BlackScholes.java


Below is the syntax highlighted version of BlackScholes.java from §2.2 Libraries.


/******************************************************************************
 *  Compilation:  javac BlackScholes.java MyMath.java
 *  Execution:    java BlackScholes s x r sigma t
 *  
 *  Reads in five command line inputs and calculates the option price
 *  according to the Black-Scholes formula.
 *
 *  % java BlackScholes 23.75 15.00 0.01 0.35 0.5
 *  8.879159279691955                                  (actual =  9.10)
 *      
 *  % java BlackScholes 30.14 15.0 0.01 0.332 0.25
 *  15.177462481562186                                 (actual = 14.50)
 *
 *
 *  Information calculated based on closing data on Monday, June 9th 2003.
 *
 *      Microsoft:   share price:             23.75
 *                   strike price:            15.00
 *                   risk-free interest rate:  1%
 *                   volatility:              35%          (historical estimate)
 *                   time until expiration:    0.5 years
 *
 *       GE:         share price:             30.14
 *                   strike price:            15.00
 *                   risk-free interest rate   1%
 *                   volatility:              33.2%         (historical estimate)
 *                   time until expiration     0.25 years
 *
 *
 *  Reference:  http://www.hoadley.net/options/develtoolsvolcalc.htm
 *
 ******************************************************************************/


public class BlackScholes {

    // Black-Scholes formula
    public static double callPrice(double s, double x, double r, double sigma, double t) {
        double d1 = (Math.log(s/x) + (r + sigma * sigma/2) * t) / (sigma * Math.sqrt(t));
        double d2 = d1 - sigma * Math.sqrt(t);
        return s * Gaussian.cdf(d1) - x * Math.exp(-r*t) * Gaussian.cdf(d2);
    }

    // estimate by Monte Carlo simulation
    public static double call(double s, double x, double r, double sigma, double t) {
        int n = 10000;
        double sum = 0.0;
        for (int i = 0; i < n; i++) {
            double eps = StdRandom.gaussian();
            double price = s * Math.exp(r*t - 0.5*sigma*sigma*t + sigma*eps*Math.sqrt(t));
            double value = Math.max(price - x, 0);
            sum += value;
        }
        double mean = sum / n;
     
        return Math.exp(-r*t) * mean;
    }

    // estimate by Monte Carlo simulation
    public static double call2(double s, double x, double r, double sigma, double t) {
        int n = 10000;
        double sum = 0.0;
        for (int i = 0; i < n; i++) {
            double price = s;
            double dt = t/10000.0;
            for (double time = 0; time <= t; time += dt) {
                price += r*price*dt +sigma*price*Math.sqrt(dt)*StdRandom.gaussian();
            }
            double value = Math.max(price - x, 0);
            sum += value;
        }
        double mean = sum / n;
     
        return Math.exp(-r*t) * mean;
    }



    public static void main(String[] args) {
        double s     = Double.parseDouble(args[0]);
        double x     = Double.parseDouble(args[1]);
        double r     = Double.parseDouble(args[2]);
        double sigma = Double.parseDouble(args[3]);
        double t     = Double.parseDouble(args[4]);
        StdOut.println(callPrice(s, x, r, sigma, t));
        StdOut.println(call(s, x, r, sigma, t));
        StdOut.println(call2(s, x, r, sigma, t));
    }
}


Copyright © 2000–2011, Robert Sedgewick and Kevin Wayne.
Last updated: Tue Aug 30 09:58:33 EDT 2016.