AsianGBM2.java

package tutorial;
 
import umontreal.ssj.rng.*;
 
import java.io.IOException;
 
import umontreal.ssj.probdist.NormalDist;
import umontreal.ssj.mcqmctools.*;
import umontreal.ssj.stat.Tally;
import umontreal.ssj.util.*;
 
// Same as AsianGBM, but this version implements the interface MonteCarloModelDouble.
public class AsianGBM2 implements MonteCarloModelDouble {
   double strike; // Strike price.
   int s; // Number of observation times.
   double discount; // Discount factor exp(-r * zeta[t]).
   double[] muDelta; // Differences * (r - sigma^2/2).
   double[] sigmaSqrtDelta; // Square roots of differences * sigma.
   double[] logS; // Log of the GBM process: logS[t] = log (S[t]).
 
   // Array zeta[0..s] must contain zeta[0]=0.0, plus the s observation times.
   public AsianGBM2(double r, double sigma, double strike, double s0, int s, double[] zeta) {
      this.strike = strike;
      this.s = s;
      discount = Math.exp(-r * zeta[s]);
      double mu = r - 0.5 * sigma * sigma;
      muDelta = new double[s];
      sigmaSqrtDelta = new double[s];
      logS = new double[s + 1];
      double delta;
      for (int j = 0; j < s; j++) {
         delta = zeta[j + 1] - zeta[j];
         muDelta[j] = mu * delta;
         sigmaSqrtDelta[j] = sigma * Math.sqrt(delta);
      }
      logS[0] = Math.log(s0);
   }
 
   // Generates the process S.
   public void simulate(RandomStream stream) {
      for (int j = 0; j < s; j++)
         logS[j + 1] = logS[j] + muDelta[j] + sigmaSqrtDelta[j] * NormalDist.inverseF01(stream.nextDouble());
   }
 
   // Computes and returns the discounted option payoff.
   public double getPerformance() {
      double average = 0.0; // Average of the GBM process.
      for (int j = 1; j <= s; j++)
         average += Math.exp(logS[j]);
      average /= s;
      if (average > strike)
         return discount * (average - strike);
      else
         return 0.0;
   }
 
   public int getDimension() {
      return s;
   }
 
   public String toString() {
      return "Asian option under GBM, for testing";
   }
   
   public String getTag() {
      return "AsianGBM";
   }
 
   public static void main(String args[]) throws IOException {
      int s = 12;
      double[] zeta = new double[s + 1];
      zeta[0] = 0.0;
      for (int j = 1; j <= s; j++)
         zeta[j] = (double) j / (double) s;
      AsianGBM2 model = new AsianGBM2(0.05, 0.5, 100.0, 100.0, s, zeta);
      Tally statValue = new Tally("Stats on value of Asian option");
      Chrono timer = new Chrono();
      int n = 100000;
      MonteCarloExperiment.simulateRuns(model, n, new LFSR113(), statValue);
      statValue.setConfidenceIntervalStudent();
      System.out.println(statValue.report(0.95, 3));
      System.out.println("Total CPU time:      " + timer.format() + "\n");
   }
}