qmcversusmc_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
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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]

*/


/*
 * SobolVersusMonteCarlo.java
 *
 * Created on April 21, 2002, 2:21 PM
 */

package Examples.Pricing;

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

/** <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 probability
 * that Monte Carlo beats the Sobol sequence is computed from a user defined 
 * number of Monte Carlo runs. The number of simulated paths is user defined.
 * </p>
 *
 * @author  java
 */
public class QMCversusMC_2 {
    
   public static void main(String[] args)
   throws java.io.FileNotFoundException, java.io.IOException
   {
      int  T, 
           nPaths,
           nStrikes=16,
           nRuns,
           nSignChange=5,       // irrelevant, but needed for asset constructor
           ldSequence;   // flag

      
       
      double S_0=50,
             mu=0.0,
             sigma=0.4,
             q=0.0,
             r=0.0,
             dt,
             K_min=45,
             K_max=90,
             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 probability that Monte Carlo beats QMC sequence is computed\n"+
       "from a number of Monte Carlo runs.\n");
      
      
      // main loop
      while(true){
          
      
      // get user input    
          
      System.out.print
      ("Which low discrepancy sequence should be used:\n"+
       "Halton ("+ConstantVolatilityAssetQMC.HALTON+
       ") or Sobol ("+ConstantVolatilityAssetQMC.SOBOL+")?\n\n"+
       "Sequence: ");
      ldSequence=io.readInt();
      
      String sqName=" ";
      switch(ldSequence)
      {
          case ConstantVolatilityAssetQMC.HALTON: sqName="Halton"; break;
          case ConstantVolatilityAssetQMC.SOBOL:  sqName="Sobol"; 
      }

      System.out.print("Enter dimension: ");
      T=io.readInt();
      dt=1.0/T;              // size of time step
      
      System.out.print("\nEnter number of Monte Carlo runs: ");
      nRuns=io.readInt();
      
      System.out.print("Enter number of paths per run: ");
      nPaths=io.readInt();
      
 
      
      // Q[j] is the probability that Sobol beats Monte Carlo at strike K_j
      double[] Q=new double[nStrikes];  
      
      // e[j] error of Sobol price at strike K_j in percent of true price
      double[] e=new double[nStrikes]; 
      
      // the underlying with ordinary random dynamics
      ConstantVolatilityAsset asset=new ConstantVolatilityAsset
      (T,dt,nSignChange,S_0,r,q,mu,sigma);

      
      // the underlying with quasi random dynamics driven by quasi
      // normal increments
      ConstantVolatilityAssetQMC 
      assetQMC=new ConstantVolatilityAssetQMC
      (T,dt,nSignChange,S_0,r,q,mu,sigma,ldSequence);

      
      // loop over the strikes
      LoopStatus loopStatus=new LoopStatus();
      long before=System.currentTimeMillis();
      int loops=0;
   
      for(int j=0;j<nStrikes;j++)
      {
          int N=nStrikes-1;
          K=K_min+(K_max-K_min)*j/N;         
               
          // the call as path independent option to ensure
          // full paths are computed when option price is evaluated.
               
          // the call based on QMC asset
          CallAsPathDependent callQMC=new CallAsPathDependent(K,assetQMC);

               
          // the call based on Monte Carlo asset
          CallAsPathDependent call=new CallAsPathDependent(K,asset);
       
             
          // analytic price
          double price=call.discountedAnalyticPrice(0);
               
     
          // QMC Monte Carlo price, absolute and relative error
          double priceQMC=callQMC.discountedMonteCarloPrice(nPaths),
                 abserrQMC=Math.abs(price-priceQMC),
                 relerrQMC=abserrQMC/price;
               

          // nRun Monte Carlo runs
          int mc_wins=0;             // number of times MC beats Sobol
          for(int l=0;l<nRuns;l++)
          {
              double priceMC=call.discountedMonteCarloPrice(nPaths),
                     abserrMC=Math.abs(price-priceMC);
              if(abserrMC<abserrQMC)mc_wins++;
              //progress report every run
              loops++;
              if(loops%100==99)
              loopStatus.progressReport(loops,nStrikes*nRuns,100,before); 
          }
               
          Q[j]=1.0*mc_wins/nRuns;
          e[j]=relerrQMC;
          
      } // end for j
          
           
      double y_axis_min=-e[nStrikes-1]/10;

      JGraph jGraph=new JGraph(K_min,K_max);
      jGraph.addSeries(Q,"Probability that MC beats QMC");
      jGraph.addSeries(e,"QMC price relative error");
      jGraph.setTitle("QMC ("+sqName+") versus MC, dimension "+T);
      jGraph.setXAxisLabel("Call strike");
      jGraph.setYAxisMin(y_axis_min);
           
      jGraph.setVisible(true);
      String filename="QMCversusMC_"+T+".dat";
      //jGraph.saveAsEPS(filename);
      jGraph.saveAsPNG();
      jGraph.saveAsASCII(filename);
      
      
      } // end main 
      
   
              
    } // end main
       

} // end SobolVesrusMonteCarlo