option pricing archived.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Collect stock and option data, price with BSM, compare accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "from math import sqrt\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "from datetime import datetime, timezone, timedelta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1607040000\n",
      "2020-12-03 19:00:00\n"
     ]
    }
   ],
   "source": [
    "# get a UTC timestamp from a date. This is used to scrape data from Yahoo Finance.\n",
    "\n",
    "expiration_datetime = datetime(2020, 12, 4, 0, 0, tzinfo=timezone.utc)\n",
    "# expiration_datetime = datetime(2020, 12, 24, 0, 0, tzinfo=timezone.utc)\n",
    "# expiration_datetime = datetime(2021, 2, 19, 0, 0, tzinfo=timezone.utc)\n",
    "# expiration_datetime = datetime(2021, 6, 18, 0, 0, tzinfo=timezone.utc)\n",
    "\n",
    "expiration_timestamp = int(expiration_datetime.timestamp())\n",
    "\n",
    "print(expiration_timestamp)\n",
    "print(datetime.fromtimestamp(expiration_timestamp)) # this is in UTC, add 5 hours to this to get EST\n",
    "\n",
    "# feb 19 2021"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Download historical stock price data for TSLA. I get a past year's worth from (https://finance.yahoo.com/quote/TSLA/history?p=TSLA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Date        Open        High         Low       Close   Adj Close  \\\n",
      "0    2019-11-21   70.902000   72.167999   70.800003   70.966003   70.966003   \n",
      "1    2019-11-22   68.031998   68.199997   66.000000   66.608002   66.608002   \n",
      "2    2019-11-25   68.863998   68.914001   66.891998   67.267998   67.267998   \n",
      "3    2019-11-26   67.054001   67.099998   65.419998   65.783997   65.783997   \n",
      "4    2019-11-27   66.223999   66.786003   65.713997   66.258003   66.258003   \n",
      "..          ...         ...         ...         ...         ...         ...   \n",
      "248  2020-11-16  408.929993  412.450012  404.089996  408.089996  408.089996   \n",
      "249  2020-11-17  460.170013  462.000000  433.010010  441.609985  441.609985   \n",
      "250  2020-11-18  448.350006  496.000000  443.500000  486.640015  486.640015   \n",
      "251  2020-11-19  492.000000  508.609985  487.570007  499.269989  499.269989   \n",
      "252  2020-11-20  497.989990  502.500000  489.059998  489.609985  489.609985   \n",
      "\n",
      "       Volume  close_day_before   returns  \n",
      "0    30550000               NaN       NaN  \n",
      "1    84353000         70.966003 -0.061410  \n",
      "2    61697500         66.608002  0.009909  \n",
      "3    39737000         67.267998 -0.022061  \n",
      "4    27778000         65.783997  0.007205  \n",
      "..        ...               ...       ...  \n",
      "248  26838600        408.500000 -0.001004  \n",
      "249  61188300        408.089996  0.082139  \n",
      "250  78044000        441.609985  0.101968  \n",
      "251  62475300        486.640015  0.025953  \n",
      "252  32807300        499.269989 -0.019348  \n",
      "\n",
      "[253 rows x 9 columns]\n",
      "          Contract Name        Last Trade Date  Strike  Last Price     Bid  \\\n",
      "0   TSLA201204C00020000  2020-11-19 3:34PM EST    20.0      478.55  466.85   \n",
      "1   TSLA201204C00100000  2020-11-20 2:56PM EST   100.0      393.70  386.85   \n",
      "2   TSLA201204C00250000  2020-11-20 3:41PM EST   250.0      242.27  237.10   \n",
      "3   TSLA201204C00260000  2020-11-20 3:08PM EST   260.0      233.73  227.00   \n",
      "4   TSLA201204C00270000  2020-11-17 9:36AM EST   270.0      183.35  217.20   \n",
      "..                  ...                    ...     ...         ...     ...   \n",
      "95  TSLA201204C00850000  2020-11-20 3:38PM EST   850.0        0.39    0.20   \n",
      "96  TSLA201204C00875000  2020-11-20 3:25PM EST   875.0        0.34    0.15   \n",
      "97  TSLA201204C00900000  2020-11-20 3:39PM EST   900.0        0.28    0.20   \n",
      "98  TSLA201204C00925000  2020-11-20 3:53PM EST   925.0        0.12    0.12   \n",
      "99  TSLA201204C00950000  2020-11-20 3:59PM EST   950.0        0.09    0.08   \n",
      "\n",
      "       Ask  Change % Change  Volume Open Interest Implied Volatility  \n",
      "0   471.75    0.00        -       5             7            968.56%  \n",
      "1   391.75  393.70        -       5            10            451.76%  \n",
      "2   241.85   -9.48   -3.77%      18             4            205.23%  \n",
      "3   231.85   35.72  +18.04%       5             6            194.68%  \n",
      "4   221.90    0.00        -       3             9            185.33%  \n",
      "..     ...     ...      ...     ...           ...                ...  \n",
      "95    0.59    0.39        -      12             -            121.58%  \n",
      "96    0.48    0.34        -       3             -            123.63%  \n",
      "97    0.42    0.28        -      11             -            128.52%  \n",
      "98    0.15    0.12        -     152             -            122.27%  \n",
      "99    0.10    0.09        -     400             -            121.88%  \n",
      "\n",
      "[100 rows x 11 columns]\n"
     ]
    }
   ],
   "source": [
    "# download annual historical data for the stock\n",
    "\n",
    "ticker = 'TSLA'\n",
    "stock_price_path = \"~/documents/quant_finance/price_data/{}.csv\".format(ticker)\n",
    "df = pd.read_csv(stock_price_path)\n",
    "df = df.sort_values(by=\"Date\")\n",
    "df = df.dropna()\n",
    "\n",
    "# calculate returns\n",
    "df = df.assign(close_day_before=df['Adj Close'].shift(1))\n",
    "df['returns'] = ((df['Adj Close'] - df.close_day_before)/df.close_day_before)\n",
    "\n",
    "# get options data\n",
    "options_data_path = 'https://finance.yahoo.com/quote/{}/options?date={}&p={}'.format(ticker, expiration_timestamp, ticker)\n",
    "options_data = pd.read_html(options_data_path) # returns two dataframes, for calls and puts\n",
    "r = options_data[0]\n",
    "calls_df = options_data[1]\n",
    "\n",
    "print(df)\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>Date</th>\n",
       "      <th>1 mo</th>\n",
       "      <th>2 mo</th>\n",
       "      <th>3 mo</th>\n",
       "      <th>6 mo</th>\n",
       "      <th>1 yr</th>\n",
       "      <th>2 yr</th>\n",
       "      <th>3 yr</th>\n",
       "      <th>5 yr</th>\n",
       "      <th>7 yr</th>\n",
       "      <th>10 yr</th>\n",
       "      <th>20 yr</th>\n",
       "      <th>30 yr</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11/02/20</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.38</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.87</td>\n",
       "      <td>1.41</td>\n",
       "      <td>1.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11/03/20</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.90</td>\n",
       "      <td>1.44</td>\n",
       "      <td>1.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11/04/20</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.33</td>\n",
       "      <td>0.55</td>\n",
       "      <td>0.78</td>\n",
       "      <td>1.33</td>\n",
       "      <td>1.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11/05/20</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.33</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.79</td>\n",
       "      <td>1.32</td>\n",
       "      <td>1.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11/06/20</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.59</td>\n",
       "      <td>0.83</td>\n",
       "      <td>1.37</td>\n",
       "      <td>1.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>11/09/20</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.44</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.96</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>11/10/20</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.98</td>\n",
       "      <td>1.53</td>\n",
       "      <td>1.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>11/12/20</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.88</td>\n",
       "      <td>1.42</td>\n",
       "      <td>1.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>11/13/20</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.89</td>\n",
       "      <td>1.43</td>\n",
       "      <td>1.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>11/16/20</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.66</td>\n",
       "      <td>0.91</td>\n",
       "      <td>1.44</td>\n",
       "      <td>1.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11/17/20</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.87</td>\n",
       "      <td>1.40</td>\n",
       "      <td>1.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11/18/20</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.88</td>\n",
       "      <td>1.42</td>\n",
       "      <td>1.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>11/19/20</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.86</td>\n",
       "      <td>1.38</td>\n",
       "      <td>1.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>11/20/20</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.38</td>\n",
       "      <td>0.62</td>\n",
       "      <td>0.83</td>\n",
       "      <td>1.33</td>\n",
       "      <td>1.53</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date  1 mo  2 mo  3 mo  6 mo  1 yr  2 yr  3 yr  5 yr  7 yr  10 yr  \\\n",
       "0   11/02/20  0.09  0.09  0.09  0.11  0.13  0.16  0.20  0.38  0.63   0.87   \n",
       "1   11/03/20  0.09  0.10  0.10  0.12  0.14  0.17  0.21  0.39  0.65   0.90   \n",
       "2   11/04/20  0.08  0.09  0.10  0.10  0.12  0.14  0.18  0.33  0.55   0.78   \n",
       "3   11/05/20  0.09  0.10  0.10  0.10  0.12  0.14  0.18  0.33  0.56   0.79   \n",
       "4   11/06/20  0.10  0.10  0.10  0.11  0.12  0.16  0.21  0.36  0.59   0.83   \n",
       "5   11/09/20  0.10  0.10  0.11  0.11  0.12  0.17  0.25  0.44  0.70   0.96   \n",
       "6   11/10/20  0.09  0.09  0.10  0.11  0.12  0.19  0.26  0.46  0.72   0.98   \n",
       "7   11/12/20  0.10  0.11  0.10  0.10  0.13  0.17  0.23  0.40  0.64   0.88   \n",
       "8   11/13/20  0.10  0.09  0.09  0.10  0.12  0.17  0.23  0.41  0.65   0.89   \n",
       "9   11/16/20  0.09  0.10  0.09  0.12  0.12  0.19  0.24  0.41  0.66   0.91   \n",
       "10  11/17/20  0.08  0.08  0.09  0.10  0.12  0.18  0.22  0.39  0.63   0.87   \n",
       "11  11/18/20  0.07  0.09  0.09  0.10  0.11  0.16  0.22  0.40  0.64   0.88   \n",
       "12  11/19/20  0.08  0.08  0.07  0.10  0.11  0.18  0.22  0.39  0.63   0.86   \n",
       "13  11/20/20  0.09  0.09  0.07  0.10  0.11  0.16  0.21  0.38  0.62   0.83   \n",
       "\n",
       "    20 yr  30 yr  \n",
       "0    1.41   1.63  \n",
       "1    1.44   1.66  \n",
       "2    1.33   1.55  \n",
       "3    1.32   1.54  \n",
       "4    1.37   1.60  \n",
       "5    1.51   1.73  \n",
       "6    1.53   1.75  \n",
       "7    1.42   1.64  \n",
       "8    1.43   1.65  \n",
       "9    1.44   1.66  \n",
       "10   1.40   1.62  \n",
       "11   1.42   1.62  \n",
       "12   1.38   1.58  \n",
       "13   1.33   1.53  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get risk free rate data\n",
    "\n",
    "rfr_data_path = 'https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield'\n",
    "rfr_df = pd.read_html(rfr_data_path)[1] # returns two dataframes, for calls and puts\n",
    "rfr_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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      "/home/amao/miniconda3/envs/datasci/lib/python3.8/site-packages/pandas/plotting/_matplotlib/core.py:1235: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the rfr\n",
    "rfr_date = rfr_df.iloc[-1][0]\n",
    "\n",
    "cur_rfr = rfr_df.iloc[-1][1:].astype(float)\n",
    "cur_rfr.plot(title=\"Treasury Curve for {}\".format(rfr_date))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# BSM model\n",
    "\n",
    "# S is the spot price \n",
    "# K is the strike price \n",
    "# T is the fraction of days to strike date divided by 252 (stock market days)\n",
    "# r is the risk free rate\n",
    "# sigma is the annual volatility of the returns of the stock \n",
    "\n",
    "def black_scholes(S, K, T, r, sigma, option_type='call'):\n",
    "    \n",
    "    d1 = (np.log(S/K) + (r + sigma**2/2)*T)/(sigma * sqrt(T))\n",
    "    d2 = d1 - sigma * np.sqrt(T)\n",
    "    \n",
    "    if option_type=='call':\n",
    "        return S * norm.cdf(d1) - K*np.exp(-r*T) * norm.cdf(d2)\n",
    "    elif option_type=='put':\n",
    "        return K*np.exp(-r*T) * norm.cdf(-d2) - S * norm.cdf(-d1)\n",
    "    \n",
    "        \n",
    "# get the (num days to expiration) / (trading days in a year)\n",
    "def get_time_to_expiration(expiration_datetime_utc):\n",
    "    return (expiration_datetime_utc - datetime.now(timezone.utc)).days / 252\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.401407649076464\n"
     ]
    }
   ],
   "source": [
    "value_s = black_scholes(S = 69, \n",
    "                        K = 70, \n",
    "                        T = 6/12, \n",
    "                        r = .05, \n",
    "                        sigma = .35,\n",
    "                        option_type='put')\n",
    "print(value_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cur_stock_price: 489.60998499999994, time to expiration: 0.04365079365079365, rfr: 0.09, vol: 0.8815712722903746\n"
     ]
    }
   ],
   "source": [
    "# the rfr should vary with time, not be constant.\n",
    "\n",
    "cur_stock_price = df.iloc[-1]['Adj Close']\n",
    "time_to_expiration = get_time_to_expiration(expiration_datetime)\n",
    "risk_free_rate = 0.09\n",
    "\n",
    "# Calculate the volatility as the annualized standard deviation of the stock returns\n",
    "sigma = np.sqrt(252) * df['returns'].std()\n",
    "\n",
    "print('cur_stock_price: {}, time to expiration: {}, rfr: {}, vol: {}'.format(cur_stock_price, time_to_expiration, risk_free_rate, sigma))\n",
    "list_estimates = []\n",
    "\n",
    "strike_start_idx, strike_end_idx = 0, r.shape[0]\n",
    "# strike_start_idx, strike_end_idx = 0, 21\n",
    "\n",
    "# run BSM for different strikes\n",
    "for x in range(strike_start_idx,strike_end_idx):\n",
    "    value_s = black_scholes(S = cur_stock_price, \n",
    "                            K = r['Strike'][x], \n",
    "                            T = time_to_expiration, \n",
    "                            r = risk_free_rate, \n",
    "                            sigma = sigma)\n",
    "    list_estimates.append(value_s)\n",
    "    \n",
    "# merge the real and computed dataframes to compare results\n",
    "df_list = pd.DataFrame(data=list_estimates, index=r.index[strike_start_idx:strike_end_idx])\n",
    "df_list['estimate'] = df_list[0]\n",
    "del df_list[0]\n",
    "df_estimate = r.merge(df_list, right_index = True, left_index = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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>Contract Name</th>\n",
       "      <th>Last Trade Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Bid</th>\n",
       "      <th>Ask</th>\n",
       "      <th>Change</th>\n",
       "      <th>% Change</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Open Interest</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>estimate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>TSLA201204C00020000</td>\n",
       "      <td>2020-11-19 3:34PM EST</td>\n",
       "      <td>20.0</td>\n",
       "      <td>478.55</td>\n",
       "      <td>466.85</td>\n",
       "      <td>471.75</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>968.56%</td>\n",
       "      <td>469.688402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>TSLA201204C00100000</td>\n",
       "      <td>2020-11-20 2:56PM EST</td>\n",
       "      <td>100.0</td>\n",
       "      <td>393.70</td>\n",
       "      <td>386.85</td>\n",
       "      <td>391.75</td>\n",
       "      <td>393.70</td>\n",
       "      <td>-</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>451.76%</td>\n",
       "      <td>390.002071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>TSLA201204C00250000</td>\n",
       "      <td>2020-11-20 3:41PM EST</td>\n",
       "      <td>250.0</td>\n",
       "      <td>242.27</td>\n",
       "      <td>237.10</td>\n",
       "      <td>241.85</td>\n",
       "      <td>-9.48</td>\n",
       "      <td>-3.77%</td>\n",
       "      <td>18</td>\n",
       "      <td>4</td>\n",
       "      <td>205.23%</td>\n",
       "      <td>240.592077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>TSLA201204C00260000</td>\n",
       "      <td>2020-11-20 3:08PM EST</td>\n",
       "      <td>260.0</td>\n",
       "      <td>233.73</td>\n",
       "      <td>227.00</td>\n",
       "      <td>231.85</td>\n",
       "      <td>35.72</td>\n",
       "      <td>+18.04%</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>194.68%</td>\n",
       "      <td>230.633927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>TSLA201204C00270000</td>\n",
       "      <td>2020-11-17 9:36AM EST</td>\n",
       "      <td>270.0</td>\n",
       "      <td>183.35</td>\n",
       "      <td>217.20</td>\n",
       "      <td>221.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>185.33%</td>\n",
       "      <td>220.678747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>TSLA201204C00850000</td>\n",
       "      <td>2020-11-20 3:38PM EST</td>\n",
       "      <td>850.0</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.59</td>\n",
       "      <td>0.39</td>\n",
       "      <td>-</td>\n",
       "      <td>12</td>\n",
       "      <td>-</td>\n",
       "      <td>121.58%</td>\n",
       "      <td>0.049544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>TSLA201204C00875000</td>\n",
       "      <td>2020-11-20 3:25PM EST</td>\n",
       "      <td>875.0</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.48</td>\n",
       "      <td>0.34</td>\n",
       "      <td>-</td>\n",
       "      <td>3</td>\n",
       "      <td>-</td>\n",
       "      <td>123.63%</td>\n",
       "      <td>0.028620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>TSLA201204C00900000</td>\n",
       "      <td>2020-11-20 3:39PM EST</td>\n",
       "      <td>900.0</td>\n",
       "      <td>0.28</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.28</td>\n",
       "      <td>-</td>\n",
       "      <td>11</td>\n",
       "      <td>-</td>\n",
       "      <td>128.52%</td>\n",
       "      <td>0.016441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>TSLA201204C00925000</td>\n",
       "      <td>2020-11-20 3:53PM EST</td>\n",
       "      <td>925.0</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.12</td>\n",
       "      <td>-</td>\n",
       "      <td>152</td>\n",
       "      <td>-</td>\n",
       "      <td>122.27%</td>\n",
       "      <td>0.009400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>TSLA201204C00950000</td>\n",
       "      <td>2020-11-20 3:59PM EST</td>\n",
       "      <td>950.0</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-</td>\n",
       "      <td>400</td>\n",
       "      <td>-</td>\n",
       "      <td>121.88%</td>\n",
       "      <td>0.005351</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Contract Name        Last Trade Date  Strike  Last Price     Bid  \\\n",
       "0   TSLA201204C00020000  2020-11-19 3:34PM EST    20.0      478.55  466.85   \n",
       "1   TSLA201204C00100000  2020-11-20 2:56PM EST   100.0      393.70  386.85   \n",
       "2   TSLA201204C00250000  2020-11-20 3:41PM EST   250.0      242.27  237.10   \n",
       "3   TSLA201204C00260000  2020-11-20 3:08PM EST   260.0      233.73  227.00   \n",
       "4   TSLA201204C00270000  2020-11-17 9:36AM EST   270.0      183.35  217.20   \n",
       "..                  ...                    ...     ...         ...     ...   \n",
       "95  TSLA201204C00850000  2020-11-20 3:38PM EST   850.0        0.39    0.20   \n",
       "96  TSLA201204C00875000  2020-11-20 3:25PM EST   875.0        0.34    0.15   \n",
       "97  TSLA201204C00900000  2020-11-20 3:39PM EST   900.0        0.28    0.20   \n",
       "98  TSLA201204C00925000  2020-11-20 3:53PM EST   925.0        0.12    0.12   \n",
       "99  TSLA201204C00950000  2020-11-20 3:59PM EST   950.0        0.09    0.08   \n",
       "\n",
       "       Ask  Change % Change  Volume Open Interest Implied Volatility  \\\n",
       "0   471.75    0.00        -       5             7            968.56%   \n",
       "1   391.75  393.70        -       5            10            451.76%   \n",
       "2   241.85   -9.48   -3.77%      18             4            205.23%   \n",
       "3   231.85   35.72  +18.04%       5             6            194.68%   \n",
       "4   221.90    0.00        -       3             9            185.33%   \n",
       "..     ...     ...      ...     ...           ...                ...   \n",
       "95    0.59    0.39        -      12             -            121.58%   \n",
       "96    0.48    0.34        -       3             -            123.63%   \n",
       "97    0.42    0.28        -      11             -            128.52%   \n",
       "98    0.15    0.12        -     152             -            122.27%   \n",
       "99    0.10    0.09        -     400             -            121.88%   \n",
       "\n",
       "      estimate  \n",
       "0   469.688402  \n",
       "1   390.002071  \n",
       "2   240.592077  \n",
       "3   230.633927  \n",
       "4   220.678747  \n",
       "..         ...  \n",
       "95    0.049544  \n",
       "96    0.028620  \n",
       "97    0.016441  \n",
       "98    0.009400  \n",
       "99    0.005351  \n",
       "\n",
       "[100 rows x 12 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Computed v Market prices for TSLA, Expiry 2020-12-04'}, xlabel='Strike'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot option prices across strikes\n",
    "\n",
    "df_estimate.plot(x='Strike',y=['Last Price','estimate'], title='Computed v Market prices for {}, Expiry {}'.format(ticker, expiration_datetime.date()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count     100.000000\n",
      "mean       57.987969\n",
      "std       285.249215\n",
      "min       -40.895065\n",
      "25%       -30.012323\n",
      "50%        -7.212643\n",
      "75%         1.183640\n",
      "max      1603.008607\n",
      "Name: estimate_error, dtype: float64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/amao/miniconda3/envs/datasci/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_estimate['estimate_error'] = ((df_estimate['Last Price'] - df_estimate['estimate'])/df_estimate['estimate'])*100\n",
    "ax = sns.distplot(df_estimate['estimate_error'])\n",
    "print(df_estimate['estimate_error'].describe())\n",
    "\n",
    "# across strikes, the median error is 34%, but there is a huge spread and outliers, \n",
    "# which mainly seem to be due to the higher strikes being very close to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>Contract Name</th>\n",
       "      <th>Last Trade Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Bid</th>\n",
       "      <th>Ask</th>\n",
       "      <th>Change</th>\n",
       "      <th>% Change</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Open Interest</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>estimate</th>\n",
       "      <th>estimate_error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>TSLA201204C00020000</td>\n",
       "      <td>2020-11-19 3:34PM EST</td>\n",
       "      <td>20.0</td>\n",
       "      <td>478.55</td>\n",
       "      <td>466.85</td>\n",
       "      <td>471.75</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>968.56%</td>\n",
       "      <td>469.688402</td>\n",
       "      <td>1.886697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>TSLA201204C00260000</td>\n",
       "      <td>2020-11-20 3:08PM EST</td>\n",
       "      <td>260.0</td>\n",
       "      <td>233.73</td>\n",
       "      <td>227.00</td>\n",
       "      <td>231.85</td>\n",
       "      <td>35.72</td>\n",
       "      <td>+18.04%</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>194.68%</td>\n",
       "      <td>230.633927</td>\n",
       "      <td>1.342419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>TSLA201204C00270000</td>\n",
       "      <td>2020-11-17 9:36AM EST</td>\n",
       "      <td>270.0</td>\n",
       "      <td>183.35</td>\n",
       "      <td>217.20</td>\n",
       "      <td>221.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>185.33%</td>\n",
       "      <td>220.678747</td>\n",
       "      <td>-16.915425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>TSLA201204C00280000</td>\n",
       "      <td>2020-11-17 9:32AM EST</td>\n",
       "      <td>280.0</td>\n",
       "      <td>175.65</td>\n",
       "      <td>207.10</td>\n",
       "      <td>211.95</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>176.25%</td>\n",
       "      <td>210.729111</td>\n",
       "      <td>-16.646542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>TSLA201204C00290000</td>\n",
       "      <td>2020-11-19 10:10AM EST</td>\n",
       "      <td>290.0</td>\n",
       "      <td>213.83</td>\n",
       "      <td>197.25</td>\n",
       "      <td>201.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>165.97%</td>\n",
       "      <td>200.789212</td>\n",
       "      <td>6.494765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>TSLA201204C00850000</td>\n",
       "      <td>2020-11-20 3:38PM EST</td>\n",
       "      <td>850.0</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.59</td>\n",
       "      <td>0.39</td>\n",
       "      <td>-</td>\n",
       "      <td>12</td>\n",
       "      <td>-</td>\n",
       "      <td>121.58%</td>\n",
       "      <td>0.049544</td>\n",
       "      <td>687.180752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>TSLA201204C00875000</td>\n",
       "      <td>2020-11-20 3:25PM EST</td>\n",
       "      <td>875.0</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.48</td>\n",
       "      <td>0.34</td>\n",
       "      <td>-</td>\n",
       "      <td>3</td>\n",
       "      <td>-</td>\n",
       "      <td>123.63%</td>\n",
       "      <td>0.028620</td>\n",
       "      <td>1087.966543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>TSLA201204C00900000</td>\n",
       "      <td>2020-11-20 3:39PM EST</td>\n",
       "      <td>900.0</td>\n",
       "      <td>0.28</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.28</td>\n",
       "      <td>-</td>\n",
       "      <td>11</td>\n",
       "      <td>-</td>\n",
       "      <td>128.52%</td>\n",
       "      <td>0.016441</td>\n",
       "      <td>1603.008607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>TSLA201204C00925000</td>\n",
       "      <td>2020-11-20 3:53PM EST</td>\n",
       "      <td>925.0</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.12</td>\n",
       "      <td>-</td>\n",
       "      <td>152</td>\n",
       "      <td>-</td>\n",
       "      <td>122.27%</td>\n",
       "      <td>0.009400</td>\n",
       "      <td>1176.658542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>TSLA201204C00950000</td>\n",
       "      <td>2020-11-20 3:59PM EST</td>\n",
       "      <td>950.0</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-</td>\n",
       "      <td>400</td>\n",
       "      <td>-</td>\n",
       "      <td>121.88%</td>\n",
       "      <td>0.005351</td>\n",
       "      <td>1581.838715</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>90 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Contract Name         Last Trade Date  Strike  Last Price     Bid  \\\n",
       "0   TSLA201204C00020000   2020-11-19 3:34PM EST    20.0      478.55  466.85   \n",
       "3   TSLA201204C00260000   2020-11-20 3:08PM EST   260.0      233.73  227.00   \n",
       "4   TSLA201204C00270000   2020-11-17 9:36AM EST   270.0      183.35  217.20   \n",
       "5   TSLA201204C00280000   2020-11-17 9:32AM EST   280.0      175.65  207.10   \n",
       "6   TSLA201204C00290000  2020-11-19 10:10AM EST   290.0      213.83  197.25   \n",
       "..                  ...                     ...     ...         ...     ...   \n",
       "95  TSLA201204C00850000   2020-11-20 3:38PM EST   850.0        0.39    0.20   \n",
       "96  TSLA201204C00875000   2020-11-20 3:25PM EST   875.0        0.34    0.15   \n",
       "97  TSLA201204C00900000   2020-11-20 3:39PM EST   900.0        0.28    0.20   \n",
       "98  TSLA201204C00925000   2020-11-20 3:53PM EST   925.0        0.12    0.12   \n",
       "99  TSLA201204C00950000   2020-11-20 3:59PM EST   950.0        0.09    0.08   \n",
       "\n",
       "       Ask  Change % Change  Volume Open Interest Implied Volatility  \\\n",
       "0   471.75    0.00        -       5             7            968.56%   \n",
       "3   231.85   35.72  +18.04%       5             6            194.68%   \n",
       "4   221.90    0.00        -       3             9            185.33%   \n",
       "5   211.95    0.00        -       1            16            176.25%   \n",
       "6   201.90    0.00        -       1             6            165.97%   \n",
       "..     ...     ...      ...     ...           ...                ...   \n",
       "95    0.59    0.39        -      12             -            121.58%   \n",
       "96    0.48    0.34        -       3             -            123.63%   \n",
       "97    0.42    0.28        -      11             -            128.52%   \n",
       "98    0.15    0.12        -     152             -            122.27%   \n",
       "99    0.10    0.09        -     400             -            121.88%   \n",
       "\n",
       "      estimate  estimate_error  \n",
       "0   469.688402        1.886697  \n",
       "3   230.633927        1.342419  \n",
       "4   220.678747      -16.915425  \n",
       "5   210.729111      -16.646542  \n",
       "6   200.789212        6.494765  \n",
       "..         ...             ...  \n",
       "95    0.049544      687.180752  \n",
       "96    0.028620     1087.966543  \n",
       "97    0.016441     1603.008607  \n",
       "98    0.009400     1176.658542  \n",
       "99    0.005351     1581.838715  \n",
       "\n",
       "[90 rows x 13 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine outliers\n",
    "\n",
    "df_estimate[df_estimate['estimate_error'].abs() > 1]\n",
    "\n",
    "# the model tends to undervalue puts especially at high strikes (deep out of the money)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# how accurate are our vol estimates?\n",
    "\n",
    "df_estimate['Implied Volatility'] = df_estimate['Implied Volatility'].str.replace(',','').str.slice(stop=-1).astype('float') / 100\n",
    "\n",
    "df_estimate['Historical Vol'] = sigma\n",
    "ax = df_estimate.plot(x='Strike',y=['Implied Volatility','Historical Vol'],title='volatility across strikes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'volume and open interest'}, xlabel='Strike'>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_estimate['Volume'] = df_estimate['Volume'].replace(to_replace='-',value=0)\n",
    "df_estimate['Volume'] = df_estimate['Volume'].astype('int')\n",
    "\n",
    "df_estimate['Open Interest'] = df_estimate['Open Interest'].replace(to_replace='-',value=0)\n",
    "df_estimate['Open Interest'] = df_estimate['Open Interest'].astype('int')\n",
    "\n",
    "df_estimate.plot(x='Strike',y=['Volume','Open Interest'],title='volume and open interest')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'estimate error across strikes'}, xlabel='Strike'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the error across strikes\n",
    "\n",
    "df_estimate.plot(x='Strike',y='estimate_error',title='estimate error across strikes')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "71.596433361587 8.461467565475093\n"
     ]
    }
   ],
   "source": [
    "# what is a measure of error?\n",
    "# MSE: average of the sum of squared errors\n",
    "\n",
    "mse = np.sum((df_estimate['Last Price'] - df_estimate['estimate'])**2) / df_estimate.shape[0]\n",
    "rmse = np.sqrt(mse)\n",
    "\n",
    "print(mse, rmse)\n",
    "# could also try MAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    88.000000\n",
      "mean    -14.575457\n",
      "std      18.037489\n",
      "min     -40.895065\n",
      "25%     -32.763989\n",
      "50%     -11.417336\n",
      "75%      -0.236306\n",
      "max      43.614032\n",
      "Name: estimate_error, dtype: float64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/amao/miniconda3/envs/datasci/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Option prices for TSLA, Expiry 2020-12-04 (Filtered Strikes)'}, xlabel='Strike'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# filter deep ITM and OTM options\n",
    "\n",
    "lower_bound, upper_bound = cur_stock_price * .5, cur_stock_price * 1.5\n",
    "put_estimate_filtered = df_estimate[(df_estimate['Strike'] > lower_bound) & (df_estimate['Strike'] < upper_bound)].reset_index()\n",
    "ax = sns.distplot(put_estimate_filtered['estimate_error'])\n",
    "print(put_estimate_filtered['estimate_error'].describe())\n",
    "\n",
    "put_estimate_filtered.plot(x='Strike',y=['Last Price','estimate'], title='Option prices for {}, Expiry {} (Filtered Strikes)'.format(ticker, expiration_datetime.date()))\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",
       "        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>index</th>\n",
       "      <th>Contract Name</th>\n",
       "      <th>Last Trade Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Bid</th>\n",
       "      <th>Ask</th>\n",
       "      <th>Change</th>\n",
       "      <th>% Change</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Open Interest</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>estimate</th>\n",
       "      <th>estimate_error</th>\n",
       "      <th>Historical Vol</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>TSLA201204C00250000</td>\n",
       "      <td>2020-11-20 3:41PM EST</td>\n",
       "      <td>250.0</td>\n",
       "      <td>242.27</td>\n",
       "      <td>237.10</td>\n",
       "      <td>241.85</td>\n",
       "      <td>-9.48</td>\n",
       "      <td>-3.77%</td>\n",
       "      <td>18</td>\n",
       "      <td>4</td>\n",
       "      <td>2.0523</td>\n",
       "      <td>240.592077</td>\n",
       "      <td>0.697414</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>TSLA201204C00260000</td>\n",
       "      <td>2020-11-20 3:08PM EST</td>\n",
       "      <td>260.0</td>\n",
       "      <td>233.73</td>\n",
       "      <td>227.00</td>\n",
       "      <td>231.85</td>\n",
       "      <td>35.72</td>\n",
       "      <td>+18.04%</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>1.9468</td>\n",
       "      <td>230.633927</td>\n",
       "      <td>1.342419</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>TSLA201204C00270000</td>\n",
       "      <td>2020-11-17 9:36AM EST</td>\n",
       "      <td>270.0</td>\n",
       "      <td>183.35</td>\n",
       "      <td>217.20</td>\n",
       "      <td>221.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>1.8533</td>\n",
       "      <td>220.678747</td>\n",
       "      <td>-16.915425</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>TSLA201204C00280000</td>\n",
       "      <td>2020-11-17 9:32AM EST</td>\n",
       "      <td>280.0</td>\n",
       "      <td>175.65</td>\n",
       "      <td>207.10</td>\n",
       "      <td>211.95</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>1.7625</td>\n",
       "      <td>210.729111</td>\n",
       "      <td>-16.646542</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>TSLA201204C00290000</td>\n",
       "      <td>2020-11-19 10:10AM EST</td>\n",
       "      <td>290.0</td>\n",
       "      <td>213.83</td>\n",
       "      <td>197.25</td>\n",
       "      <td>201.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>1.6597</td>\n",
       "      <td>200.789212</td>\n",
       "      <td>6.494765</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>85</td>\n",
       "      <td>TSLA201204C00670000</td>\n",
       "      <td>2020-11-20 3:59PM EST</td>\n",
       "      <td>670.0</td>\n",
       "      <td>1.88</td>\n",
       "      <td>1.72</td>\n",
       "      <td>2.13</td>\n",
       "      <td>1.88</td>\n",
       "      <td>-</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>0.9775</td>\n",
       "      <td>2.006664</td>\n",
       "      <td>-6.312166</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>86</td>\n",
       "      <td>TSLA201204C00680000</td>\n",
       "      <td>2020-11-20 3:59PM EST</td>\n",
       "      <td>680.0</td>\n",
       "      <td>1.68</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.71</td>\n",
       "      <td>-1.04</td>\n",
       "      <td>-38.24%</td>\n",
       "      <td>2810</td>\n",
       "      <td>364</td>\n",
       "      <td>0.9797</td>\n",
       "      <td>1.659336</td>\n",
       "      <td>1.245288</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>87</td>\n",
       "      <td>TSLA201204C00690000</td>\n",
       "      <td>2020-11-20 3:34PM EST</td>\n",
       "      <td>690.0</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1.33</td>\n",
       "      <td>1.74</td>\n",
       "      <td>1.50</td>\n",
       "      <td>-</td>\n",
       "      <td>214</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0051</td>\n",
       "      <td>1.368984</td>\n",
       "      <td>9.570331</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>88</td>\n",
       "      <td>TSLA201204C00700000</td>\n",
       "      <td>2020-11-20 3:58PM EST</td>\n",
       "      <td>700.0</td>\n",
       "      <td>1.38</td>\n",
       "      <td>1.26</td>\n",
       "      <td>1.54</td>\n",
       "      <td>-0.77</td>\n",
       "      <td>-35.81%</td>\n",
       "      <td>625</td>\n",
       "      <td>1133</td>\n",
       "      <td>1.0217</td>\n",
       "      <td>1.126960</td>\n",
       "      <td>22.453372</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>89</td>\n",
       "      <td>TSLA201204C00720000</td>\n",
       "      <td>2020-11-20 3:55PM EST</td>\n",
       "      <td>720.0</td>\n",
       "      <td>1.09</td>\n",
       "      <td>1.01</td>\n",
       "      <td>1.29</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>-30.57%</td>\n",
       "      <td>512</td>\n",
       "      <td>584</td>\n",
       "      <td>1.0503</td>\n",
       "      <td>0.758979</td>\n",
       "      <td>43.614032</td>\n",
       "      <td>0.881571</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>88 rows × 15 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    index        Contract Name         Last Trade Date  Strike  Last Price  \\\n",
       "0       2  TSLA201204C00250000   2020-11-20 3:41PM EST   250.0      242.27   \n",
       "1       3  TSLA201204C00260000   2020-11-20 3:08PM EST   260.0      233.73   \n",
       "2       4  TSLA201204C00270000   2020-11-17 9:36AM EST   270.0      183.35   \n",
       "3       5  TSLA201204C00280000   2020-11-17 9:32AM EST   280.0      175.65   \n",
       "4       6  TSLA201204C00290000  2020-11-19 10:10AM EST   290.0      213.83   \n",
       "..    ...                  ...                     ...     ...         ...   \n",
       "83     85  TSLA201204C00670000   2020-11-20 3:59PM EST   670.0        1.88   \n",
       "84     86  TSLA201204C00680000   2020-11-20 3:59PM EST   680.0        1.68   \n",
       "85     87  TSLA201204C00690000   2020-11-20 3:34PM EST   690.0        1.50   \n",
       "86     88  TSLA201204C00700000   2020-11-20 3:58PM EST   700.0        1.38   \n",
       "87     89  TSLA201204C00720000   2020-11-20 3:55PM EST   720.0        1.09   \n",
       "\n",
       "       Bid     Ask  Change % Change  Volume  Open Interest  \\\n",
       "0   237.10  241.85   -9.48   -3.77%      18              4   \n",
       "1   227.00  231.85   35.72  +18.04%       5              6   \n",
       "2   217.20  221.90    0.00        -       3              9   \n",
       "3   207.10  211.95    0.00        -       1             16   \n",
       "4   197.25  201.90    0.00        -       1              6   \n",
       "..     ...     ...     ...      ...     ...            ...   \n",
       "83    1.72    2.13    1.88        -      29              0   \n",
       "84    1.51    1.71   -1.04  -38.24%    2810            364   \n",
       "85    1.33    1.74    1.50        -     214              0   \n",
       "86    1.26    1.54   -0.77  -35.81%     625           1133   \n",
       "87    1.01    1.29   -0.48  -30.57%     512            584   \n",
       "\n",
       "    Implied Volatility    estimate  estimate_error  Historical Vol  \n",
       "0               2.0523  240.592077        0.697414        0.881571  \n",
       "1               1.9468  230.633927        1.342419        0.881571  \n",
       "2               1.8533  220.678747      -16.915425        0.881571  \n",
       "3               1.7625  210.729111      -16.646542        0.881571  \n",
       "4               1.6597  200.789212        6.494765        0.881571  \n",
       "..                 ...         ...             ...             ...  \n",
       "83              0.9775    2.006664       -6.312166        0.881571  \n",
       "84              0.9797    1.659336        1.245288        0.881571  \n",
       "85              1.0051    1.368984        9.570331        0.881571  \n",
       "86              1.0217    1.126960       22.453372        0.881571  \n",
       "87              1.0503    0.758979       43.614032        0.881571  \n",
       "\n",
       "[88 rows x 15 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "put_estimate_filtered"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cur_stock_price: 489.60998499999994, time to expiration: 0.04365079365079365, rfr: 0.09, vol: 0.8815712722903746\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Option Prices for TSLA, Expiry 2020-12-04, with Implied Vol'}, xlabel='Strike'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if we use implied vol instead of historical vol, our estimate should improve\n",
    "\n",
    "def calculate_prices_across_strikes(options_df, cur_stock_price, time_to_expiration, risk_free_rate, sigma):\n",
    "\n",
    "    print('cur_stock_price: {}, time to expiration: {}, rfr: {}, vol: {}'.format(cur_stock_price, time_to_expiration, risk_free_rate, sigma))\n",
    "    list_estimates = []\n",
    "\n",
    "    strike_start_idx, strike_end_idx = 0, options_df.shape[0]\n",
    "\n",
    "    # run BSM for different strikes\n",
    "    for x in range(strike_start_idx,strike_end_idx):\n",
    "#         print(options_df['Strike'][x])\n",
    "        value_s = black_scholes(S = cur_stock_price, \n",
    "                                K = options_df['Strike'][x], \n",
    "                                T = time_to_expiration, \n",
    "                                r = risk_free_rate, \n",
    "                                sigma = options_df['Implied Volatility'][x])\n",
    "        list_estimates.append(value_s)\n",
    "\n",
    "    # merge the real and computed dataframes to compare results\n",
    "    options_df['estimate_with_implied'] = list_estimates\n",
    "\n",
    "    return options_df\n",
    "\n",
    "df_estimate = calculate_prices_across_strikes(put_estimate_filtered, cur_stock_price, time_to_expiration, risk_free_rate, sigma)\n",
    "df_estimate.plot(x='Strike',y=['Last Price','estimate','estimate_with_implied'], title='Option Prices for {}, Expiry {}, with Implied Vol'.format(ticker, expiration_datetime.date()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    88.000000\n",
      "mean    -11.715594\n",
      "std      15.723901\n",
      "min     -49.267853\n",
      "25%     -22.878953\n",
      "50%      -6.016633\n",
      "75%       0.809531\n",
      "max       8.954699\n",
      "Name: estimate_with_implied_error, dtype: float64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/amao/miniconda3/envs/datasci/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Estimate Percent Error Across Strikes (Filtered Strikes)'}, xlabel='Strike'>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "df_estimate['estimate_with_implied_error'] = ((df_estimate['Last Price'] - df_estimate['estimate_with_implied'])/df_estimate['estimate_with_implied'])*100\n",
    "ax = sns.distplot(df_estimate['estimate_with_implied_error'])\n",
    "print(df_estimate['estimate_with_implied_error'].describe())\n",
    "put_estimate_filtered.plot(x='Strike',y='estimate_with_implied_error',title='Estimate Percent Error Across Strikes (Filtered Strikes)')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "53.05644604654185 7.283985588024035\n"
     ]
    }
   ],
   "source": [
    "mse = np.sum((df_estimate['Last Price'] - df_estimate['estimate_with_implied'])**2) / df_estimate.shape[0]\n",
    "rmse = np.sqrt(mse)\n",
    "\n",
    "print(mse, rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 4\n"
     ]
    }
   ],
   "source": [
    "# how accurate is BSM for different expiration dates?\n",
    "\n",
    "import os \n",
    "\n",
    "data_path = \"/home/amao/options_data/2020-11-19 17:00:01.568118\"\n",
    "\n",
    "ticker = 'TSLA'\n",
    "calls_data, puts_data = dict(), dict()\n",
    "\n",
    "for filename in os.listdir(data_path):\n",
    "    if ticker in filename:\n",
    "        df = pd.read_csv(os.path.join(data_path, filename))\n",
    "        if 'puts' in filename :\n",
    "            puts_data[filename] = df\n",
    "        elif 'calls' in filename:\n",
    "            calls_data[filename] = df\n",
    "        \n",
    "print(len(calls_data), len(puts_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# stock_price_df = df\n",
    "\n",
    "# for k,v in calls_data.items():\n",
    "#     print(k, v.head())\n",
    "#     bsm_estimate_df = calculate_prices_across_strikes(v, cur_stock_price, time_to_expiration, risk_free_rate, sigma):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u and d: 1.2214027581601699 0.8187307530779818\n",
      "p 0.47512469600943963\n"
     ]
    }
   ],
   "source": [
    "# binomial tree\n",
    "import math\n",
    "\n",
    "sigma = .2\n",
    "rfr = .02\n",
    "delta_t = 1\n",
    "\n",
    "u = math.exp(sigma * math.sqrt(delta_t))\n",
    "d = math.exp(-sigma * math.sqrt(delta_t))\n",
    "print('u and d:',u,d)\n",
    "\n",
    "# a = math.exp(rfr * delta_t)\n",
    "a = math.exp((rfr - .01) * delta_t)\n",
    "p = (a - d)/(u - d)\n",
    "\n",
    "print('p', p)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price 0\n",
      "price 18.65195571686643\n",
      "price 17.452716560268637\n",
      "price 25.695678025946652\n",
      "price 24.44307753439426\n"
     ]
    }
   ],
   "source": [
    "# N period binomial tree model\n",
    "\n",
    "def price_option_european(S_0, u, d, K, option_type: str, num_periods: int):\n",
    "    \n",
    "    if num_periods == 0:\n",
    "        if option_type == 'call':\n",
    "            return max(S_0-K, 0)\n",
    "        elif option_type == 'put':\n",
    "            return max(K-S_0, 0)\n",
    "    else:\n",
    "        S_u = S_0 * u\n",
    "        S_d = S_0 * d\n",
    "        \n",
    "        f_u = price_option_european(S_0 * u,u,d,K,option_type,num_periods-1)\n",
    "        f_d = price_option_european(S_0 * d,u,d,K,option_type,num_periods-1)\n",
    "        \n",
    "#         print('f_u and f_d:', f_u, f_d)\n",
    "\n",
    "        return math.exp(-rfr*delta_t) * (p*f_u + (1-p)*f_d)\n",
    "\n",
    "S_0 = 200\n",
    "K = 200\n",
    "option_type = 'put'\n",
    "\n",
    "for i in range(5):\n",
    "    price = price_option_european(S_0, u, d, K, option_type, num_periods=i)\n",
    "    print('price',price)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price 0\n",
      "price 18.65195571686643\n",
      "price 18.65195571686643\n",
      "price 18.65195571686643\n",
      "price 18.65195571686643\n"
     ]
    }
   ],
   "source": [
    "def price_option_american(S_0, u, d, K, option_type: str, num_periods: int):\n",
    "    \n",
    "    if num_periods == 0:\n",
    "        if option_type == 'call':\n",
    "            return max(S_0-K, 0)\n",
    "        elif option_type == 'put':\n",
    "            return max(K-S_0, 0)\n",
    "    else:\n",
    "        S_u = S_0 * u\n",
    "        S_d = S_0 * d\n",
    "        \n",
    "        f_u = price_option_american(S_0 * u,u,d,K,option_type,num_periods-1)\n",
    "        f_d = price_option_american(S_0 * d,u,d,K,option_type,num_periods-1)\n",
    "        \n",
    "        if option_type == 'call':\n",
    "            f_u_early = max(S_u-K, 0)\n",
    "            f_d_early = max(S_d-K, 0)\n",
    "        elif option_type == 'put':\n",
    "            f_u_early = max(K-S_u, 0)\n",
    "            f_d_early = max(K-S_d, 0)\n",
    "#         print('f_u,f_d,f_u_early,f_d_early:',f_u,f_d,f_u_early,f_d_early)\n",
    "        f_u = max(f_u,f_u_early)\n",
    "        f_d = max(f_u,f_d_early)\n",
    "        \n",
    "#         print('f_u and f_d:', f_u, f_d)\n",
    "\n",
    "        return math.exp(-rfr*delta_t) * (p*f_u + (1-p)*f_d)\n",
    "\n",
    "S_0 = 200\n",
    "K = 200\n",
    "option_type = 'put'\n",
    "\n",
    "for i in range(5):\n",
    "    price = price_option_american(S_0, u, d, K, option_type, num_periods=i)\n",
    "    print('price',price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:datasci]",
   "language": "python",
   "name": "conda-env-datasci-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
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