option-pricing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Option Pricing and Prepare for Risk\n",
    "- Uehara Takahiro\n",
    "- Tokyo Institute of Technology  \n",
    "- Master Degree  \n",
    "- takahiro.steadtler@gmail.com"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ready const\n",
    "ready constant given by task mail"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# current price of underlying asset\n",
    "current_price = 100\n",
    "# array of pair of probability and tommorow price\n",
    "# lower_price must be lower than current price, higher_price must be higher than current price, \n",
    "patterns = {'lower_price' : {'probability': 0.5, 'tomorrow_rate': 0.9}, 'higher_price' : {'probability': 0.5, 'tomorrow_rate': 1.2}}\n",
    "# ten year risk free rate\n",
    "ten_year_risk_free_rate = 0.0081\n",
    "# one day risk free rate\n",
    "one_day_risk_free_rate = 1.0081 ** (1/3650)\n",
    "# calc probability based on risk free rate and tomorrow rate\n",
    "q = (one_day_risk_free_rate - patterns['lower_price']['tomorrow_rate']) / (patterns['higher_price']['tomorrow_rate'] - patterns['lower_price']['tomorrow_rate'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to solve task2\n",
    "I would like to use binomial model to find the option premium corresponding to the strike price.  \n",
    "In addition, I would like to use the same theory to construct a portfolio to protect against risk."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions to calculate the option premium based on the strike price\n",
    "In this case, we define the variables as follows.  \n",
    "$u : $The first of the underlying asset price projections  \n",
    "$d : $The second of the underlying asset price projections  \n",
    "$R : $Risk-free interest rate  \n",
    "The price of the options if each state of $u$ and $d$ is realized is as shown in the equation below.  \n",
    "$C_u = max(uS - K, 0)$  \n",
    "$C_d = max(dS - K, 0)$  \n",
    "The function named \"option_premium_depends_on_tomorrow_rate_and_strike_price\" at the bottom represents the two expressions above.  \n",
    "  \n",
    "If we know the probability of each state happening, we can find the current option price as an expected value.  \n",
    "The reason we divide by R is to take into account the risk-free assets.  \n",
    "We have expressed this in the equation below.  \n",
    "$C = \\frac{1}{R}[qC_u + (1-q)C_d]$  \n",
    "The function named \"option_premium_based_on_probability\" represents the above equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "_cell_guid": "79c7e3d0-c299-4dcb-8224-4455121ee9b0",
    "_uuid": "d629ff2d2480ee46fbb7e2d37f6b5fab8052498a"
   },
   "outputs": [],
   "source": [
    "def option_premium_depends_on_tomorrow_rate_and_strike_price(strike_price, pattern):\n",
    "    return max(pattern['tomorrow_rate'] * current_price - strike_price, 0)\n",
    "\n",
    "def option_premium_based_on_probability(strike_price, probability = q):\n",
    "    return (probability * option_premium_depends_on_tomorrow_rate_and_strike_price(strike_price, patterns['higher_price']) + (1 - probability) * option_premium_depends_on_tomorrow_rate_and_strike_price(strike_price, patterns['lower_price'])) / one_day_risk_free_rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function to structure the portfolio based on the strike price\n",
    "I would like to replicate the option prices in the event of each of $u$ and $d$, with a portfolio of risk-free assets and the underlying assets.  \n",
    "The $x$ represents the amount of the underlying asset should have.  \n",
    "The $b$ represents the amount of the risk-free assets should have.  \n",
    "$ux + Rb = C_u$  \n",
    "$dx + Rb = C_d$  \n",
    "Solving this simultaneous equation, $x$ and $b$ are obtained as follows.  \n",
    "$x = \\frac{C_u - C_d}{u - d}$  \n",
    "$b = \\frac{uC_d - dC_u}{R(u - d)}$  \n",
    "The function named \"doller_to_have_stock\" at the bottom represents $x$ above.  \n",
    "The function named \"doller_to_have_risk_free\" at the bottom represents $b$ above.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def doller_to_have_stock(strike_price):\n",
    "    return (option_premium_depends_on_tomorrow_rate_and_strike_price(strike_price, patterns['higher_price']) - option_premium_depends_on_tomorrow_rate_and_strike_price(strike_price, patterns['lower_price'])) / (patterns['higher_price']['tomorrow_rate'] - patterns['lower_price']['tomorrow_rate'])\n",
    "\n",
    "def doller_to_have_risk_free(strike_price):\n",
    "    return (patterns['higher_price']['tomorrow_rate'] * option_premium_depends_on_tomorrow_rate_and_strike_price(strike_price, patterns['lower_price']) - patterns['lower_price']['tomorrow_rate'] * option_premium_depends_on_tomorrow_rate_and_strike_price(strike_price, patterns['higher_price'])) / (one_day_risk_free_rate * (patterns['higher_price']['tomorrow_rate'] - patterns['lower_price']['tomorrow_rate']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Outputs values according to the strike price\n",
    "I output each value by varying the strike price from 0 to 200.  \n",
    "- \"option_premium represents\" represents an option premium that requires the customer to pay(The probability of $u$ and $d$ are based on the above q).  \n",
    "- \"option_premium_equal_probability\" represents an option premium that requires the customer to pay(The probability of $u$ and $d$ are equal.).  \n",
    "- \"stock_doller_in_portfolio\" represents how much of the underlying asset  we should hold when we sell one option.  \n",
    "- \"risk_free_doller_in_portfolio\" represents how much of a risk-free asset we should hold when we sell one option.  \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fc8fe1b3d10>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = pd.DataFrame(columns = ['strike_price', 'option_premium', 'option_premium_equal_probability', 'stock_doller_in_portfolio', 'risk_free_doller_in_portfolio'])\n",
    "strike_prices = []\n",
    "option_premiums = []\n",
    "stock_dollers_in_portfolio = []\n",
    "option_premiums_equal_probability = []\n",
    "risk_free_dollers_in_portfolio = []\n",
    "for strike_price in range(max(current_price - 1000, 0), current_price * 2):\n",
    "    strike_prices.append(strike_price)\n",
    "    option_premiums.append(option_premium_based_on_probability(strike_price, q))\n",
    "    option_premiums_equal_probability.append(option_premium_based_on_probability(strike_price, 0.5))\n",
    "    stock_dollers_in_portfolio.append(doller_to_have_stock(strike_price))\n",
    "    risk_free_dollers_in_portfolio.append(doller_to_have_risk_free(strike_price))   \n",
    "results['strike_price'] = strike_prices\n",
    "results['option_premium'] = option_premiums\n",
    "results['option_premium_equal_probability'] = option_premiums_equal_probability\n",
    "results['stock_doller_in_portfolio'] = stock_dollers_in_portfolio\n",
    "results['risk_free_doller_in_portfolio'] = risk_free_dollers_in_portfolio\n",
    "results = results.set_index('strike_price')\n",
    "results.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Answer\n",
    "For \"task2\", I have to sell 1000 options, so I have to multiply the value in results by 1000.  \n",
    "For example, if I sell the right to buy stock A for $105 to a customer, it would look like this below.  \n",
    "(If it is negative, it indicates that we are taking out a loan.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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>option_price</th>\n",
       "      <th>option_price_equal_probability</th>\n",
       "      <th>stock_doller_in_portfolio</th>\n",
       "      <th>risk_free_doller_in_portfolio</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>strike_price</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>105</th>\n",
       "      <td>5000.099461</td>\n",
       "      <td>7499.983423</td>\n",
       "      <td>50000.0</td>\n",
       "      <td>-44999.900539</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              option_price  option_price_equal_probability  \\\n",
       "strike_price                                                 \n",
       "105            5000.099461                     7499.983423   \n",
       "\n",
       "              stock_doller_in_portfolio  risk_free_doller_in_portfolio  \n",
       "strike_price                                                            \n",
       "105                             50000.0                  -44999.900539  "
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results[105:106] * 1000"
   ]
  }
 ],
 "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",
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