, 5, 6, 7]\n",
      "\n",
      " conditional expectation function:  intercept:  0.7392450315816508 coef:  [-0.6418829]\n",
      "\n",
      " choose to execute on these paths Int64Index([0, 3, 4, 5], dtype='int64')\n"
     ]
    },
    {
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       "      <th>2</th>\n",
       "      <th>3</th>\n",
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       "      <th>6</th>\n",
       "      <th>7</th>\n",
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       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.991354</td>\n",
       "      <td>0.987061</td>\n",
       "      <td>0.984422</td>\n",
       "      <td>0.987900</td>\n",
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       "      <td>0.996598</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.001648</td>\n",
       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
       "      <td>1.014421</td>\n",
       "      <td>1.026246</td>\n",
       "      <td>1.023345</td>\n",
       "      <td>1.014924</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>8</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.011235</td>\n",
       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
       "      <td>0.992844</td>\n",
       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.107209</td>\n",
       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.095493</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.112298</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003065</td>\n",
       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>8</td>\n",
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       "</table>\n",
       "</div>"
      ],
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       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
       "1  1.0  1.001648  1.011402  1.015786  1.012167  1.014421  1.026246  1.023345   \n",
       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.115993            5  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.107209            5  \n",
       "4  1.003804             0.096196                  0.095493            5  \n",
       "5  0.978821             0.121179                  0.112298            5  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.072115            8  "
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    {
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     "text": [
      "\n",
      " day 4 ITM path:  [0, 1, 2, 3, 4, 5, 6, 7]\n",
      "\n",
      " conditional expectation function:  intercept:  0.8735264619540146 coef:  [-0.77445644]\n",
      "\n",
      " choose to execute on these paths Int64Index([0, 3, 5, 7], dtype='int64')\n"
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    },
    {
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       "      <td>0.984065</td>\n",
       "      <td>0.992569</td>\n",
       "      <td>0.995158</td>\n",
       "      <td>0.996598</td>\n",
       "      <td>0.103402</td>\n",
       "      <td>0.112174</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.001648</td>\n",
       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
       "      <td>1.014421</td>\n",
       "      <td>1.026246</td>\n",
       "      <td>1.023345</td>\n",
       "      <td>1.014924</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.011235</td>\n",
       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
       "      <td>0.992844</td>\n",
       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.113046</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.095493</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.106570</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003065</td>\n",
       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.100104</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
       "1  1.0  1.001648  1.011402  1.015786  1.012167  1.014421  1.026246  1.023345   \n",
       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.112174            4  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.113046            4  \n",
       "4  1.003804             0.096196                  0.095493            5  \n",
       "5  0.978821             0.121179                  0.106570            4  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.100104            4  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " day 3 ITM path:  [0, 1, 2, 3, 4, 5, 6, 7]\n",
      "\n",
      " conditional expectation function:  intercept:  0.8772929086519928 coef:  [-0.77347466]\n",
      "\n",
      " choose to execute on these paths Int64Index([], dtype='int64')\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>pay_off_at_maturity</th>\n",
       "      <th>option value at maturity</th>\n",
       "      <th>executed on</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.991354</td>\n",
       "      <td>0.987061</td>\n",
       "      <td>0.984422</td>\n",
       "      <td>0.987900</td>\n",
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       "      <td>0.995158</td>\n",
       "      <td>0.996598</td>\n",
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       "      <td>0.112174</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.001648</td>\n",
       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
       "      <td>1.014421</td>\n",
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       "      <td>1.023345</td>\n",
       "      <td>1.014924</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>8</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.011235</td>\n",
       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
       "      <td>0.992844</td>\n",
       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.113046</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.095493</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.106570</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003065</td>\n",
       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.100104</td>\n",
       "      <td>4</td>\n",
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       "</table>\n",
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       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
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       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.112174            4  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.113046            4  \n",
       "4  1.003804             0.096196                  0.095493            5  \n",
       "5  0.978821             0.121179                  0.106570            4  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.100104            4  "
      ]
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    },
    {
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     "output_type": "stream",
     "text": [
      "\n",
      " day 2 ITM path:  [0, 1, 2, 3, 4, 5, 6, 7]\n",
      "\n",
      " conditional expectation function:  intercept:  0.8139963993645697 coef:  [-0.71047948]\n",
      "\n",
      " choose to execute on these paths Int64Index([0], dtype='int64')\n"
     ]
    },
    {
     "data": {
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       "      <th>6</th>\n",
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       "      <th>pay_off_at_maturity</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.991354</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.001648</td>\n",
       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
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       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
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       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
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       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.113046</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.095493</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.106570</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003065</td>\n",
       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.100104</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
       "1  1.0  1.001648  1.011402  1.015786  1.012167  1.014421  1.026246  1.023345   \n",
       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.113051            2  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.113046            4  \n",
       "4  1.003804             0.096196                  0.095493            5  \n",
       "5  0.978821             0.121179                  0.106570            4  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.100104            4  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " day 1 ITM path:  [0, 1, 2, 3, 4, 5, 6, 7]\n",
      "\n",
      " conditional expectation function:  intercept:  0.7482760031941841 coef:  [-0.64824551]\n",
      "\n",
      " choose to execute on these paths Int64Index([0, 3, 5], dtype='int64')\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>pay_off_at_maturity</th>\n",
       "      <th>option value at maturity</th>\n",
       "      <th>executed on</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.991354</td>\n",
       "      <td>0.987061</td>\n",
       "      <td>0.984422</td>\n",
       "      <td>0.987900</td>\n",
       "      <td>0.984065</td>\n",
       "      <td>0.992569</td>\n",
       "      <td>0.995158</td>\n",
       "      <td>0.996598</td>\n",
       "      <td>0.103402</td>\n",
       "      <td>0.108771</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.001648</td>\n",
       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
       "      <td>1.014421</td>\n",
       "      <td>1.026246</td>\n",
       "      <td>1.023345</td>\n",
       "      <td>1.014924</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>0.085076</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.011235</td>\n",
       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
       "      <td>0.992844</td>\n",
       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.102327</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.095493</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.105542</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003065</td>\n",
       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.100104</td>\n",
       "      <td>4</td>\n",
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       "</div>"
      ],
      "text/plain": [
       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
       "1  1.0  1.001648  1.011402  1.015786  1.012167  1.014421  1.026246  1.023345   \n",
       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.108771            1  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.102327            1  \n",
       "4  1.003804             0.096196                  0.095493            5  \n",
       "5  0.978821             0.121179                  0.105542            1  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.100104            4  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make decision on full path\n",
    "for day_i in range(T-1,0,-1):\n",
    "    process_day_i(day_i)\n",
    "    display(path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>0</th>\n",
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       "      <td>0.987061</td>\n",
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       "      <td>1.011402</td>\n",
       "      <td>1.015786</td>\n",
       "      <td>1.012167</td>\n",
       "      <td>1.014421</td>\n",
       "      <td>1.026246</td>\n",
       "      <td>1.023345</td>\n",
       "      <td>1.014924</td>\n",
       "      <td>0.085076</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.011235</td>\n",
       "      <td>1.020061</td>\n",
       "      <td>1.012158</td>\n",
       "      <td>1.007627</td>\n",
       "      <td>1.011172</td>\n",
       "      <td>1.006574</td>\n",
       "      <td>1.004922</td>\n",
       "      <td>0.994782</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>0.105218</td>\n",
       "      <td>8</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.997791</td>\n",
       "      <td>0.997359</td>\n",
       "      <td>0.991687</td>\n",
       "      <td>0.987028</td>\n",
       "      <td>0.992844</td>\n",
       "      <td>0.998920</td>\n",
       "      <td>1.009306</td>\n",
       "      <td>1.007829</td>\n",
       "      <td>0.092171</td>\n",
       "      <td>0.102327</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.003945</td>\n",
       "      <td>1.011428</td>\n",
       "      <td>1.017763</td>\n",
       "      <td>1.010067</td>\n",
       "      <td>1.004554</td>\n",
       "      <td>1.005879</td>\n",
       "      <td>1.009486</td>\n",
       "      <td>1.003804</td>\n",
       "      <td>0.096196</td>\n",
       "      <td>0.095493</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.994579</td>\n",
       "      <td>0.998988</td>\n",
       "      <td>0.994572</td>\n",
       "      <td>0.993500</td>\n",
       "      <td>0.987758</td>\n",
       "      <td>0.984092</td>\n",
       "      <td>0.986628</td>\n",
       "      <td>0.978821</td>\n",
       "      <td>0.121179</td>\n",
       "      <td>0.105542</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000465</td>\n",
       "      <td>1.012071</td>\n",
       "      <td>1.022378</td>\n",
       "      <td>1.027729</td>\n",
       "      <td>1.033585</td>\n",
       "      <td>1.032208</td>\n",
       "      <td>1.027781</td>\n",
       "      <td>1.020960</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>0.079040</td>\n",
       "      <td>8</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
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       "      <td>1.005846</td>\n",
       "      <td>1.004966</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.017923</td>\n",
       "      <td>1.025125</td>\n",
       "      <td>1.029549</td>\n",
       "      <td>1.027885</td>\n",
       "      <td>0.072115</td>\n",
       "      <td>0.100104</td>\n",
       "      <td>4</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0         1         2         3         4         5         6         7  \\\n",
       "0  1.0  0.991354  0.987061  0.984422  0.987900  0.984065  0.992569  0.995158   \n",
       "1  1.0  1.001648  1.011402  1.015786  1.012167  1.014421  1.026246  1.023345   \n",
       "2  1.0  1.011235  1.020061  1.012158  1.007627  1.011172  1.006574  1.004922   \n",
       "3  1.0  0.997791  0.997359  0.991687  0.987028  0.992844  0.998920  1.009306   \n",
       "4  1.0  1.003945  1.011428  1.017763  1.010067  1.004554  1.005879  1.009486   \n",
       "5  1.0  0.994579  0.998988  0.994572  0.993500  0.987758  0.984092  0.986628   \n",
       "6  1.0  1.000465  1.012071  1.022378  1.027729  1.033585  1.032208  1.027781   \n",
       "7  1.0  1.003065  1.005846  1.004966  0.999962  1.017923  1.025125  1.029549   \n",
       "\n",
       "          8  pay_off_at_maturity  option value at maturity  executed on  \n",
       "0  0.996598             0.103402                  0.108771            1  \n",
       "1  1.014924             0.085076                  0.085076            8  \n",
       "2  0.994782             0.105218                  0.105218            8  \n",
       "3  1.007829             0.092171                  0.102327            1  \n",
       "4  1.003804             0.096196                  0.095493            5  \n",
       "5  0.978821             0.121179                  0.105542            1  \n",
       "6  1.020960             0.079040                  0.079040            8  \n",
       "7  1.027885             0.072115                  0.100104            4  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated price under default setting:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.09756799239313535"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# option value on day 0\n",
    "print('Simulated price under default setting:')\n",
    "path['option value at maturity'].mean() * (1+r_daily)**(-T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# wrap the whole process into a function, output option price\n",
    "def american_option_price(basis = polynomial_power, n = 1, display = False,\n",
    "                         npath = 1000, s = 1, r = 0.06, sigma = 0.1, T =100, strike = 1.1):\n",
    "    path = initiate_path(npath = npath,\n",
    "                         s = s, r = r, sigma = sigma, T = T, strike = strike)\n",
    "    r_daily = r / 365\n",
    "    T = path.shape[1]-4\n",
    "    for day_i in range(T-1,0,-1):\n",
    "        process_day_i(i = day_i, path = path, basis = basis, n = n, strike = strike,\n",
    "                      display = False)\n",
    "        path['option value at maturity'].mean() * (1+r_daily)**(-T)\n",
    "    if display:\n",
    "        display(path)\n",
    "    return (path['option value at maturity'].mean() * (1+r_daily)**(-T))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pricing examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 1 term power polynomial baisis:\n",
      "$ 0.05\n"
     ]
    }
   ],
   "source": [
    "# power polynomial with 1 term\n",
    "p = american_option_price(basis = polynomial_power, n = 1, strike = 1.05)\n",
    "print('Option price using 1 term power polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 2 term power polynomial baisis:\n",
      "$ 0.05\n"
     ]
    }
   ],
   "source": [
    "# power polynomial with 2 term\n",
    "p = american_option_price(basis = polynomial_power, n = 2, strike = 1.05)\n",
    "print('Option price using 2 term power polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 2 term legendre polynomial baisis:\n",
      "$ 0.05\n"
     ]
    }
   ],
   "source": [
    "# legendre polynomial\n",
    "# legendre polynomial with 1 term is just x itself, so we skip it\n",
    "p = american_option_price(basis = polynomial_legendre, n = 2, strike = 1.05)\n",
    "print('Option price using 2 term legendre polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pricing examples, compared with Moreno, Manuel, Javier (2003)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting: ATM American put, with strike price of $40, maturing in 1 year, risk free rate 0.06, sigma 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 1 term power polynomial baisis:\n",
      "$ 2.17\n"
     ]
    }
   ],
   "source": [
    "# power polynomial with 1 term\n",
    "p = american_option_price(basis = polynomial_power, n = 1, display = False,\n",
    "                         npath = 1000, s = 40, r = 0.06, sigma = 0.2, T =365, strike = 40)\n",
    "print('Option price using 1 term power polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 2 term power polynomial baisis:\n",
      "$ 2.32\n"
     ]
    }
   ],
   "source": [
    "# power polynomial with 2 terms\n",
    "p = american_option_price(basis = polynomial_power, n = 2, display = False,\n",
    "                         npath = 1000, s = 40, r = 0.06, sigma = 0.2, T =365, strike = 40)\n",
    "print('Option price using 2 term power polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 2 term legendre polynomial baisis:\n",
      "$ 2.36\n"
     ]
    }
   ],
   "source": [
    "# legendre polynomial with 2 terms\n",
    "p = american_option_price(basis = polynomial_legendre, n = 2, display = False,\n",
    "                         npath = 1000, s = 40, r = 0.06, sigma = 0.2, T =365, strike = 40)\n",
    "print('Option price using 2 term legendre polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 48,
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 800
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='/Users/Simon-CWG/Pictures/Screenshot/Screen Shot 2020-02-29 at 9.02.00 PM.png',width=800, height=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In MMJ(2001), simulated price for these 3 kinds of basis are:\n",
    "2.09671, 2.26853, 2.26853\n",
    "\n",
    "We got slightly different result, partly due to the differences in setting. In their paper they assume there are 70 execution day throughout the year. Here we assume it can be executed everyday.\n",
    "\n",
    "Note that the result is not robust (small variation between simulations). Npath should be increased to improve robustness. However it is set as 1000 here for the sake of computation speed.\n",
    "\n",
    "The fact that our simulation prices are higher than MMJ's result can be expalined by option pricing intuition: more frequent execution days add value to American option. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pricing example, compared with market quotes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "S&P 500 American Put, with specifications as of Feb 29:\n",
    "    \n",
    "    maturing at: Mar 20, 2020\n",
    "    strike price: $2950\n",
    "currently trading at: $109\n",
    "\n",
    "current VIX index (used as implied vol): 40.11\n",
    "    \n",
    "Other market information needed:\n",
    "    \n",
    "    SPX latest close price: 2954.22\n",
    "    US 1 month bond yield: 1.47%\n",
    "\n",
    "(more info: https://www.cmegroup.com/trading/equity-index/us-index/e-mini-sandp500_quotes_globex_options.html?optionProductId=138&optionExpiration=138-H0#optionProductId=138&optionExpiration=138-H0&strikeRange=ATM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 1 term power polynomial baisis:\n",
      "$ 110.65\n"
     ]
    }
   ],
   "source": [
    "# Simulate using 1 term power polynomial\n",
    "p = american_option_price(basis = polynomial_power, n = 1, display = False,\n",
    "                         npath = 10000, s = 2954.22, r = 0.0147,\n",
    "                      sigma = 0.4011, T = 21, strike = 2950)\n",
    "print('Option price using 1 term power polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 2 term power polynomial baisis:\n",
      "$ 110.88\n"
     ]
    }
   ],
   "source": [
    "# Simulate using 2 term power polynomial\n",
    "p = american_option_price(basis = polynomial_power, n = 2, display = False,\n",
    "                         npath = 10000, s = 2954.22, r = 0.0147,\n",
    "                      sigma = 0.4011, T = 21, strike = 2950)\n",
    "print('Option price using 2 term power polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option price using 2 term legendre polynomial baisis:\n",
      "$ 108.39\n"
     ]
    }
   ],
   "source": [
    "# Simulate using 2 term power polynomial\n",
    "p = american_option_price(basis = polynomial_legendre, n = 2, display = False,\n",
    "                         npath = 10000, s = 2954.22, r = 0.0147,\n",
    "                      sigma = 0.4011, T = 21, strike = 2950)\n",
    "print('Option price using 2 term legendre polynomial baisis:')\n",
    "print('$', round(p,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulated results are close to market price ($109). However more path need to be used to generate more robust simulation results."
   ]
  }
 ],
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