Pricing Options with MC.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "7a36dd5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np, math\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "import yfinance as yf\n",
    "from scipy import stats\n",
    "from scipy.stats import norm\n",
    "import pandas_datareader as pdr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "bffbabe8-706a-4165-bbf2-d5c28ae13a83",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Asset list\n",
    "lst=['AAPL','WMT','ADM','GM','HD','JNJ']\n",
    "\n",
    "#dates for model calibration\n",
    "start_data='2018-01-01'\n",
    "end_data='2019-01-01'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1905ef8-6eae-46ab-b061-6fd685702ae6",
   "metadata": {},
   "source": [
    "## Volatility estimate for list of stocks in 2018"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "f22a1248-624e-466c-87f0-17e30f0c590c",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma=[]\n",
    "for i in range(0,len(lst)):\n",
    "    stock = pdr.get_data_yahoo(lst[i],start = start_data,end=end_data)['Adj Close']\n",
    "    dlogstock = np.diff(np.log(stock))\n",
    "    dlogstock.mean()\n",
    "    M = dlogstock.size\n",
    "    Δt = T/M\n",
    "    dlogstock.mean()/Δt\n",
    "\n",
    "    σbar = dlogstock.std()/math.sqrt(Δt)\n",
    "    sigma.append(σbar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "8f959355-9dfc-4b89-a494-c5b3dceb58eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        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>AAPL</th>\n",
       "      <th>WMT</th>\n",
       "      <th>ADM</th>\n",
       "      <th>GM</th>\n",
       "      <th>HD</th>\n",
       "      <th>JNJ</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Vol</th>\n",
       "      <td>0.286035</td>\n",
       "      <td>0.239924</td>\n",
       "      <td>0.187269</td>\n",
       "      <td>0.314638</td>\n",
       "      <td>0.225919</td>\n",
       "      <td>0.221443</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         AAPL       WMT       ADM        GM        HD       JNJ\n",
       "Vol  0.286035  0.239924  0.187269  0.314638  0.225919  0.221443"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#performance metrics\n",
    "vol_df = pd.DataFrame(index=['Vol'], columns=['AAPL', 'WMT', 'ADM', 'GM', 'HD','JNJ'])\n",
    "vol_df.loc['Vol'] = sigma\n",
    "vol_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1f443b2-a5e4-4ba6-813d-03672520f060",
   "metadata": {},
   "source": [
    "## Pricing euro call using MC\n",
    "## Comparison with Black-Scholes pricing (that I implemented previously)\n",
    "## Graph of how fast the MC price will converge with Black-Scholes price per number of MC simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "6e6aa144",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data 1 year maturity call\n",
    "T = 1 # five years\n",
    "M = T*252\n",
    "Δt = T/M\n",
    "S0 = 100\n",
    "r = 0.05\n",
    "σ = 0.20\n",
    "K = 105\n",
    "\n",
    "N = 1000000 # number of simulations\n",
    "rng = np.random.default_rng(seed=12345)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "f1ce0189",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f1(N_M_Δt_S0_r_σ):\n",
    "    N,M,Δt,S0,r,σ = N_M_Δt_S0_r_σ\n",
    "    S = np.empty((N,M+1))\n",
    "    S[:,0] = S0\n",
    "    S[:,1:] = np.exp((r-σ**2/2)*Δt + σ*math.sqrt(Δt)*rng.standard_normal(size=(N,M)))\n",
    "    return S.cumprod(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "1772f625",
   "metadata": {},
   "outputs": [],
   "source": [
    "sims = f1((N,M,Δt,S0,r,σ))\n",
    "Sfinal = sims[:,-1]\n",
    "values = np.maximum(Sfinal - K,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "fab3499c-9f32-4331-891f-58d57d16b2ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.018005146541974"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eurocallvalue = values.mean()*math.exp(-r*T)\n",
    "eurocallvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "6c0bc2a1-6009-40cd-aa84-364907413cf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ask_for_input():\n",
    "    T = float(input('Please enter time to maturity:'))\n",
    "    r = float(input('Please enter a rate:'))\n",
    "    d = float(input('Please enter dividend rate:'))\n",
    "    K = float(input('Please enter strike:'))\n",
    "    S = float(input('Please enter spot price:'))\n",
    "    sigma = float(input('Please enter volatility:'))\n",
    "    return T, r, d, K, S, sigma\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "cfa12e70-8c37-4875-9ef1-765774d1e6e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Please enter time to maturity: 1\n",
      "Please enter a rate: 0.05\n",
      "Please enter dividend rate: 0\n",
      "Please enter strike: 105\n",
      "Please enter spot price: 100\n",
      "Please enter volatility: 0.2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.021352235143176\n"
     ]
    }
   ],
   "source": [
    "#compare with Black Scholes pricing model\n",
    "def get_call():\n",
    "    T, r, d, K, S, sigma = ask_for_input()\n",
    "    if K==0 or T==0 or sigma ==0:\n",
    "        print('Not a valid input')\n",
    "    elif d == 0:\n",
    "        d1 = (np.log(S/K)+(r+0.5*sigma**2)*T) / (sigma*np.sqrt(T))\n",
    "        d2 = d1-sigma*np.sqrt(T)\n",
    "\n",
    "        call = S*norm.cdf(d1) - K*np.exp(-r*T)*norm.cdf(d2)\n",
    "        print(call)\n",
    "        return call\n",
    "    elif d < 0:\n",
    "        print('Not a valid dividend input')\n",
    "    else:\n",
    "        d1 = (np.log(S/K)+(r+0.5*sigma**2)*T) / (sigma*np.sqrt(T))\n",
    "        d2 = d1-sigma*np.sqrt(T)\n",
    "\n",
    "        call = np.exp(-d*T)*S*norm.cdf(d1) - K*np.exp(-r*T)*norm.cdf(d2)\n",
    "    return(call)\n",
    "bs_call=get_call()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "fcbe4d5f-2ce8-4a6d-8682-538774357efd",
   "metadata": {},
   "outputs": [],
   "source": [
    "#let's take a look how fast monte carlo converges with blackscholes depending on number of simulations\n",
    "num_sims=np.arange(1,10000,10)\n",
    "mc_call=[]\n",
    "for i in range(len(num_sims)):\n",
    "    N=num_sims[i]\n",
    "    sims = f1((N,M,Δt,S0,r,σ))\n",
    "    Sfinal = sims[:,-1]\n",
    "    values = np.maximum(Sfinal - K,0)\n",
    "    eurocallvalue = values.mean()*math.exp(-r*T)\n",
    "    mc_call.append(eurocallvalue)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "ade0b932-7898-453d-b13e-fa4690b917fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7fea92f256d0>"
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     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(num_sims,mc_call)\n",
    "plt.xlabel('Number of Simulations')\n",
    "plt.ylabel('Call Price')\n",
    "plt.axhline(y = bs_call, color = 'r', linestyle = '-')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efb58528-dd78-4aa4-ae2a-2fb1af70d8b0",
   "metadata": {},
   "source": [
    "## As we can see, monte carlo simulation will converge to the Black Scholes price of the option as the number of simulations increases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e928bb6-8ae8-4925-925f-812446376d8b",
   "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
}