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finmath lib is a Mathematical Finance Library in Java.
It provides algorithms and methodologies related to mathematical finance.
package net.finmath.montecarlo.assetderivativevaluation.models;
import java.util.Map;
import net.finmath.exception.CalculationException;
import net.finmath.marketdata.model.curves.DiscountCurve;
import net.finmath.montecarlo.model.AbstractProcessModel;
import net.finmath.montecarlo.model.ProcessModel;
import net.finmath.stochastic.RandomVariable;
/**
* This class implements a Variance Gamma Model, that is, it provides the drift and volatility specification
* and performs the calculation of the numeraire (consistent with the dynamics, i.e. the drift).
*
* The model is
* \[
* dS_t = r S dt + S dL, \quad S(0) = S_{0},
* \]
* \[
* dN = r N dt, \quad N(0) = N_{0},
* \]
*
* where the process L is a {@link net.finmath.montecarlo.VarianceGammaProcess}.
*
* @author Alessandro Gnoatto
* @see net.finmath.montecarlo.process.MonteCarloProcess The interface for numerical schemes.
* @see net.finmath.montecarlo.model.ProcessModel The interface for models provinding parameters to numerical schemes.
* @version 1.0
*/
public class VarianceGammaModel extends AbstractProcessModel {
private final double initialValue;
private final DiscountCurve discountCurveForForwardRate;
private final double riskFreeRate; // Actually the same as the drift (which is not stochastic)
private final DiscountCurve discountCurveForDiscountRate;
private final double discountRate; // Constant rate, used if discountCurveForForwardRate is null
private final double sigma;
private final double theta;
private final double nu;
/**
* Construct a Variance Gamma model with discount curves for the forward price (i.e. repo rate minus dividend yield) and for discounting.
*
* @param initialValue \( S_{0} \) - spot - initial value of S
* @param discountCurveForForwardRate The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate
* @param discountCurveForDiscountRate The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate
* @param sigma The parameter \( \sigma \)
* @param theta The parameter \( \theta \)
* @param nu The parameter \( \nu \)
*/
public VarianceGammaModel(final double initialValue, final DiscountCurve discountCurveForForwardRate,
final DiscountCurve discountCurveForDiscountRate, final double sigma, final double theta, final double nu) {
super();
this.initialValue = initialValue;
this.discountCurveForForwardRate = discountCurveForForwardRate;
riskFreeRate = Double.NaN;
this.discountCurveForDiscountRate = discountCurveForDiscountRate;
discountRate = Double.NaN;
this.sigma = sigma;
this.theta = theta;
this.nu = nu;
}
/**
* Construct a Variance Gamma model with constant rates for the forward price (i.e. repo rate minus dividend yield) and for the discount curve.
*
* @param initialValue \( S_{0} \) - spot - initial value of S
* @param riskFreeRate The constant risk free rate for the drift (repo rate of the underlying).
* @param discountRate The constant rate used for discounting.
* @param sigma The parameter \( \sigma \)
* @param theta The parameter \( \theta \)
* @param nu The parameter \( \nu \)
*/
public VarianceGammaModel(final double initialValue, final double riskFreeRate, final double discountRate, final double sigma, final double theta,
final double nu) {
super();
this.initialValue = initialValue;
discountCurveForForwardRate = null;
this.riskFreeRate = riskFreeRate;
discountCurveForDiscountRate = null;
this.discountRate = discountRate;
this.sigma = sigma;
this.theta = theta;
this.nu = nu;
}
/**
* Construct a Variance Gamma model with constant rates for the forward price (i.e. repo rate minus dividend yield) and for the discount curve.
*
* @param initialValue \( S_{0} \) - spot - initial value of S
* @param riskFreeRate The constant risk free rate for the drift (repo rate of the underlying).
* @param sigma The parameter \( \sigma \)
* @param theta The parameter \( \theta \)
* @param nu The parameter \( \nu \)
*/
public VarianceGammaModel(final double initialValue, final double riskFreeRate, final double sigma, final double theta, final double nu) {
this(initialValue,riskFreeRate,riskFreeRate,sigma,theta,nu);
}
@Override
public int getNumberOfComponents() {
return 1;
}
@Override
public RandomVariable applyStateSpaceTransform(final int componentIndex, final RandomVariable randomVariable) {
return randomVariable.exp();
}
@Override
public RandomVariable applyStateSpaceTransformInverse(final int componentIndex, final RandomVariable randomVariable) {
return randomVariable.log();
}
@Override
public RandomVariable[] getInitialState() {
return new RandomVariable[] {getProcess().getStochasticDriver().getRandomVariableForConstant(Math.log(initialValue))};
}
@Override
public RandomVariable getNumeraire(final double time) throws CalculationException {
if(discountCurveForDiscountRate != null) {
return getProcess().getStochasticDriver().getRandomVariableForConstant(1.0/discountCurveForDiscountRate.getDiscountFactor(time));
}
else {
return getProcess().getStochasticDriver().getRandomVariableForConstant(Math.exp(discountRate * time));
}
}
@Override
public RandomVariable[] getDrift(final int timeIndex, final RandomVariable[] realizationAtTimeIndex,
final RandomVariable[] realizationPredictor) {
double riskFreeRateAtTimeStep = 0.0;
if(discountCurveForForwardRate != null) {
final double time = getTime(timeIndex);
final double timeNext = getTime(timeIndex+1);
riskFreeRateAtTimeStep = Math.log(discountCurveForForwardRate.getDiscountFactor(time) / discountCurveForForwardRate.getDiscountFactor(timeNext)) / (timeNext-time);
}else {
riskFreeRateAtTimeStep = riskFreeRate;
}
return new RandomVariable[] {getProcess().getStochasticDriver()
.getRandomVariableForConstant(riskFreeRateAtTimeStep-1/nu * Math.log(1/(1.0-theta*nu-0.5*sigma*sigma*nu)))};
}
@Override
public RandomVariable[] getFactorLoading(final int timeIndex, final int componentIndex,
final RandomVariable[] realizationAtTimeIndex) {
final RandomVariable[] factors = new RandomVariable[1];
factors[0] = getProcess().getStochasticDriver().getRandomVariableForConstant(1.0);
return factors;
}
/*
* (non-Javadoc)
* @see net.finmath.montecarlo.model.ProcessModel#getRandomVariableForConstant(double)
*/
@Override
public RandomVariable getRandomVariableForConstant(final double value) {
return getProcess().getStochasticDriver().getRandomVariableForConstant(value);
}
@Override
public ProcessModel getCloneWithModifiedData(final Map dataModified) throws CalculationException {
final double newInitialValue = (double) dataModified.getOrDefault("initialValue", initialValue);
final double newRiskFreeRate = (double) dataModified.getOrDefault("riskFreeRate", riskFreeRate);
final double newDiscountRate = (double) dataModified.getOrDefault("discountRate", discountRate);
final double newSigma = (double) dataModified.getOrDefault("volatility", sigma);
final double newTheta = (double) dataModified.getOrDefault("volatility", theta);
final double newNu = (double) dataModified.getOrDefault("volatility", nu);
return new VarianceGammaModel(newInitialValue,newRiskFreeRate,newDiscountRate,newSigma,newTheta,newNu);
}
/**
* @return the discountCurveForForwardRate
*/
public DiscountCurve getDiscountCurveForForwardRate() {
return discountCurveForForwardRate;
}
/**
* @return the riskFreeRate
*/
public double getRiskFreeRate() {
return riskFreeRate;
}
/**
* @return the discountCurveForDiscountRate
*/
public DiscountCurve getDiscountCurveForDiscountRate() {
return discountCurveForDiscountRate;
}
/**
* @return the discountRate
*/
public double getDiscountRate() {
return discountRate;
}
/**
* @return the sigma
*/
public double getSigma() {
return sigma;
}
/**
* @return the theta
*/
public double getTheta() {
return theta;
}
/**
* @return the nu
*/
public double getNu() {
return nu;
}
/* (non-Javadoc)
* @see java.lang.Object#toString()
*/
@Override
public String toString() {
return "VarianceGammaModel [initialValue=" + initialValue + ", discountCurveForForwardRate="
+ discountCurveForForwardRate + ", riskFreeRate=" + riskFreeRate + ", discountCurveForDiscountRate="
+ discountCurveForDiscountRate + ", discountRate=" + discountRate + ", sigma=" + sigma + ", theta="
+ theta + ", nu=" + nu + "]";
}
}
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