net.finmath.montecarlo.interestrate.models.covariance.LIBORCovarianceModelStochasticHestonVolatility Maven / Gradle / Ivy
Go to download
Show more of this group Show more artifacts with this name
Show all versions of finmath-lib Show documentation
Show all versions of finmath-lib Show documentation
finmath lib is a Mathematical Finance Library in Java.
It provides algorithms and methodologies related to mathematical finance.
package net.finmath.montecarlo.interestrate.models.covariance;
import java.time.LocalDateTime;
import java.util.Map;
import net.finmath.exception.CalculationException;
import net.finmath.montecarlo.BrownianMotion;
import net.finmath.montecarlo.RandomVariableFactory;
import net.finmath.montecarlo.model.ProcessModel;
import net.finmath.montecarlo.process.EulerSchemeFromProcessModel;
import net.finmath.montecarlo.process.MonteCarloProcess;
import net.finmath.stochastic.RandomVariable;
import net.finmath.stochastic.Scalar;
/**
* As Heston like stochastic volatility model, using a process \( \lambda(t) = \sqrt(V(t)) \)
* \[
* dV(t) = \kappa ( \theta - V(t) ) dt + \xi \sqrt{V(t)} dW_{1}(t), \quad V(0) = 1.0,
* \]
* where \( \lambda(0) = 1 \) to scale all factor loadings \( f_{i} \) returned by a given covariance model.
*
* The model constructed is \( \lambda(t) F(t) \) where \( \lambda(t) \) is
* a discretization of the above process and \( F = ( f_{1}, \ldots, f_{m} ) \) is the factor loading
* from the given covariance model.
*
* The process uses the first factor of the Brownian motion provided by an object implementing
* {@link net.finmath.montecarlo.BrownianMotion}. This can be used to generate correlations to
* other objects. If you like to reuse a factor of another Brownian motion use a
* {@link net.finmath.montecarlo.BrownianMotionView}
* to delegate \( ( \mathrm{d} W_{1}(t) ) \) to a different object.
*
* The parameter of this model is a joint parameter vector, consisting
* of the parameter vector of the given base covariance model and
* appending the parameters κ, θ and ξ at the end.
*
* If this model is not calibrateable, its parameter vector is that of the
* covariance model, i.e., ν and ρ will be not
* part of the calibration.
*
* For an illustration of its usage see the associated unit test.
*
* @author Christian Fries
* @version 1.0
*/
public class LIBORCovarianceModelStochasticHestonVolatility extends AbstractLIBORCovarianceModelParametric {
private static final long serialVersionUID = -1438451123632424212L;
private AbstractLIBORCovarianceModelParametric covarianceModel;
private final BrownianMotion brownianMotion;
private RandomVariable kappa, theta, xi;
private boolean isCalibrateable = false;
private transient MonteCarloProcess stochasticVolatilityScalings = null;
/**
* Create a modification of a given {@link AbstractLIBORCovarianceModelParametric} with a stochastic volatility scaling.
*
* @param covarianceModel A given AbstractLIBORCovarianceModelParametric.
* @param brownianMotion An object implementing {@link BrownianMotion} with at least two factors. This class uses the first two factors, but you may use {@link net.finmath.montecarlo.BrownianMotionView} to change this.
* @param kappa The initial value for κ, the mean reversion speed of the variance process V.
* @param theta The initial value for θ the mean reversion level of the variance process V.
* @param xi The initial value for ξ the volatility of the variance process V.
* @param isCalibrateable If true, the parameters ν and ρ are parameters. Note that the covariance model (covarianceModel) may have its own parameter calibration settings.
*/
public LIBORCovarianceModelStochasticHestonVolatility(final AbstractLIBORCovarianceModelParametric covarianceModel, final BrownianMotion brownianMotion, final RandomVariable kappa, final RandomVariable theta, final RandomVariable xi, final boolean isCalibrateable) {
super(covarianceModel.getTimeDiscretization(), covarianceModel.getLiborPeriodDiscretization(), covarianceModel.getNumberOfFactors());
this.covarianceModel = covarianceModel;
this.brownianMotion = brownianMotion;
this.kappa = kappa;
this.theta = theta;
this.xi = xi;
this.isCalibrateable = isCalibrateable;
}
/**
* Create a modification of a given {@link AbstractLIBORCovarianceModelParametric} with a stochastic volatility scaling.
*
* @param covarianceModel A given AbstractLIBORCovarianceModelParametric.
* @param brownianMotion An object implementing {@link BrownianMotion} with at least two factors. This class uses the first two factors, but you may use {@link net.finmath.montecarlo.BrownianMotionView} to change this.
* @param kappa The initial value for κ, the mean reversion speed of the variance process V.
* @param theta The initial value for θ the mean reversion level of the variance process V.
* @param xi The initial value for ξ the volatility of the variance process V.
* @param isCalibrateable If true, the parameters ν and ρ are parameters. Note that the covariance model (covarianceModel) may have its own parameter calibration settings.
*/
public LIBORCovarianceModelStochasticHestonVolatility(final AbstractLIBORCovarianceModelParametric covarianceModel, final BrownianMotion brownianMotion, final double kappa, final double theta, final double xi, final boolean isCalibrateable) {
super(covarianceModel.getTimeDiscretization(), covarianceModel.getLiborPeriodDiscretization(), covarianceModel.getNumberOfFactors());
this.covarianceModel = covarianceModel;
this.brownianMotion = brownianMotion;
this.kappa = new Scalar(kappa);
this.theta = new Scalar(theta);
this.xi = new Scalar(xi);
this.isCalibrateable = isCalibrateable;
}
@Override
public RandomVariable[] getParameter() {
if(!isCalibrateable) {
return covarianceModel.getParameter();
}
final RandomVariable[] covarianceParameters = covarianceModel.getParameter();
if(covarianceParameters == null) {
return new RandomVariable[] { theta, kappa, xi };
}
// Append nu and rho to the end of covarianceParameters
final RandomVariable[] jointParameters = new RandomVariable[covarianceParameters.length+3];
System.arraycopy(covarianceParameters, 0, jointParameters, 0, covarianceParameters.length);
jointParameters[covarianceParameters.length+0] = kappa;
jointParameters[covarianceParameters.length+1] = theta;
jointParameters[covarianceParameters.length+2] = xi;
return jointParameters;
}
// @Override
private void setParameter(final RandomVariable[] parameter) {
if(parameter == null || parameter.length == 0) {
return;
}
if(!isCalibrateable) {
covarianceModel = covarianceModel.getCloneWithModifiedParameters(parameter);
return;
}
final RandomVariable[] covarianceParameters = new RandomVariable[parameter.length-3];
System.arraycopy(parameter, 0, covarianceParameters, 0, covarianceParameters.length);
covarianceModel = covarianceModel.getCloneWithModifiedParameters(covarianceParameters);
kappa = parameter[covarianceParameters.length + 0];
theta = parameter[covarianceParameters.length + 1];
xi = parameter[covarianceParameters.length + 2];
stochasticVolatilityScalings = null;
}
@Override
public Object clone() {
final LIBORCovarianceModelStochasticHestonVolatility newModel = new LIBORCovarianceModelStochasticHestonVolatility((AbstractLIBORCovarianceModelParametric) covarianceModel.clone(), brownianMotion, kappa, theta, xi, isCalibrateable);
return newModel;
}
@Override
public AbstractLIBORCovarianceModelParametric getCloneWithModifiedParameters(final RandomVariable[] parameters) {
final LIBORCovarianceModelStochasticHestonVolatility model = (LIBORCovarianceModelStochasticHestonVolatility)this.clone();
model.setParameter(parameters);
return model;
}
@Override
public AbstractLIBORCovarianceModelParametric getCloneWithModifiedParameters(final double[] parameters) {
return getCloneWithModifiedParameters(Scalar.arrayOf(parameters));
}
@Override
public double[] getParameterAsDouble() {
final RandomVariable[] parameters = getParameter();
final double[] parametersAsDouble = new double[parameters.length];
for(int i=0; i dataModified) {
throw new UnsupportedOperationException("Method not implemented");
}
};
stochasticVolatilityScalings = new EulerSchemeFromProcessModel(model, brownianMotion);
}
}
RandomVariable stochasticVolatilityScaling = null;
try {
stochasticVolatilityScaling = stochasticVolatilityScalings.getProcessValue(timeIndex,0);
} catch (final CalculationException e) {
// Exception is not handled explicitly, we just return null
}
RandomVariable[] factorLoading = null;
if(stochasticVolatilityScaling != null) {
factorLoading = covarianceModel.getFactorLoading(timeIndex, component, realizationAtTimeIndex);
for(int i=0; i dataModified)
throws CalculationException {
AbstractLIBORCovarianceModelParametric covarianceModel = this.covarianceModel;
BrownianMotion brownianMotion = this.brownianMotion;
RandomVariable kappa = this.kappa;
RandomVariable theta = this.theta;
RandomVariable xi = this.xi;
boolean isCalibrateable = this.isCalibrateable;
RandomVariableFactory randomVariableFactory = null;
if(dataModified != null) {
if(dataModified.containsKey("randomVariableFactory")) {
randomVariableFactory = (RandomVariableFactory)dataModified.get("randomVariableFactory");
kappa = randomVariableFactory.createRandomVariable(kappa.doubleValue());
theta = randomVariableFactory.createRandomVariable(theta.doubleValue());
xi = randomVariableFactory.createRandomVariable(xi.doubleValue());
}
if(!dataModified.containsKey("covarianceModel")) {
covarianceModel = covarianceModel.getCloneWithModifiedData(dataModified);
}
// Explicitly passed covarianceModel has priority
covarianceModel = (AbstractLIBORCovarianceModelParametric)dataModified.getOrDefault("covarianceModel", covarianceModel);
isCalibrateable = (boolean)dataModified.getOrDefault("isCalibrateable", isCalibrateable);
brownianMotion = (BrownianMotion)dataModified.getOrDefault("brownianMotion", brownianMotion);
if(dataModified.getOrDefault("kappa", kappa) instanceof RandomVariable) {
kappa = (RandomVariable)dataModified.getOrDefault("kappa", kappa);
}else if(randomVariableFactory==null){
kappa = new Scalar((double)dataModified.get("kappa"));
}else {
kappa = randomVariableFactory.createRandomVariable((double)dataModified.get("kappa"));
}
if(dataModified.getOrDefault("theta", theta) instanceof RandomVariable) {
theta = (RandomVariable)dataModified.getOrDefault("rho", theta);
}else if(randomVariableFactory==null){
theta = new Scalar((double)dataModified.get("theta"));
}else {
theta = randomVariableFactory.createRandomVariable((double)dataModified.get("theta"));
}
if(dataModified.getOrDefault("xi", xi) instanceof RandomVariable) {
xi = (RandomVariable)dataModified.getOrDefault("xi", xi);
}else if(randomVariableFactory==null){
xi = new Scalar((double)dataModified.get("xi"));
}else {
xi = randomVariableFactory.createRandomVariable((double)dataModified.get("xi"));
}
}
final AbstractLIBORCovarianceModelParametric newModel = new LIBORCovarianceModelStochasticHestonVolatility(covarianceModel, brownianMotion, kappa, theta, xi, isCalibrateable);
return newModel;
}
}