Bull_Call_Spread_assignment.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2c9381b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#pip install py_vollib\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f5cbda5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from datetime import datetime\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7dbe2889",
   "metadata": {},
   "outputs": [],
   "source": [
    "import yfinance as yf\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fb426ac9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as ss\n",
    "\n",
    "import py_vollib.black_scholes.greeks.analytical as derivatives\n",
    "\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "44189331",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Symbol</th>\n",
       "      <th>Date</th>\n",
       "      <th>Expiry</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>LTP</th>\n",
       "      <th>Settle Price</th>\n",
       "      <th>No. of contracts</th>\n",
       "      <th>Turnover in Lacs</th>\n",
       "      <th>Open Int</th>\n",
       "      <th>Change in OI</th>\n",
       "      <th>Underlying Value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>28-May-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>35499.00</td>\n",
       "      <td>35670.00</td>\n",
       "      <td>35150.00</td>\n",
       "      <td>35321.80</td>\n",
       "      <td>35394.05</td>\n",
       "      <td>35321.80</td>\n",
       "      <td>151658</td>\n",
       "      <td>1340811.02</td>\n",
       "      <td>1745000</td>\n",
       "      <td>27775</td>\n",
       "      <td>35141.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>31-May-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>35280.00</td>\n",
       "      <td>35650.00</td>\n",
       "      <td>35063.15</td>\n",
       "      <td>35602.90</td>\n",
       "      <td>35578.25</td>\n",
       "      <td>35602.90</td>\n",
       "      <td>141916</td>\n",
       "      <td>1257088.18</td>\n",
       "      <td>1723450</td>\n",
       "      <td>-21550</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>01-Jun-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>35677.95</td>\n",
       "      <td>35797.45</td>\n",
       "      <td>35313.95</td>\n",
       "      <td>35454.10</td>\n",
       "      <td>35470.00</td>\n",
       "      <td>35454.10</td>\n",
       "      <td>145631</td>\n",
       "      <td>1292727.92</td>\n",
       "      <td>1731125</td>\n",
       "      <td>7675</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>02-Jun-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>35380.00</td>\n",
       "      <td>35560.00</td>\n",
       "      <td>35180.00</td>\n",
       "      <td>35524.25</td>\n",
       "      <td>35540.00</td>\n",
       "      <td>35524.25</td>\n",
       "      <td>113559</td>\n",
       "      <td>1003669.30</td>\n",
       "      <td>1700025</td>\n",
       "      <td>-31100</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>03-Jun-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>35662.20</td>\n",
       "      <td>35890.00</td>\n",
       "      <td>35553.00</td>\n",
       "      <td>35781.95</td>\n",
       "      <td>35775.00</td>\n",
       "      <td>35781.95</td>\n",
       "      <td>121729</td>\n",
       "      <td>1086929.72</td>\n",
       "      <td>1690250</td>\n",
       "      <td>-9775</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Symbol         Date       Expiry      Open      High       Low  \\\n",
       "0  BANKNIFTY  28-May-2021  24-Jun-2021  35499.00  35670.00  35150.00   \n",
       "1  BANKNIFTY  31-May-2021  24-Jun-2021  35280.00  35650.00  35063.15   \n",
       "2  BANKNIFTY  01-Jun-2021  24-Jun-2021  35677.95  35797.45  35313.95   \n",
       "3  BANKNIFTY  02-Jun-2021  24-Jun-2021  35380.00  35560.00  35180.00   \n",
       "4  BANKNIFTY  03-Jun-2021  24-Jun-2021  35662.20  35890.00  35553.00   \n",
       "\n",
       "      Close       LTP  Settle Price  No. of contracts  Turnover in Lacs  \\\n",
       "0  35321.80  35394.05      35321.80            151658        1340811.02   \n",
       "1  35602.90  35578.25      35602.90            141916        1257088.18   \n",
       "2  35454.10  35470.00      35454.10            145631        1292727.92   \n",
       "3  35524.25  35540.00      35524.25            113559        1003669.30   \n",
       "4  35781.95  35775.00      35781.95            121729        1086929.72   \n",
       "\n",
       "   Open Int  Change in OI Underlying Value   \n",
       "0   1745000         27775          35141.45  \n",
       "1   1723450        -21550                 -  \n",
       "2   1731125          7675                 -  \n",
       "3   1700025        -31100                 -  \n",
       "4   1690250         -9775                 -  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_fut = pd.read_csv('FUTIDX_BANKNIFTY_28-May-2021_TO_24-Jun-2021.txt')  #Fill in with the address of where you downloaded the file. You can check in properties of the file\n",
    "df_fut.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1c2bb5c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Symbol</th>\n",
       "      <th>Date</th>\n",
       "      <th>Expiry</th>\n",
       "      <th>Option Type</th>\n",
       "      <th>Strike Price</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>LTP</th>\n",
       "      <th>Settle Price</th>\n",
       "      <th>No. of contracts</th>\n",
       "      <th>Turnover in Lacs</th>\n",
       "      <th>Premium Turnover in Lacs</th>\n",
       "      <th>Open Int</th>\n",
       "      <th>Change in OI</th>\n",
       "      <th>Underlying Value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>28-May-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>CE</td>\n",
       "      <td>36000</td>\n",
       "      <td>849.95</td>\n",
       "      <td>924.50</td>\n",
       "      <td>665.60</td>\n",
       "      <td>730.80</td>\n",
       "      <td>743.30</td>\n",
       "      <td>730.80</td>\n",
       "      <td>26704</td>\n",
       "      <td>245464.26</td>\n",
       "      <td>5128.26</td>\n",
       "      <td>320700</td>\n",
       "      <td>116225</td>\n",
       "      <td>35141.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>31-May-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>CE</td>\n",
       "      <td>36000</td>\n",
       "      <td>693.90</td>\n",
       "      <td>790.00</td>\n",
       "      <td>598.10</td>\n",
       "      <td>772.95</td>\n",
       "      <td>752.05</td>\n",
       "      <td>772.95</td>\n",
       "      <td>19525</td>\n",
       "      <td>179242.57</td>\n",
       "      <td>3517.57</td>\n",
       "      <td>331150</td>\n",
       "      <td>10450</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>01-Jun-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>CE</td>\n",
       "      <td>36000</td>\n",
       "      <td>782.00</td>\n",
       "      <td>832.00</td>\n",
       "      <td>633.35</td>\n",
       "      <td>660.65</td>\n",
       "      <td>661.00</td>\n",
       "      <td>660.65</td>\n",
       "      <td>31536</td>\n",
       "      <td>289503.11</td>\n",
       "      <td>5679.11</td>\n",
       "      <td>313700</td>\n",
       "      <td>-17450</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>02-Jun-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>CE</td>\n",
       "      <td>36000</td>\n",
       "      <td>575.50</td>\n",
       "      <td>625.95</td>\n",
       "      <td>533.85</td>\n",
       "      <td>612.70</td>\n",
       "      <td>606.85</td>\n",
       "      <td>612.70</td>\n",
       "      <td>19060</td>\n",
       "      <td>174293.32</td>\n",
       "      <td>2753.32</td>\n",
       "      <td>324475</td>\n",
       "      <td>10775</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BANKNIFTY</td>\n",
       "      <td>03-Jun-2021</td>\n",
       "      <td>24-Jun-2021</td>\n",
       "      <td>CE</td>\n",
       "      <td>36000</td>\n",
       "      <td>659.05</td>\n",
       "      <td>753.90</td>\n",
       "      <td>596.50</td>\n",
       "      <td>698.40</td>\n",
       "      <td>696.00</td>\n",
       "      <td>698.40</td>\n",
       "      <td>24549</td>\n",
       "      <td>225062.12</td>\n",
       "      <td>4121.12</td>\n",
       "      <td>328425</td>\n",
       "      <td>3950</td>\n",
       "      <td>-</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Symbol         Date       Expiry Option Type  Strike Price    Open  \\\n",
       "0  BANKNIFTY  28-May-2021  24-Jun-2021          CE         36000  849.95   \n",
       "1  BANKNIFTY  31-May-2021  24-Jun-2021          CE         36000  693.90   \n",
       "2  BANKNIFTY  01-Jun-2021  24-Jun-2021          CE         36000  782.00   \n",
       "3  BANKNIFTY  02-Jun-2021  24-Jun-2021          CE         36000  575.50   \n",
       "4  BANKNIFTY  03-Jun-2021  24-Jun-2021          CE         36000  659.05   \n",
       "\n",
       "     High     Low   Close     LTP  Settle Price  No. of contracts  \\\n",
       "0  924.50  665.60  730.80  743.30        730.80             26704   \n",
       "1  790.00  598.10  772.95  752.05        772.95             19525   \n",
       "2  832.00  633.35  660.65  661.00        660.65             31536   \n",
       "3  625.95  533.85  612.70  606.85        612.70             19060   \n",
       "4  753.90  596.50  698.40  696.00        698.40             24549   \n",
       "\n",
       "   Turnover in Lacs  Premium Turnover in Lacs  Open Int  Change in OI  \\\n",
       "0         245464.26                   5128.26    320700        116225   \n",
       "1         179242.57                   3517.57    331150         10450   \n",
       "2         289503.11                   5679.11    313700        -17450   \n",
       "3         174293.32                   2753.32    324475         10775   \n",
       "4         225062.12                   4121.12    328425          3950   \n",
       "\n",
       "  Underlying Value  \n",
       "0         35141.45  \n",
       "1                -  \n",
       "2                -  \n",
       "3                -  \n",
       "4                -  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_call_36000 = pd.read_csv('OPTIDX_BANKNIFTY_CE_28-May-2021_TO_24-Jun-2021.txt')\n",
    "df_call_36000.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "eed3ea14",
   "metadata": {},
   "outputs": [],
   "source": [
    "symbol = '^NSEBANK'\n",
    "end = '2021-06-25'\n",
    "start = '2021-05-28'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ccda38bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    },
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
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       "      <th>Adj Close</th>\n",
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       "    <tr>\n",
       "      <th>2021-05-28</th>\n",
       "      <td>35345.648438</td>\n",
       "      <td>35436.648438</td>\n",
       "      <td>34977.199219</td>\n",
       "      <td>35141.449219</td>\n",
       "      <td>35141.449219</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-05-31</th>\n",
       "      <td>35097.449219</td>\n",
       "      <td>35584.300781</td>\n",
       "      <td>34930.101562</td>\n",
       "      <td>35526.648438</td>\n",
       "      <td>35526.648438</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-06-01</th>\n",
       "      <td>35639.750000</td>\n",
       "      <td>35713.898438</td>\n",
       "      <td>35241.199219</td>\n",
       "      <td>35337.199219</td>\n",
       "      <td>35337.199219</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-06-02</th>\n",
       "      <td>35271.601562</td>\n",
       "      <td>35415.851562</td>\n",
       "      <td>35070.300781</td>\n",
       "      <td>35373.750000</td>\n",
       "      <td>35373.750000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-06-03</th>\n",
       "      <td>35536.449219</td>\n",
       "      <td>35723.699219</td>\n",
       "      <td>35413.000000</td>\n",
       "      <td>35649.000000</td>\n",
       "      <td>35649.000000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Open          High           Low         Close  \\\n",
       "Date                                                                 \n",
       "2021-05-28  35345.648438  35436.648438  34977.199219  35141.449219   \n",
       "2021-05-31  35097.449219  35584.300781  34930.101562  35526.648438   \n",
       "2021-06-01  35639.750000  35713.898438  35241.199219  35337.199219   \n",
       "2021-06-02  35271.601562  35415.851562  35070.300781  35373.750000   \n",
       "2021-06-03  35536.449219  35723.699219  35413.000000  35649.000000   \n",
       "\n",
       "               Adj Close  Volume  \n",
       "Date                              \n",
       "2021-05-28  35141.449219       0  \n",
       "2021-05-31  35526.648438       0  \n",
       "2021-06-01  35337.199219       0  \n",
       "2021-06-02  35373.750000       0  \n",
       "2021-06-03  35649.000000       0  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = yf.download(symbol,start,end)\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "068a62b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "symbol = '^NSEBANK'\n",
    "end = '2021-05-28'\n",
    "start = '2020-05-28'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "71e9a381",
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
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       "<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>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2020-05-28</th>\n",
       "      <td>18924.449219</td>\n",
       "      <td>19455.550781</td>\n",
       "      <td>18818.949219</td>\n",
       "      <td>19169.800781</td>\n",
       "      <td>19169.800781</td>\n",
       "      <td>561100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-29</th>\n",
       "      <td>18962.000000</td>\n",
       "      <td>19358.050781</td>\n",
       "      <td>18729.900391</td>\n",
       "      <td>19297.250000</td>\n",
       "      <td>19297.250000</td>\n",
       "      <td>581700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-01</th>\n",
       "      <td>19728.900391</td>\n",
       "      <td>20225.349609</td>\n",
       "      <td>19632.900391</td>\n",
       "      <td>19959.900391</td>\n",
       "      <td>19959.900391</td>\n",
       "      <td>558100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-02</th>\n",
       "      <td>20120.599609</td>\n",
       "      <td>20615.750000</td>\n",
       "      <td>19852.550781</td>\n",
       "      <td>20530.199219</td>\n",
       "      <td>20530.199219</td>\n",
       "      <td>448300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-03</th>\n",
       "      <td>20966.599609</td>\n",
       "      <td>21619.550781</td>\n",
       "      <td>20822.000000</td>\n",
       "      <td>20940.699219</td>\n",
       "      <td>20940.699219</td>\n",
       "      <td>616900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Open          High           Low         Close  \\\n",
       "Date                                                                 \n",
       "2020-05-28  18924.449219  19455.550781  18818.949219  19169.800781   \n",
       "2020-05-29  18962.000000  19358.050781  18729.900391  19297.250000   \n",
       "2020-06-01  19728.900391  20225.349609  19632.900391  19959.900391   \n",
       "2020-06-02  20120.599609  20615.750000  19852.550781  20530.199219   \n",
       "2020-06-03  20966.599609  21619.550781  20822.000000  20940.699219   \n",
       "\n",
       "               Adj Close  Volume  \n",
       "Date                              \n",
       "2020-05-28  19169.800781  561100  \n",
       "2020-05-29  19297.250000  581700  \n",
       "2020-06-01  19959.900391  558100  \n",
       "2020-06-02  20530.199219  448300  \n",
       "2020-06-03  20940.699219  616900  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_year= yf.download(symbol,start,end)\n",
    "df_year.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "d71be321",
   "metadata": {},
   "outputs": [],
   "source": [
    "ret = df_year['Close'].pct_change()[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "d94c4a2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2020-05-29    0.006648\n",
       "2020-06-01    0.034339\n",
       "2020-06-02    0.028572\n",
       "2020-06-03    0.019995\n",
       "2020-06-04   -0.026277\n",
       "Name: Close, dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ret.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "28f87a7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.018580334637206992"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "daily_vol = ret.std()\n",
    "daily_vol\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e2c00c2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2949536683584554"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual_vol=math.sqrt(252)*daily_vol\n",
    "annual_vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "085bd8f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "expiry = datetime.strptime('2021-06-24', '%Y-%m-%d')   #Expiry date\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "ef0b5fbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TimedeltaIndex(['392 days', '391 days', '388 days', '387 days', '386 days',\n",
       "                '385 days', '384 days', '381 days', '380 days', '379 days',\n",
       "                ...\n",
       "                 '41 days',  '38 days',  '37 days',  '36 days',  '35 days',\n",
       "                 '34 days',  '31 days',  '30 days',  '29 days',  '28 days'],\n",
       "               dtype='timedelta64[ns]', name='Date', length=249, freq=None)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time = expiry-df.index    #Time left in days\n",
    "time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "757c4c4c",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Int64Index' object has no attribute 'days'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_26912/3362039915.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mtime\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdays\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m: 'Int64Index' object has no attribute 'days'"
     ]
    }
   ],
   "source": [
    "time=time.days\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "472fbf90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Int64Index([392, 391, 388, 387, 386, 385, 384, 381, 380, 379,\n",
       "            ...\n",
       "             41,  38,  37,  36,  35,  34,  31,  30,  29,  28],\n",
       "           dtype='int64', name='Date', length=249)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import datetime as dt\n",
    "time"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a90eb7ae",
   "metadata": {},
   "source": [
    "Initial buying and selling\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "7ee0d833",
   "metadata": {},
   "outputs": [],
   "source": [
    "no_of_lots_fut = 10           #number of future lots we bought at start of the month\n",
    "buy_avg_future = df_fut['Open'][0]       #buying average of that lot\n",
    "lot_size = 25     #lot size of bank nifty\n",
    "delta = 1*no_of_lots_fut*lot_size    #taking delta of future is 1 as if banknifty changes by 1 the future would also change by 1\n",
    "delta_to_maintain = 0.8*no_of_lots_fut*lot_size#Maintain 0.8 delta per future contract"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "22a3892c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04091615824385745"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flag = 'c'   #for call or put option\n",
    "S = df['Open'][0]    #price of the underlying\n",
    "K = 36000   #strike price\n",
    "t = time[0]/365   #time left to expiry in years\n",
    "sigma = annual_vol   #volatility\n",
    "r = 0.06  #risk free rate\n",
    "delta_per_lot_call =derivatives.delta(flag,S,K,t,r,sigma) #Calculate delta per lot\n",
    "delta_per_lot_call"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "ab80f73a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200.0"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_to_maintain\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "814dc7ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "250"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "105a54c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "number_of_lots_call = int((delta-delta_to_maintain)/delta_per_lot_call) #Calculate Number of call lots we have to sell to keep delta of 200\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "6760b4e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1222"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "number_of_lots_call\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "6b472c13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "849.95"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sell_avg_call = df_call_36000['Open'][0]  #selling avg of call \n",
    "sell_avg_call"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "1a082e7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Before moving on to managing delta, answer a few questions:\n",
    "\n",
    "#Q1 : What do you think would happen to the delta of call option as banknifty goes up? (increase/decrease) \n",
    "#Ans : Delta will increase\n",
    "\n",
    "#Q2 : So to manage the delta what would be done to call options already sold? (Buy some call options / Sell more) \n",
    "#Hint : Remember selling call options would give negative delta\n",
    "#Ans : To maintain delta at 200 we need to sell more call option"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3988d0ce",
   "metadata": {},
   "source": [
    "Managing delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "8c8f4d78",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35321.8 35499.0 849.95 730.8\n",
      "35602.9 35499.0 693.9 772.95\n",
      "35454.1 35499.0 782.0 660.65\n",
      "35524.25 35499.0 575.5 612.7\n",
      "35781.95 35499.0 659.05 698.4\n",
      "35508.5 35499.0 677.1 549.15\n",
      "35622.2 35499.0 563.0 537.05\n",
      "35265.3 35499.0 501.95 349.15\n",
      "34929.35 35499.0 330.7 234.7\n",
      "35266.35 35499.0 218.95 306.15\n",
      "35169.35 35499.0 352.7 242.95\n",
      "35065.1 35499.0 192.6 172.55\n",
      "35330.4 35499.0 176.35 203.7\n",
      "35101.35 35499.0 177.25 145.05\n",
      "34682.2 35499.0 86.95 55.9\n",
      "34596.75 35499.0 57.3 32.05\n",
      "34911.1 35499.0 28.0 25.65\n",
      "34775.8 35499.0 64.05 14.7\n",
      "34611.9 35499.0 19.9 8.1\n",
      "34819.95 35499.0 4.4 0.25\n"
     ]
    },
    {
     "ename": "KeyError",
     "evalue": "20",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\indexes\\range.py\u001b[0m in \u001b[0;36mget_loc\u001b[1;34m(self, key, method, tolerance)\u001b[0m\n\u001b[0;32m    384\u001b[0m                 \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 385\u001b[1;33m                     \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_range\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnew_key\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    386\u001b[0m                 \u001b[1;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0merr\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: 20 is not in range",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_26912/2695877545.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      7\u001b[0m     \u001b[0mcurrent_number_of_lots_call\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnumber_of_lots_call\u001b[0m\u001b[1;31m#number of lots required to sell\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m     \u001b[0mno_of_lots_added\u001b[0m \u001b[1;33m=\u001b[0m  \u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mceil\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdelta\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdelta_to_maintain\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mdelta_per_lot_call\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mcurrent_number_of_lots_call\u001b[0m\u001b[1;31m#number of lots added/subtracted for selling\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m     \u001b[0msell_avg_call\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf_call_36000\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Open'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;31m#new selling avg of call\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m     \u001b[0mnumber_of_lots_call\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcurrent_number_of_lots_call\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mno_of_lots_added\u001b[0m\u001b[1;31m#update number of lots of calls sold\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m     \u001b[0mprofit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf_fut\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Close'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mbuy_avg_future\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mno_of_lots_fut\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mlot_size\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0msell_avg_call\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdf_call_36000\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Close'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mlot_size\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mnumber_of_lots_call\u001b[0m\u001b[1;33m)\u001b[0m  \u001b[1;31m#unrealised profit\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36m__getitem__\u001b[1;34m(self, key)\u001b[0m\n\u001b[0;32m    940\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    941\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0mkey_is_scalar\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 942\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    943\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    944\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mis_hashable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\series.py\u001b[0m in \u001b[0;36m_get_value\u001b[1;34m(self, label, takeable)\u001b[0m\n\u001b[0;32m   1049\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1050\u001b[0m         \u001b[1;31m# Similar to Index.get_value, but we do not fall back to positional\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1051\u001b[1;33m         \u001b[0mloc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1052\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_values_for_loc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1053\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\indexes\\range.py\u001b[0m in \u001b[0;36mget_loc\u001b[1;34m(self, key, method, tolerance)\u001b[0m\n\u001b[0;32m    385\u001b[0m                     \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_range\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnew_key\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    386\u001b[0m                 \u001b[1;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0merr\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 387\u001b[1;33m                     \u001b[1;32mraise\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0merr\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    388\u001b[0m             \u001b[1;32mraise\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    389\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0msuper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmethod\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtolerance\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtolerance\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyError\u001b[0m: 20"
     ]
    }
   ],
   "source": [
    "number_of_lots_call = math.ceil((delta-delta_to_maintain)/delta_per_lot_call)  #number of call lots we have to sell to keep delta of 200\n",
    "sell_avg_call = df_call_36000['Open'][0]  #selling avg of call \n",
    "profit= []\n",
    "\n",
    "for i in range(len(df)-1):\n",
    "    delta_per_lot_call = derivatives.delta(flag,df['Open'][i],K,time[i]/365,r,sigma)#Calculate delta per lot at the next closing day\n",
    "    current_number_of_lots_call = number_of_lots_call#number of lots required to sell\n",
    "    no_of_lots_added =  math.ceil((delta-delta_to_maintain)/delta_per_lot_call) - current_number_of_lots_call#number of lots added/subtracted for selling\n",
    "    sell_avg_call = df_call_36000['Open'][i]#new selling avg of call\n",
    "    number_of_lots_call = current_number_of_lots_call + no_of_lots_added#update number of lots of calls sold\n",
    "    profit.append((df_fut['Close'][i]-buy_avg_future)*no_of_lots_fut*lot_size + (sell_avg_call-df_call_36000['Close'][i])*lot_size*number_of_lots_call)  #unrealised profit \n",
    "    print(df_fut['Close'][i], buy_avg_future, sell_avg_call, df_call_36000['Close'][i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "71d9da03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "470"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#As you can see that the number of lots of call sold is way too many as the delta of out of money call option approches 0 in the end\n",
    "#Thus this strategy would practically be possible by changing the strike price of the call option as it goes deep out of money\n",
    "#But that would require much higher level programming thats why we have given this simple assignment jst theoretically make\n",
    "#you realise the power of hedging\n",
    "number_of_lots_call"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "e4abcf31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.4"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sell_avg_call"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "f379dce7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0743111846347983"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_per_lot_call"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "328dcced",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3598711.2500000037,\n",
       " -2373192.500000002,\n",
       " 2849601.25,\n",
       " -768377.5000000009,\n",
       " -563781.250000001,\n",
       " 2097556.250000001,\n",
       " 515416.2500000001,\n",
       " 2027295.000000001,\n",
       " 1307187.4999999995,\n",
       " -1610322.5000000002,\n",
       " 1698281.2499999995,\n",
       " 435381.2499999992,\n",
       " -593252.4999999995,\n",
       " 544587.4999999994,\n",
       " 499858.7499999994,\n",
       " 350768.75,\n",
       " -105732.50000000032,\n",
       " 573021.2500000006,\n",
       " -58639.99999999965,\n",
       " -121000.00000000073]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "profit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "2df194e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x21684d97bb0>"
      ]
     },
     "execution_count": 74,
     "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": [
    "plt.plot(profit[:14], label = 'strategy_profit')\n",
    "plt.plot((df_fut['Close']-df_fut['Open'][0])[:14]*250, label = 'futures_profit')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe0ef539",
   "metadata": {},
   "source": [
    "As you can see from the above graph of first first 14 days of the strategy that though the futures did fall very down but\n",
    "We were able to hedge this with selling of call option and our strategy did give better returns overall\n",
    "\n",
    "\n",
    "We didnt plot the whole graph as in the end many lots of call options were sold which is practically not possible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecde1167",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}