DOP_Options Payoff Calculator (3).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivatives and Options Pricing: Calculator for Option Strategies\n",
    "\n",
    "***Written by the PGDM Research and Analytics cell***\n",
    "\n",
    "# Basics of option payoffs\n",
    "\n",
    "Before starting out, here are some common notations used in Options pricing:\n",
    "\n",
    "1. Strike Price: $K$\n",
    "\n",
    "2. Price of Asset at Maturity: $S_T$\n",
    "\n",
    "3. Price of the **call option** is: c\n",
    "\n",
    "4. The price of the **put option** is: p\n",
    "\n",
    "Note that we will mention all **payoffs** by including the option price. With this, here are the payoffs for various types of Options and across different positions.\n",
    "\n",
    "1. **Long call payoff**: $\\max(S_T - K - c, -c)$\n",
    "\n",
    "2. **Short call payoff**: $-\\max(S_T - K - c, -c)$\n",
    "\n",
    "3. **Long put payoff**: $\\max(K - S_T - p, -p)$\n",
    "\n",
    "4. **Short put payoff**: $-\\max(K - S_T - p, -p)$\n",
    "\n",
    "\n",
    "# About combined payoffs\n",
    "\n",
    "In this report we will present the combined payoffs resulting from holding a portfolio which could be a combination of long/short positions in stock and long/short positions in multiple types of options. The idea is to plot the payoffs from the constituents of the portfolio and then plot the combined payoffs as well. \n",
    "\n",
    "# About the program\n",
    "\n",
    "Here some features about this Options payoff calculator:\n",
    "\n",
    "1. This is an interactive program - It allows users to enter values on the basis of which, the payoff plots are generated. **First** the user enters **today's stock price** on the basis of which random numbers simulating stock prices are generated. **Secondly** the user can enter whatever instruments he/she desires. We give the user the choice of - long/short Call options, Long/short Put options, Long/short share positions. \n",
    "\n",
    "2. This program has been coded entirely using **basic Python functionality** of conditional statements, functions and loops. The only libraries that have been used are the **plotting** libraries and **random number generator** libraries. \n",
    "\n",
    "3. In addition to plotting the payoffs (combined and individual), the program also outputs the **maximum** payoff and the **stock prices** at which maximum payoff occurs. \n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn-whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "def long_call(c, ST, K):\n",
    "    payoff_LC = []\n",
    "    for i in ST:\n",
    "        if i <= K:\n",
    "            payoff_LC.append(-c)\n",
    "        else:\n",
    "            payoff_LC.append(i - K - c)\n",
    "    return np.array(payoff_LC)\n",
    "\n",
    "def long_put(p, ST, K):\n",
    "    payoff_LP = []\n",
    "    for i in ST:\n",
    "        if i < K:\n",
    "            payoff_LP.append(K - i - p)\n",
    "        else:\n",
    "            payoff_LP.append(-p)\n",
    "    return np.array(payoff_LP)\n",
    "\n",
    "def short_call(c, ST, K):\n",
    "    payoff_SC = []\n",
    "    for i in ST:\n",
    "        if i <= K:\n",
    "            payoff_SC.append(c)\n",
    "        else:\n",
    "            payoff_SC.append(-(i - K - c))\n",
    "    return np.array(payoff_SC)\n",
    "        \n",
    "def short_put(p, ST, K):\n",
    "    payoff_SP = []\n",
    "    for i in ST:\n",
    "        if i < K:\n",
    "            payoff_SP.append(-(K - i - p))\n",
    "        else:\n",
    "            payoff_SP.append(p)\n",
    "    return np.array(payoff_SP)\n",
    "            \n",
    "def short_stock(price, ST):\n",
    "    short_S = []\n",
    "    for i in ST:\n",
    "        short_S.append(-(-price + i))\n",
    "    return np.array(short_S)\n",
    "        \n",
    "def long_stock(price, ST):\n",
    "    long_S = []\n",
    "    for i in ST:\n",
    "        long_S.append(-price + i)\n",
    "    return np.array(long_S)\n",
    "\n",
    "def combined_payoff(ST_1, args):\n",
    "    color = cm.rainbow(np.linspace(0, 1, len(args)))\n",
    "    total_payoff = np.zeros(len(ST_1))\n",
    "    fig = plt.figure(figsize = (7, 7))\n",
    "    for i, c in zip(range(len(args)), color):\n",
    "        total_payoff += args[i]()\n",
    "        plt.plot(ST_1, args[i](), c=c, linestyle='--')\n",
    "    plt.plot(ST_1, total_payoff, 'r')\n",
    "    \n",
    "def extract_function_args(ST_1, port):\n",
    "    func_args = {}\n",
    "    color = cm.rainbow(np.linspace(0, 1, len(port)))\n",
    "    total_pay = np.zeros(len(ST_1))\n",
    "    fig = plt.figure(figsize = (7, 7))\n",
    "    for key, value in port.items():\n",
    "        if len(port[key]) == 0:\n",
    "            pass\n",
    "        elif len(port[key]) != 0:\n",
    "            func_args[key] = value\n",
    "    return func_args\n",
    "\n",
    "def plot_funcs(ST_1, port):\n",
    "    plt.figure(figsize = (8, 8))\n",
    "    func_args = extract_function_args(ST_1, port)\n",
    "    total_payoff = np.zeros(len(ST_1))\n",
    "    for key, value in func_args.items():\n",
    "        if key == 'sell call':\n",
    "            color = cm.rainbow(np.linspace(0, 1, len(value)))\n",
    "            for i, c in zip(range(len(value)), color):\n",
    "                plt.plot(ST_1, short_call(value[i], ST_1,\n",
    "                                        func_args['strike_SC'][i]), c=c, linestyle='--')\n",
    "                total_payoff += short_call(value[i], ST_1, func_args['strike_SC'][i])\n",
    "        elif key == 'buy call':\n",
    "            color = cm.rainbow(np.linspace(0, 1, len(value)))\n",
    "            for i, c in zip(range(len(value)), color):\n",
    "                plt.plot(ST_1, long_call(value[i], ST_1,\n",
    "                                          func_args['strike_LC'][i]), c=c, linestyle='--') \n",
    "                total_payoff += long_call(value[i], ST_1, func_args['strike_LC'][i])\n",
    "        elif key == 'sell put':\n",
    "            color = cm.rainbow(np.linspace(0, 1, len(value)))\n",
    "            for i, c in zip(range(len(value)), color):\n",
    "                plt.plot(ST_1, short_put(value[i], ST_1,\n",
    "                                          func_args['strike_SP'][i]), c=c, linestyle='--') \n",
    "                total_payoff += short_put(value[i], ST_1, func_args['strike_SP'][i])\n",
    "        elif key == 'buy put':\n",
    "            color = cm.rainbow(np.linspace(0, 1, len(value)))\n",
    "            for i, c in zip(range(len(value)), color):\n",
    "                plt.plot(ST_1, long_put(value[i], ST_1,\n",
    "                                          func_args['strike_LP'][i]), c=c, linestyle='--') \n",
    "                total_payoff += long_put(value[i], ST_1, func_args['strike_LP'][i])\n",
    "        elif key == 'buy share':\n",
    "            color = cm.rainbow(np.linspace(0, 1, len(value)))\n",
    "            for i, c in zip(range(len(value)), color):\n",
    "                plt.plot(ST_1, long_stock(value[i], ST_1),\n",
    "                                          c=c, linestyle='--') \n",
    "                total_payoff += long_stock(value[i], ST_1)\n",
    "        elif key == 'sell share':\n",
    "            color = cm.rainbow(np.linspace(0, 1, len(value)))\n",
    "            for i, c in zip(range(len(value)), color):\n",
    "                plt.plot(ST_1, short_stock(value[i], ST_1),\n",
    "                                          c=c, linestyle='--')\n",
    "                total_payoff += short_stock(value[i], ST_1)    \n",
    "    plt.plot(ST_1, total_payoff, 'g', linewidth=4)  \n",
    "    plt.xlabel('ST')\n",
    "    plt.ylabel('Payoff')\n",
    "    plt.ylim(-17, 17)\n",
    "    m = np.max(total_payoff)\n",
    "    print(\"****************\")\n",
    "    print()\n",
    "    print(\"Max payoff is: \", m)\n",
    "    print()\n",
    "    print(\"****************\")\n",
    "    print()\n",
    "    print(\"Stock price at which max payoff is achieved: \", \n",
    "          ST_1[np.where(total_payoff == m)])\n",
    "    print()\n",
    "    print(\"****************\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "def display_menu():\n",
    "    print(\"****************\")\n",
    "    print()\n",
    "    print(\"Here are your options for creating a portfolio:\")\n",
    "    print(\"1. Buy a share (long stock position) -- type 'buy share'\")\n",
    "    print(\"2. Sell a share (short stock position) -- type 'sell share'\")\n",
    "    print(\"3. Buy a call option (long call position) -- type 'buy call'\")\n",
    "    print(\"4. Sell a call option (short call position) -- type 'sell call'\")\n",
    "    print(\"5. Buy a put option (long put position) -- type 'buy put'\")\n",
    "    print(\"6. Sell a put option (short put position) -- type 'sell put'\")\n",
    "    print()\n",
    "    print(\"****************\")\n",
    "    print()\n",
    "\n",
    "def create_folio():   \n",
    "    sigma = 20\n",
    "    print(\"*********\")\n",
    "    print()\n",
    "    print(\"Calculator is now running\")\n",
    "    print()\n",
    "    today = float(input(\"ENTER TODAY'S STOCK PRICE: \"))\n",
    "    print()\n",
    "    ST_1 = np.sort(np.array(np.random.normal(today, sigma, size = 1000)))\n",
    "    folio_dict = {'buy share': [], 'sell share': [], 'buy call': [], 'sell call': [],\n",
    "                  'buy put': [], 'sell put': [], 'strike_LC': [], 'strike_SC': [],\n",
    "                  'strike_LP': [], 'strike_SP': []}\n",
    "    args_main = {}\n",
    "    bool1 = True\n",
    "    counter = 0\n",
    "    while bool1 == True:\n",
    "        display_menu()\n",
    "        print()\n",
    "        a = input(\"What would you like ? (type 'nothing' to exit || type the action words otherise): \")\n",
    "        if a == 'nothing':\n",
    "            bool1 = False\n",
    "            return folio_dict, ST_1, args_main\n",
    "        elif a == 'buy share':\n",
    "            st = float(input(\"enter a stock price: \"))\n",
    "            folio_dict['buy share'].append(st)\n",
    "            args_main[counter] = (lambda: long_stock(st, ST_1))\n",
    "        elif a == 'sell share':\n",
    "            st = float(input(\"enter a stock price: \"))\n",
    "            folio_dict['sell share'].append(st)\n",
    "            args_main[counter] = (lambda: short_stock(st, ST_1))\n",
    "        elif a == 'buy call':\n",
    "            c = float(input(\"enter a long call price: \"))\n",
    "            folio_dict['buy call'].append(c)\n",
    "            k = float(input(\"enter a long call strike price: \"))\n",
    "            folio_dict['strike_LC'].append(k)\n",
    "            args_main[counter] = (lambda: long_call(folio_dict['buy call'][-1], \n",
    "                                                    ST_1, folio_dict['strike_LC'][-1]))\n",
    "        elif a == 'sell call':\n",
    "            c = float(input(\"enter a short call price: \"))\n",
    "            folio_dict['sell call'].append(c)\n",
    "            k = float(input(\"enter a short call strike price: \"))\n",
    "            folio_dict['strike_SC'].append(k)\n",
    "            args_main[counter] = (lambda: short_call(folio_dict['sell call'][-1], \n",
    "                                                     ST_1, folio_dict['sell call'][-1]))\n",
    "        elif a == 'buy put':\n",
    "            p = float(input(\"enter a long put price: \"))\n",
    "            folio_dict['buy put'].append(p)\n",
    "            k = float(input(\"enter a long put strike price: \"))\n",
    "            folio_dict['strike_LP'].append(k)\n",
    "            args_main[counter] = (lambda: long_put(p, ST_1, k))\n",
    "        elif a == 'sell put':\n",
    "            p = float(input(\"enter a short put price: \"))\n",
    "            folio_dict['sell put'].append(p)\n",
    "            k = float(input(\"enter a short put strike price: \"))\n",
    "            folio_dict['strike_SP'].append(k)\n",
    "            args_main[counter] = (lambda: short_put(p, ST_1, k))\n",
    "        counter += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*********\n",
      "\n",
      "Calculator is now running\n",
      "\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "ENTER TODAY'S STOCK PRICE:  212.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "****************\n",
      "\n",
      "Here are your options for creating a portfolio:\n",
      "1. Buy a share (long stock position) -- type 'buy share'\n",
      "2. Sell a share (short stock position) -- type 'sell share'\n",
      "3. Buy a call option (long call position) -- type 'buy call'\n",
      "4. Sell a call option (short call position) -- type 'sell call'\n",
      "5. Buy a put option (long put position) -- type 'buy put'\n",
      "6. Sell a put option (short put position) -- type 'sell put'\n",
      "\n",
      "****************\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "What would you like ? (type 'nothing' to exit || type the action words otherise):  sell call\n",
      "enter a short call price:  7.63\n",
      "enter a short call strike price:  215.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "****************\n",
      "\n",
      "Here are your options for creating a portfolio:\n",
      "1. Buy a share (long stock position) -- type 'buy share'\n",
      "2. Sell a share (short stock position) -- type 'sell share'\n",
      "3. Buy a call option (long call position) -- type 'buy call'\n",
      "4. Sell a call option (short call position) -- type 'sell call'\n",
      "5. Buy a put option (long put position) -- type 'buy put'\n",
      "6. Sell a put option (short put position) -- type 'sell put'\n",
      "\n",
      "****************\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "What would you like ? (type 'nothing' to exit || type the action words otherise):  buy call\n",
      "enter a long call price:  5.35\n",
      "enter a long call strike price:  220.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "****************\n",
      "\n",
      "Here are your options for creating a portfolio:\n",
      "1. Buy a share (long stock position) -- type 'buy share'\n",
      "2. Sell a share (short stock position) -- type 'sell share'\n",
      "3. Buy a call option (long call position) -- type 'buy call'\n",
      "4. Sell a call option (short call position) -- type 'sell call'\n",
      "5. Buy a put option (long put position) -- type 'buy put'\n",
      "6. Sell a put option (short put position) -- type 'sell put'\n",
      "\n",
      "****************\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "What would you like ? (type 'nothing' to exit || type the action words otherise):  sell put\n",
      "enter a short put price:  7.20\n",
      "enter a short put strike price:  210.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "****************\n",
      "\n",
      "Here are your options for creating a portfolio:\n",
      "1. Buy a share (long stock position) -- type 'buy share'\n",
      "2. Sell a share (short stock position) -- type 'sell share'\n",
      "3. Buy a call option (long call position) -- type 'buy call'\n",
      "4. Sell a call option (short call position) -- type 'sell call'\n",
      "5. Buy a put option (long put position) -- type 'buy put'\n",
      "6. Sell a put option (short put position) -- type 'sell put'\n",
      "\n",
      "****************\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "What would you like ? (type 'nothing' to exit || type the action words otherise):  buy put\n",
      "enter a long put price:  5.52\n",
      "enter a long put strike price:  205.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "****************\n",
      "\n",
      "Here are your options for creating a portfolio:\n",
      "1. Buy a share (long stock position) -- type 'buy share'\n",
      "2. Sell a share (short stock position) -- type 'sell share'\n",
      "3. Buy a call option (long call position) -- type 'buy call'\n",
      "4. Sell a call option (short call position) -- type 'sell call'\n",
      "5. Buy a put option (long put position) -- type 'buy put'\n",
      "6. Sell a put option (short put position) -- type 'sell put'\n",
      "\n",
      "****************\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "What would you like ? (type 'nothing' to exit || type the action words otherise):  nothing\n"
     ]
    }
   ],
   "source": [
    "port, stockprice, args_new = create_folio()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "****************\n",
      "\n",
      "Max payoff is:  3.960000000000001\n",
      "\n",
      "****************\n",
      "\n",
      "Stock price at which max payoff is achieved:  [210.09351361 210.10931189 210.12162234 210.1479404  210.37354535\n",
      " 210.37802388 210.40941773 210.43035845 210.51629986 210.54384544\n",
      " 210.5702641  210.69586815 210.72617827 210.76814736 210.85472929\n",
      " 210.8996444  210.90986321 210.95642239 211.03321548 211.03844615\n",
      " 211.32609667 211.3500987  211.35491179 211.37484952 211.4127775\n",
      " 211.43572116 211.43845164 211.45965838 211.50401281 211.51315087\n",
      " 211.5153173  211.53691179 211.56357563 211.58737399 211.60859266\n",
      " 211.71862069 211.76252338 211.77482281 211.7827204  211.82288762\n",
      " 211.89464912 211.98606812 212.00868331 212.03929908 212.06800805\n",
      " 212.14531804 212.17870298 212.21683909 212.29437943 212.46625862\n",
      " 212.47128283 212.54313672 212.55292043 212.58838154 212.60744497\n",
      " 212.62085106 212.62737567 212.65237964 212.67595977 212.67692876\n",
      " 212.68950448 212.70669153 212.71210216 212.8650327  212.90962392\n",
      " 212.98596332 213.00223006 213.15828451 213.18976974 213.19699491\n",
      " 213.25794247 213.29945451 213.30186962 213.36990762 213.39982764\n",
      " 213.76323243 213.79810217 214.01198576 214.04187497 214.0434398\n",
      " 214.08784205 214.0884731  214.14243885 214.23503727 214.2560961\n",
      " 214.32386617 214.48059652 214.50496987 214.52285196 214.57676944\n",
      " 214.69262625 214.77770516 214.83148794 214.83251096]\n",
      "\n",
      "****************\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_funcs(stockprice, port)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}