commit

Author: gsamarakoon

.gitignore

@@ -67,3 +67,4 @@ target/
 # Mac
 .DS_Store
 
+dcf/

Quant finance and Algo trading - Derivatives pricing - Black-Scholes Model implementation via Monte-Carlo .ipynb

@@ -1,6 +1,120 @@
 {
- "cells": [],
- "metadata": {},
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 159,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import math\n",
+    "import time"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 176,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Call option price with Monte carlo approach:   10.45805672244926\n",
+      "Put option price wiht Monte carlo approach:   5.574003411737752\n"
+     ]
+    }
+   ],
+   "source": [
+    "class OptionPricing:\n",
+    "    def __init__(self, s0, E, T, rf,sigma, iterations):\n",
+    "        self.s0 = s0\n",
+    "        self.E = E\n",
+    "        self.T = T\n",
+    "        self.rf = rf\n",
+    "        self.iterations = iterations\n",
+    "        self.sigma = sigma\n",
+    "    \n",
+    "    def call_option_simulation(self):\n",
+    "        #2 columns. column one for zeors, and column 2 for payoff max(0, S-E) for call option\n",
+    "        option_data = np.zeros([self.iterations,2])\n",
+    "        \n",
+    "        #1d array with items as many as Iterations\n",
+    "        rand = np.random.normal(0,1,[1, self.iterations])\n",
+    "        \n",
+    "        #stock price equation\n",
+    "        stock_price = self.s0*np.exp(self.T*(self.rf- 0.5*self.sigma**2)+self.sigma*np.sqrt(self.T)*rand)\n",
+    "        \n",
+    "        #calculate S-E\n",
+    "        option_data[:,1] = stock_price - self.E\n",
+    "        \n",
+    "        #np.amax() to return the max(0,S-E)\n",
+    "        average = np.sum(np.amax(option_data, axis=1))/(float(self.iterations))\n",
+    "        \n",
+    "        #using exp(-rT) to discount the price\n",
+    "        return np.exp(-1.0*self.rf*self.T)*average\n",
+    "    \n",
+    "    \n",
+    "    def put_option_simulation(self):\n",
+    "        \n",
+    "        #2 columns. column one for zeors, and column 2 for payoff max(0, S-E) for call option\n",
+    "        option_data = np.zeros([self.iterations,2])\n",
+    "        \n",
+    "        #1d array with items as many as Iterations\n",
+    "        rand = np.random.normal(0,1,[1, self.iterations])\n",
+    "               \n",
+    "        #stock price equation\n",
+    "        stock_price = self.s0*np.exp(self.T*(self.rf-0.5*self.sigma**2)+self.sigma*np.sqrt(self.T)*rand)\n",
+    "        \n",
+    "        #calculate E-S - put options\n",
+    "        option_data[:,1] = self.E - stock_price\n",
+    "        \n",
+    "        #np.amax() to return the max(0,S-E)\n",
+    "        average = np.sum(np.amax(option_data,axis=1))/float(self.iterations)\n",
+    "        \n",
+    "        #using exp(-rT) to discount the price\n",
+    "        return np.exp(-1.0*self.rf*self.T)*average\n",
+    "    \n",
+    "if __name__ == \"__main__\":\n",
+    "    s0 = 100                  #stock price at t=0\n",
+    "    E = 100                   #strike price\n",
+    "    T = 1                     #time to maturity\n",
+    "    rf = 0.05                 #risk free rate\n",
+    "    sigma = 0.2               #volatility of underlying stock\n",
+    "    iterations = 1000000     #number of iterations in the Monte carlo simulation\n",
+    "    \n",
+    "    model = OptionPricing(s0,E,T,rf,sigma,iterations)\n",
+    "    print ('Call option price with Monte carlo approach:  ', model.call_option_simulation())\n",
+    "    print('Put option price wiht Monte carlo approach:  ', model.put_option_simulation())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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": "3.6.5"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 2
 }