lognormallibor.java

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/* 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]

*/

/*
 * LogNormalLibor.java
 *
 * Created on September 5, 2002, 9:00 AM
 */

package Examples.Libor;

import Libor.LiborProcess.*;
import Statistics.*;
import com.skylit.io.EasyReader;

/** <p>Computes histograms of the errors with which the log-normal approximations
 *  <code>L0_j(T_j)</code> and <code>L1_j(T_j)</code> approximate true Libor
 *  <code>L_j(T_j)</code>. Simulations show that the approximations can be
 *  much larger than true Libor with a very small probability. In other words
 *  the errors</p>
 *  <p>
 *  <center>
 *  <code>err0:=L_j(T_j)-L0_j(T_j)</code>
 *  and 
 *  <code>err1:=L_j(T_j)-L1_j(T_j)</code>
 *  </center>
 *  </p>
 *  <p>can assume very large negative values (with small probability). If these
 *  values were displayed resolution of the display of the histogram would
 *  suffer. Thus we cut the values off at the low and and compute
 *  histograms of the random variables</p>
 *  <p>
 *  <center>
 *  <code>D0:=max{err0,-0.02}</code>
 *  and 
 *  <code>D1:=max{err1,-0.02}</code>
 *  </center>
 *  </p>
 *  The outliers below then show up as a point mass at -0.02. All Libors are
 *  initialized at <code>L_j(0)=0.04</code> with annulaized volatilities
 *  of about <code>0.39</code>.
 *
 * @author  Michael J. Meyer
 */
public class LogNormalLibor {
   
       
       public static void main(String[] args)
       {
           EasyReader io=new EasyReader();
           
           // read dimension n, index j
           
           System.out.print
           ("LIBOR: computing histograms of approximation errors\n"+
            "L_i(T_i)-L0_i(T_i) and L_i(T_i)-L1_i(T_i).\n");
           
           // main loop
           int more=1;
           while(more==1){
               
           System.out.print
           ("Enter dimension n of Libor process: ");
           final int n=io.readInt();
           
           System.out.print("Enter Libor index j: ");
           final int j=io.readInt(); 
           
           System.out.print("Enter number of sample paths: ");
           final int nPaths=io.readInt(); 
           
           // Libor parameter sample 
           final LMM_Parameters 
           lmmParams=new LMM_Parameters(n,LMM_Parameters.CS);
           final LiborProcess LP=new LiborProcess(lmmParams);
           
           // D0=L_j(T_j)-L0_j(T_j)
           final RandomVariable D0=new RandomVariable(){
               
               public double getValue(int t)
               {
                   LP.newPath(j,j,true,true,false);
                   double diff=LP.L(j,j)-LP.L0(j,j);
                   // cutting off outliers
                   return (diff>-0.02)? diff : -0.02;
               }
           }; // end D0
           
           
           // D0=L_j(T_j)-L1_j(T_j)
           final RandomVariable D1=new RandomVariable(){
               
               public double getValue(int t)
               {
                   LP.newPath(j,j,true,false,true);
                   double diff=LP.L(j,j)-LP.L1(j,j);
                   // cutting off outliers
                   return (diff>-0.02)? diff : -0.02;
               }
           }; // end D1
           
           int nBins=200;
           
          
           // HISTOGRAMS
           String title="log-normal approximation error",
                  xAxisLabel="L_"+j+"(T_"+j+")-L0_"+j+"(T_"+j+")";;
           D0.displayHistogram(nPaths,nBins,true,title,xAxisLabel);

           title="log-normal approximation error";
           xAxisLabel="L_"+j+"(T_"+j+")-L1_"+j+"(T_"+j+")";;
           D1.displayHistogram(nPaths,nBins,true,title,xAxisLabel);
          
           /* MEAN AND STANDARD DEVIATION
           double[] d0mstdv=D0.meanAndStandardDeviation(nPaths);
           String message=
           "\nL0-APPROXIMATION:\n"+
           "Approximation error L_"+j+"(T_"+j+")-L0_"+j+"(T_"+j+")\n"+
           "mean: "+d0mstdv[0]+"\n"+
           "standard deviation: "+d0mstdv[1];
           System.out.println(message);
           
           double[] d1mstdv=D1.meanAndStandardDeviation(nPaths);
           message=
           "\nL1-APPROXIMATION:\n"+
           "Approximation error L_"+j+"(T_"+j+")-L1_"+j+"(T_"+j+")\n"+
           "mean: "+d1mstdv[0]+"\n"+
           "standard deviation: "+d1mstdv[1];
           System.out.println(message);
           */
           
           System.out.println("Another run? (0/1)");
           more=io.readInt();
           
           } // end main loop
           
       } // end main
           
} // end LogNormalLibor