qmcversusmc_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
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

Copyright (C) Michael J. Meyer

[e-mail]
[e-mail]

*/


/*
 * QMCversusMC_1.java
 *
 * Created on May 2, 2002, 10:30 AM
 */

package Examples.Pricing;

import com.skylit.io.EasyReader;
import Statistics.*;
import jas.hist.*;
import QuasiRandom.*;
import Market.*;
import Options.*;
import Graphics.Frame;


/** <p>A call on a constant volatility asset is valued using Monte Carlo
 *  and Quasi Monte Carlo simulation using the Sobol sequence.
 *  The valuation is carried out as a problem in any user defined dimension
 *  (the number of time steps to the horizon).</p>
 *
 * <p>The results are compared to the analytic call price and the relative 
 * error of the following methods compared:</p>
 *
 *<ul>
 *  <li>Monte Carlo simulation (Meresenne twister)</li>
 *  <li>Quasi Monte Carlo, Sobol sequence.</li>
 *  <li>Quasi Monte Carlo, Halton sequence.</li>
 *</ul>
 *
 *<p>In each case uniform vectors are converted to normal ones using
 * the inverse normal CDF on each coordinate. The relative error of the Monte 
 * Carlo price is reported as a histogram over a user defined number of Monte 
 * Carlo runs. Quasi Monte Carlo prices are deterministic, so only the
 * value of the relative error is reported.</p>
 *
 *<p>The user chooses the number of simulated paths for each Monte Carlo or 
 * Quasi Monte Carlo computation.
 * </p>
 *
 * @author  Michael J. Meyer
 */

public class QMCversusMC_1 {
    
   public static void main(String[] args)
   throws java.io.FileNotFoundException, java.io.IOException
   {
      int  T, 
           nPaths,           // number of paths per run
           nRuns,            // number of Monte Carlo runs
           nSignChange=5,    // irrelevant, but needed for asset constructor
           nBins=100;        // number of bins for histogram of MC price errors

      
       
      double S_0=50,
             mu=0.0,
             sigma=0.4,
             q=0.0,
             r=0.0,
             dt,
             K;
      
      
      // read dimension and number of Monte Carlo runs:
      EasyReader io=new EasyReader();
      
      System.out.println
      ("Call price will be computed by QMC and ordinary Monte Carlo\n"+
       "The dimension is the number T of time steps to call expiry.\n"+
       "The QMC relative error (Halton and Sobol) and histogram of Monte Carlo"+
       "\nrelative errors (user chooses number of runs) are computed.\n"+
       "S(0)="+S_0+".\n\n");
      
      
      // main loop
      while(true){
          
      System.out.print("Enter call strike: ");
      K=io.readDouble();
      System.out.print("Enter dimension: ");
      T=io.readInt();
      dt=1.0/T;              // size of time step
      
      System.out.print("Enter number of paths per simulation: ");
      nPaths=io.readInt();
      
      System.out.print("Enter number of Monte Carlo runs: ");
      nRuns=io.readInt();
            
      // ordinary Monte Carlo dynamics
      
      // the underlying
      ConstantVolatilityAsset asset=new ConstantVolatilityAsset
      (T,dt,nSignChange,S_0,r,q,mu,sigma);
      
      // the call as path independent option to ensure
      // full paths are computed when option price is evaluated.
      final CallAsPathDependent call=new CallAsPathDependent(K,asset);
      
      // analytic call price
      final double price=call.discountedAnalyticPrice(0);


      
      // QMC dynamics driven by the Sobol sequence
      
      // the underlying 
      ConstantVolatilityAssetQMC assetSOBOL=new ConstantVolatilityAssetQMC
      (T,dt,nSignChange,S_0,r,q,mu,sigma,ConstantVolatilityAssetQMC.SOBOL);
      
      // the call
      CallAsPathDependent callSOBOL=new CallAsPathDependent(K,assetSOBOL);
      
      // call Sobol price
      double priceSOBOL=callSOBOL.discountedMonteCarloPrice(0,nPaths);

      
      
      // QMC dynamics driven by the Sobol sequence
      
      // the underlying 
      ConstantVolatilityAssetQMC assetHALTON=new ConstantVolatilityAssetQMC
      (T,dt,nSignChange,S_0,r,q,mu,sigma,ConstantVolatilityAssetQMC.HALTON);
      
      // the call 
      CallAsPathDependent callHALTON=new CallAsPathDependent(K,assetHALTON);
      
      // call Halton price
      double priceHALTON=callHALTON.discountedMonteCarloPrice(0,nPaths);
      
      
      
      // the relative errors
      
      // make final so can be accessed by inner class
      final int N=nPaths;
      
      // Monte Carlo relative error as a random variable
      RandomVariable errorMC=new RandomVariable(){
          
          public double getValue(int t)
          {
               double priceMC=call.discountedMonteCarloPrice(0,N),
                      relErrorMC=(price-priceMC)/price;
               return 100*relErrorMC;
          }
      }; // end errorMC
      
      // histogram of Monte Carlo price relative errors
      JASHist histMC=errorMC.histogram
      (nRuns,nBins,true,"MC","price relative error (%)");
      histMC.setTitle("Call strike="+K+", dim="+T);
      
      // Halton price  relative error
      double relErrorHALTON=100*(price-priceHALTON)/price;
      
      // Sobol price and relative error
      double relErrorSOBOL=100*(price-priceSOBOL)/price;
      
      // add the Sobol and Halton price to the histogram as one point  
      // data sources
      PointDataSource 
      haltonBar=new PointDataSource
      ("Halton",relErrorHALTON,0.05,0.2,java.awt.Color.red);
      histMC.addData(haltonBar).show(true);
      PointDataSource 
      sobolBar=new PointDataSource
      ("Sobol",relErrorSOBOL,0.05,0.2,java.awt.Color.green);
      histMC.addData(sobolBar).show(true);
      
      // add it to a JFrame and display it
      Graphics.Frame window=new Graphics.Frame("Histogram");
      window.setContentPane(histMC);
      window.setBounds(50,120,600,400);
      window.setVisible(true);
      
      // save it
      String filename="Pictures/Histograms/QMCversusMC/HistDim"+T+".eps";
      window.saveAsEPS(filename);
      
      System.out.println("\n\nContinue (1/0)");
      int cnt=io.readInt();
      if(cnt==0)break;
      
      } // end main loop
    
   } // end main
    
 
    
} // end QMCversusMC