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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.modelling.descriptor.VarianceGammaModelDescriptor;
import net.finmath.montecarlo.RandomVariableFactory;
import net.finmath.montecarlo.RandomVariableFromArrayFactory;
import net.finmath.montecarlo.model.AbstractProcessModel;
import net.finmath.montecarlo.model.ProcessModel;
import net.finmath.montecarlo.process.MonteCarloProcess;
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 RandomVariableFactory randomVariableFactory;
private final RandomVariable initialValue;
private final DiscountCurve discountCurveForForwardRate;
private final RandomVariable riskFreeRate; // Actually the same as the drift (which is not stochastic)
private final DiscountCurve discountCurveForDiscountRate;
private final RandomVariable discountRate; // Constant rate, used if discountCurveForForwardRate is null
private final RandomVariable sigma;
private final RandomVariable theta;
private final RandomVariable 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 \( \nu \).
* @param randomVariableFactory The factory to be used to construct random variables.
*/
public VarianceGammaModel(final RandomVariable initialValue, final DiscountCurve discountCurveForForwardRate,
final DiscountCurve discountCurveForDiscountRate, final RandomVariable sigma, final RandomVariable theta, final RandomVariable nu,
final RandomVariableFactory randomVariableFactory) {
super();
this.randomVariableFactory = randomVariableFactory;
this.initialValue = initialValue;
this.discountCurveForForwardRate = discountCurveForForwardRate;
riskFreeRate = null;
this.discountCurveForDiscountRate = discountCurveForDiscountRate;
discountRate = null;
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 \( \nu \).
* @param randomVariableFactory The factory to be used to construct random variables.
*/
public VarianceGammaModel(final RandomVariable initialValue, final RandomVariable riskFreeRate, final RandomVariable discountRate, final RandomVariable sigma, final RandomVariable theta,
final RandomVariable nu,
final RandomVariableFactory randomVariableFactory) {
super();
this.randomVariableFactory = new RandomVariableFromArrayFactory();
this.initialValue = initialValue;
discountCurveForForwardRate = null;
this.riskFreeRate = riskFreeRate;
discountCurveForDiscountRate = null;
this.discountRate = discountRate;
this.sigma = sigma;
this.theta = theta;
this.nu = nu;
}
/**
* Create the model from a descriptor.
*
* @param descriptor A descriptor of the model.
*/
public VarianceGammaModel(VarianceGammaModelDescriptor descriptor) {
this(descriptor.getInitialValue(),
descriptor.getDiscountCurveForForwardRate(),
descriptor.getDiscountCurveForDiscountRate(),
descriptor.getSigma(),
descriptor.getTheta(),
descriptor.getNu());
}
/**
* 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 \( \nu \).
* @param randomVariableFactory The factory to be used to construct random variables.
*/
public VarianceGammaModel(final double initialValue, final DiscountCurve discountCurveForForwardRate,
final DiscountCurve discountCurveForDiscountRate, final double sigma, final double theta, final double nu,
final RandomVariableFactory randomVariableFactory) {
super();
this.initialValue = randomVariableFactory.createRandomVariable(initialValue);
this.discountCurveForForwardRate = discountCurveForForwardRate;
riskFreeRate = null;
this.discountCurveForDiscountRate = discountCurveForDiscountRate;
discountRate = null;
this.sigma = randomVariableFactory.createRandomVariable(sigma);
this.theta = randomVariableFactory.createRandomVariable(theta);
this.nu = randomVariableFactory.createRandomVariable(nu);
this.randomVariableFactory = randomVariableFactory;
}
/**
* 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) {
this(initialValue, discountCurveForDiscountRate, discountCurveForDiscountRate, sigma, theta, nu, new RandomVariableFromArrayFactory());
}
/**
* 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.randomVariableFactory = new RandomVariableFromArrayFactory();
this.initialValue = this.randomVariableFactory.createRandomVariable(initialValue);
discountCurveForForwardRate = null;
this.riskFreeRate = this.randomVariableFactory.createRandomVariable(riskFreeRate);
discountCurveForDiscountRate = null;
this.discountRate = this.randomVariableFactory.createRandomVariable(discountRate);
this.sigma = this.randomVariableFactory.createRandomVariable(sigma);
this.theta = this.randomVariableFactory.createRandomVariable(theta);
this.nu = this.randomVariableFactory.createRandomVariable(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 RandomVariable applyStateSpaceTransform(final MonteCarloProcess process, final int timeIndex, final int componentIndex, final RandomVariable randomVariable) {
return randomVariable.exp();
}
@Override
public RandomVariable applyStateSpaceTransformInverse(final MonteCarloProcess process, final int timeIndex, final int componentIndex, final RandomVariable randomVariable) {
return randomVariable.log();
}
@Override
public RandomVariable[] getInitialState(MonteCarloProcess process) {
return new RandomVariable[] { initialValue.log() };
}
@Override
public RandomVariable getNumeraire(MonteCarloProcess process, final double time) {
if(discountCurveForDiscountRate != null) {
return getRandomVariableForConstant(1.0/discountCurveForDiscountRate.getDiscountFactor(time));
}
else {
return discountRate.mult(time).exp();
}
}
@Override
public RandomVariable[] getDrift(final MonteCarloProcess process, final int timeIndex, final RandomVariable[] realizationAtTimeIndex, final RandomVariable[] realizationPredictor) {
RandomVariable riskFreeRateAtTimeStep;
if(discountCurveForForwardRate != null) {
final double time = process.getTime(timeIndex);
final double timeNext = process.getTime(timeIndex+1);
riskFreeRateAtTimeStep = getRandomVariableForConstant(Math.log(discountCurveForForwardRate.getDiscountFactor(time) / discountCurveForForwardRate.getDiscountFactor(timeNext)) / (timeNext-time));
}
else {
riskFreeRateAtTimeStep = riskFreeRate;
}
// r + log(1 - theta * nu - 0.5 nu sigma^2)
return new RandomVariable[] { riskFreeRateAtTimeStep.add(theta.mult(nu).add(sigma.squared().mult(nu).mult(0.5)).mult(-1).add(1.0).log().div(nu)) };
}
@Override
public RandomVariable[] getFactorLoading(final MonteCarloProcess process, final int timeIndex, final int componentIndex,
final RandomVariable[] realizationAtTimeIndex) {
final RandomVariable[] factors = new RandomVariable[1];
factors[0] = getRandomVariableForConstant(1.0);
return factors;
}
@Override
public int getNumberOfComponents() {
return 1;
}
@Override
public int getNumberOfFactors() {
return 1;
}
@Override
public RandomVariable getRandomVariableForConstant(final double value) {
return randomVariableFactory.createRandomVariable(value);
}
@Override
public ProcessModel getCloneWithModifiedData(final Map dataModified) throws CalculationException {
/*
* Determine the new model parameters from the provided parameter map.
*/
final RandomVariableFactory newRandomVariableFactory = (RandomVariableFactory)dataModified.getOrDefault("randomVariableFactory", randomVariableFactory);
final RandomVariable newInitialValue = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("initialValue"), initialValue);
final RandomVariable newRiskFreeRate = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("riskFreeRate"), riskFreeRate);
final RandomVariable newDiscountRate = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("discountRate"), discountRate);
final RandomVariable newSigma = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("sigma"), sigma);
final RandomVariable newTheta = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("theta"), theta);
final RandomVariable newNu = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("nu"), nu);
return new VarianceGammaModel(newInitialValue, newRiskFreeRate, newDiscountRate, newSigma, newTheta, newNu, newRandomVariableFactory);
}
/**
* @return the discountCurveForForwardRate
*/
public DiscountCurve getDiscountCurveForForwardRate() {
return discountCurveForForwardRate;
}
/**
* @return the riskFreeRate
*/
public RandomVariable getRiskFreeRate() {
return riskFreeRate;
}
/**
* @return the discountCurveForDiscountRate
*/
public DiscountCurve getDiscountCurveForDiscountRate() {
return discountCurveForDiscountRate;
}
/**
* @return the discountRate
*/
public RandomVariable getDiscountRate() {
return discountRate;
}
/**
* @return the sigma
*/
public RandomVariable getSigma() {
return sigma;
}
/**
* @return the theta
*/
public RandomVariable getTheta() {
return theta;
}
/**
* @return the nu
*/
public RandomVariable 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 + "]";
}
}