Pricing American-Options Using the Trinomial Model with Memoization

By Dongliang “Larry” Yi

1. Code

//  main.cpp

//  American_Option_Tri_Memoi

//

//  Created by Dongliang Yi on 11/23/15.

//  Copyright © 2015 Dongliang Yi. All rights reserved.

//

#include <iostream>

#include <iomanip>

#include <cmath>

#include <fstream>

#include <cstdlib>

#include <vector>

using namespace std;

//Used class for calculating the price with ease

class Option_Calculation

{

   

    //double **Call_Option;

    vector <vector <double> > Call_Option;//this is used for memoization for call;

    vector <vector <double> > Put_Option;//this is used for memoization for put;

    double up_factor, uptick_prob, downtick_prob, notick_prob, risk_free_rate, strike_price;

    double initial_stock_price, expiration_time, volatility, R;

    int no_of_divisions;

   

double max(double a, double b) {

    return (b < a )? a:b;

}

         

double american_call_option(int k, int i, double current_stock_price)

{

    // check whether there have been the value stored?

    if (Call_Option[k][i+no_of_divisions]> -0.1) {

        return Call_Option[k][i+no_of_divisions]; //shift "no_of_divisions" to store value

    }

   

    if (k == no_of_divisions)

    {

        //store the value

        Call_Option[k][i+no_of_divisions]=max(0.0, (current_stock_price - strike_price));

        return Call_Option[k][i+no_of_divisions];

    }

    else

    {

        //store the value

        Call_Option[k][i+no_of_divisions]=max((current_stock_price - strike_price),(uptick_prob*american_call_option(k+1, i+1, current_stock_price*up_factor)+(notick_prob)*american_call_option(k+1, i, current_stock_price)+(downtick_prob)*american_call_option(k+1, i-1, current_stock_price/up_factor))/R);

        return Call_Option[k][i+no_of_divisions];

    }

}

double american_put_option(int k, int i, double current_stock_price)

{

        // check whether there have been the value stored?

    if (Put_Option[k][i+no_of_divisions]> -0.1) {

        return Put_Option[k][i+no_of_divisions];

    }

   

    if (k == no_of_divisions)

    {

        //store the value

        Put_Option[k][i+no_of_divisions]=max(0.0, (strike_price - current_stock_price));

        return Put_Option[k][i+no_of_divisions];

    }

    else

    {

        //store the value

        Put_Option[k][i+no_of_divisions]=max((strike_price - current_stock_price),(uptick_prob*american_put_option(k+1, i+1, current_stock_price*up_factor) +notick_prob*american_put_option(k+1, i, current_stock_price)+ (downtick_prob)*american_put_option(k+1, i-1, current_stock_price/up_factor))/R);

        return Put_Option[k][i+no_of_divisions];

    }

}

public:

    void initialize(int argc, char* argv[])

    {

   

        sscanf (argv[1], "%lf", &expiration_time);

        sscanf (argv[2], "%d", &no_of_divisions);

        sscanf (argv[3], "%lf", &risk_free_rate);

        sscanf (argv[4], "%lf", &volatility);

        sscanf (argv[5], "%lf", &initial_stock_price);

        sscanf (argv[6], "%lf", &strike_price);

       

        R = exp(risk_free_rate*expiration_time/((float) no_of_divisions));

        up_factor = exp(volatility*sqrt((2*expiration_time)/((float) no_of_divisions)));

        uptick_prob = pow((sqrt(R) - 1/sqrt(up_factor))/(sqrt(up_factor)-1/sqrt(up_factor)),2);

        downtick_prob = pow((sqrt(up_factor) - sqrt(R))/(sqrt(up_factor)-1/sqrt(up_factor)),2);

        notick_prob = 1 - uptick_prob - downtick_prob;

       

       

        vector <double> temp(2*no_of_divisions+1,-1);

       

        for (int i = 0; i <= no_of_divisions; i++)

        {

            Put_Option.push_back(temp);

            Call_Option.push_back(temp);

        }

       

    }

   

    void print()

    {

       

        cout << "Recursive Trinomial American Option Pricing" << endl;

        cout << "Expiration Time (Years) = " << expiration_time << endl;

        cout << "Number of Divisions = " << no_of_divisions << endl;

        cout << "Risk Free Interest Rate = " << risk_free_rate << endl;

        cout << "Volatility (%age of stock value) = " << volatility*100 << endl;

        cout << "Initial Stock Price = " << initial_stock_price << endl;

        cout << "Strike Price = " << strike_price << endl;

        cout << "--------------------------------------" << endl;

        cout << "R = " << R << endl;

        cout << "Up Factor = " << up_factor << endl;

        cout << "Uptick Probability = " << uptick_prob << endl;

        cout << "Downtick Probability = " << downtick_prob << endl;

        cout << "Notick Probability = " << notick_prob << endl;

        cout << "--------------------------------------" << endl;

        cout << "Trinomial Price of an American Call Option = " << american_call_option(0, 0,initial_stock_price) << endl;

        cout << "Trinomial Price of an American Put Option = " << american_put_option(0, 0, initial_stock_price) << endl;

    }

      

};

int main (int argc, char* argv[])

{

   

    Option_Calculation Option_Cal;

    Option_Cal.initialize(argc, argv);

    Option_Cal.print();

   

}

2.     Result

Got questions? I’m happy to discuss. Email me at yidongliang@gmail.com