controlvariatetest_2.java

金融资产定价,随机过程,MONTE CARLO 模拟 JAVA 程序和文档资料

/* WARANTY NOTICE AND COPYRIGHT
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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You should have received a copy of the GNU General Public License
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Copyright (C) Michael J. Meyer

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*/



/*
 * ControlVariateTest_2.java
 *
 * Created on January 20, 2002, 5PM
 */
 
package Examples.ControlVariates;

import Statistics.*;
import java.lang.Math.*;

 

/** <p>Compares a Monte Carlo mean to a Monte Carlo mean computed using a
 * control variate.</p>
 *
 * <p>We set up the random variable X=U+eN where U is uniform on [0,1], N
 * standard normal and independent of U and e=0.1. As a control variate we use 
 * Y=U-eN. Then the correlation rho(X,Y)=(1-12e^2)/(1+12e^2)=0.78571.</p>
 *
 * <p>We compute this correlation and also the mean of X both with and without 
 * the use of the control variate from a sample of 100,000 observations of X.
 * The objective is to see how much closer the controlled mean is to the true 
 * mean E(X)=1/2 than the uncontrolled mean.</p>
 *
 * @author  Michael J. Meyer
 */
public class ControlVariateTest_2{

    public static void main(String[] args)
    {   
        int nSamples=100;  // sample size
        
        /* X without control variate
         * Recall that Random.U1() delivers a uniform draw from [0,1] 
         * and Random.STN() delivers a standard normal deviate.
         */
        RandomVariable X=new RandomVariable(){
        
            public double getValue(int t)
            {
                double U=Random.U1(),   // uniform in [0,1]
                       N=Random.STN(),  // standard normal
                       e=0.1;
                return U+e*N;
                
             } // end getValue
        
        }; //end X
        
        //Monte Carlo mean without control variate
        double mean=X.expectation(nSamples);
        //cut this down to 5 decimals
        mean=1.0*Math.round(10000*mean)/10000;
        
        String 
        message="True mean = 1/2\n"+
                "Monte carlo mean without control variate = "+mean+
                "\n\n";
        System.out.println(message);
        
        // X with control variate
        ControlledRandomVariable Xc=new ControlledRandomVariable(){
        
            public double[] getControlledValue(int t)
            {
                double U=Random.U1(),   // uniform in [0,1]
                       N=Random.STN(),  // standard normal
                       e=0.1,
                       x=U+e*N,         // X
                       y=U-e*N;         // control variate Y
                       
                double[] result={x,y};
                
                return result;
                
            } // end getValue
             
            public double getControlVariateMean(int t)
            { return 0.5; }
        
        }; //end Xc
        
        
        //correlation of X with control variate
        double rho=Xc.correlationWithControlVariate(20000);
        //cut this down to 5 decimals
        rho=1.0*Math.round(10000*rho)/10000;
        
        //Monte Carlo mean with control variate
        mean=Xc.expectation(nSamples);
        //cut this down to 5 decimals
        mean=1.0*Math.round(10000*mean)/10000;
        
        message="Correlation with  control variate = "+rho+
                "\nMonte carlo mean with control variate = "+mean;
        System.out.println(message);
        
        
    } // end main
    
 } // end CVTest1