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finmath lib is a Mathematical Finance Library in Java.
It provides algorithms and methodologies related to mathematical finance.
/*
* (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
*
* Created on 29.06.2004
*/
package net.finmath.montecarlo;
import java.io.Serializable;
import net.finmath.functions.GammaDistribution;
import net.finmath.randomnumbers.MersenneTwister;
import net.finmath.stochastic.RandomVariable;
import net.finmath.time.TimeDiscretization;
/**
* Implementation of a time-discrete n-dimensional Gamma process
* \(
* \Gamma = (\Gamma_{1},\ldots,\Gamma_{n})
* \), where \( \Gamma_{i} \) is
* a Gamma process and \( \Gamma_{i} \), \( \Gamma_{j} \) are
* independent for i not equal j.
*
* The increments \( \Delta \Gamma \) are Gamma distributed with shape parameter shape * (t-s)
* for \( t-s = \Delta t \) and scale parameter 1.
*
* Here the dimension n is called factors since this Gamma process is used to
* generate multi-dimensional multi-factor Levy processes and there one might
* use a different number of factors to generate Levy processes of different
* dimension.
*
* The quintruppel (time discretization, number of factors, number of paths, seed, shape)
* defines the state of an object of this class, i.e., GammaProcess for which
* there parameters agree, generate the same random numbers.
*
* The class is immutable and thread safe. It uses lazy initialization.
*
* @author Christian Fries
* @version 1.6
*/
public class GammaProcess implements IndependentIncrements, Serializable {
/**
*
*/
private static final long serialVersionUID = -5430067621669213475L;
private final double shape;
private final double scale;
private final TimeDiscretization timeDiscretization;
private final int numberOfFactors;
private final int numberOfPaths;
private final int seed;
private final RandomVariableFactory randomVariableFactory = new RandomVariableFromArrayFactory();
private transient RandomVariable[][] gammaIncrements;
/**
* Construct a Gamma process with a given shape parameter.
*
* @param timeDiscretization The time discretization used for the Gamma increments.
* @param numberOfFactors Number of factors.
* @param numberOfPaths Number of paths to simulate.
* @param seed The seed of the random number generator.
* @param shape The shape parameter of the Gamma distribution.
* @param scale The scale parameter of the Gamma distribution.
*/
public GammaProcess(
final TimeDiscretization timeDiscretization,
final int numberOfFactors,
final int numberOfPaths,
final int seed,
final double shape,
final double scale) {
super();
this.timeDiscretization = timeDiscretization;
this.numberOfFactors = numberOfFactors;
this.numberOfPaths = numberOfPaths;
this.seed = seed;
this.shape = shape;
this.scale = scale;
gammaIncrements = null; // Lazy initialization
}
/**
* Construct a Gamma process with a given shape parameter.
*
* @param timeDiscretization The time discretization used for the Gamma increments.
* @param numberOfFactors Number of factors.
* @param numberOfPaths Number of paths to simulate.
* @param seed The seed of the random number generator.
* @param shape The shape parameter of the Gamma distribution.
*/
public GammaProcess(
final TimeDiscretization timeDiscretization,
final int numberOfFactors,
final int numberOfPaths,
final int seed,
final double shape) {
this(timeDiscretization, numberOfFactors, numberOfPaths, seed, shape, 1.0);
}
@Override
public IndependentIncrements getCloneWithModifiedSeed(final int seed) {
return new GammaProcess(getTimeDiscretization(), getNumberOfFactors(), getNumberOfPaths(), seed, shape);
}
@Override
public IndependentIncrements getCloneWithModifiedTimeDiscretization(final TimeDiscretization newTimeDiscretization) {
/// @TODO This can be improved: a complete recreation of the Gamma process wouldn't be necessary!
return new GammaProcess(newTimeDiscretization, getNumberOfFactors(), getNumberOfPaths(), getSeed(), shape);
}
@Override
public RandomVariable getIncrement(final int timeIndex, final int factor) {
// Thread safe lazy initialization
synchronized(this) {
if(gammaIncrements == null) {
doGenerateGammaIncrements();
}
}
/*
* For performance reasons we return directly the stored data (no defensive copy).
* We return an immutable object to ensure that the receiver does not alter the data.
*/
return gammaIncrements[timeIndex][factor];
}
/**
* Lazy initialization of gammaIncrement. Synchronized to ensure thread safety of lazy init.
*/
private void doGenerateGammaIncrements() {
if(gammaIncrements != null) {
return; // Nothing to do
}
// Create random number sequence generator
final MersenneTwister mersenneTwister = new MersenneTwister(seed);
// Allocate memory
final double[][][] gammaIncrementsArray = new double[timeDiscretization.getNumberOfTimeSteps()][numberOfFactors][numberOfPaths];
// Pre-calculate distributions
final GammaDistribution[] gammaDistributions = new GammaDistribution[timeDiscretization.getNumberOfTimeSteps()];
for(int timeIndex=0; timeIndex