controlvariatetest_1.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
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
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Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

Copyright (C) Michael J. Meyer

[e-mail]
[e-mail]

*/



/*
 * ControlVariateTest_1.java
 *
 * Created on January 20, 2002, 5PM
 */



 
package Examples.ControlVariates;

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

 

/** 
 * <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>The Monte Carlo mean and controlled Monte Carlo mean of X using a sample 
 * of size 100 are defined as random variables in their own right and the
 * variance of these random variables computed.</p>
 *
 * <p>The two variances are computed from a sample of size 100</p>
 *
 * <p>The idea is to check if use of the control variate does reduce 
 * the variance</p> 
 *
 * @author  Michael J. Meyer
 */
public class ControlVariateTest_1{

    public static void main(String[] args)
    {   
        final int nSamples=100;  // sample size
        
        /* The random variable X without control variate.
         * Recall that Random.U1() delivers a uniform draw from [0,1] 
         * and Random.STN() delivers a standard normal deviate.
         * No conditioning so the time parameter t is ignored.
         */
        final 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
        
        // the Monte Carlo mean as a random variable
        final RandomVariable mean=new RandomVariable(){
        
            public double getValue(int t)
            {
                return X.expectation(nSamples);
            } // end getValue
        
        }; //end X
        
     
        // variance of the uncontrolled mean
        double variance=mean.variance(100);
        
        String 
        message="Variance of uncontrolled mean = "+variance;
        System.out.println(message);
        
        
        
        // The random variable X with control variate.
        final 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
        
        
        // the controlled Monte Carlo mean as a random variable
        final RandomVariable controlled_mean=new RandomVariable(){
        
            public double getValue(int t)
            {
                return Xc.expectation(nSamples);
            } // end getValue
        
        }; //end Xc
        
     
        // variance of the controlled mean
        double controlled_variance=controlled_mean.variance(100);
        
        message="Variance of controlled mean = "+controlled_variance;
        System.out.println(message);
        
      
        
        
    } // end main
    
 } // end CVTest1