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/*
* (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
*
* Created on 15 Jan 2015
*/
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.BrownianMotionView;
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;
/**
* Simple stochastic volatility model, using a process
* \[
* d\lambda(t) = \nu \lambda(t) \left( \rho \mathrm{d} W_{1}(t) + \sqrt{1-\rho^{2}} \mathrm{d} W_{2}(t) \right) \text{,}
* \]
* 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
* the (Euler 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 two factors 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 \( ( \mathrm{d} W_{1}(t) , \mathrm{d} W_{2}(t) ) \) 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 ν and ρ 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 LIBORCovarianceModelStochasticVolatility extends AbstractLIBORCovarianceModelParametric {
private static final long serialVersionUID = -559341617850035368L;
private AbstractLIBORCovarianceModelParametric covarianceModel;
private final BrownianMotion brownianMotion;
private RandomVariable rho, nu;
private boolean isCalibrateable = false;
private 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 BrownianMotionView} to change this.
* @param nu The initial value for ν, the volatility of the volatility.
* @param rho The initial value for ρ the correlation to the first factor.
* @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 LIBORCovarianceModelStochasticVolatility(final AbstractLIBORCovarianceModelParametric covarianceModel, final BrownianMotion brownianMotion, final RandomVariable nu, final RandomVariable rho, final boolean isCalibrateable) {
super(covarianceModel.getTimeDiscretization(), covarianceModel.getLiborPeriodDiscretization(), covarianceModel.getNumberOfFactors());
this.covarianceModel = covarianceModel;
this.brownianMotion = brownianMotion;
this.nu = nu;
this.rho = rho;
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 BrownianMotionView} to change this.
* @param nu The initial value for ν, the volatility of the volatility.
* @param rho The initial value for ρ the correlation to the first factor.
* @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 LIBORCovarianceModelStochasticVolatility(final AbstractLIBORCovarianceModelParametric covarianceModel, final BrownianMotion brownianMotion, final double nu, final double rho, final boolean isCalibrateable) {
super(covarianceModel.getTimeDiscretization(), covarianceModel.getLiborPeriodDiscretization(), covarianceModel.getNumberOfFactors());
this.covarianceModel = covarianceModel;
this.brownianMotion = brownianMotion;
this.nu = new Scalar(nu);
this.rho = new Scalar(rho);
this.isCalibrateable = isCalibrateable;
}
@Override
public RandomVariable[] getParameter() {
if(!isCalibrateable) {
return covarianceModel.getParameter();
}
final RandomVariable[] covarianceParameters = covarianceModel.getParameter();
if(covarianceParameters == null) {
return new RandomVariable[] { nu, rho };
}
// Append nu and rho to the end of covarianceParameters
final RandomVariable[] jointParameters = new RandomVariable[covarianceParameters.length+2];
System.arraycopy(covarianceParameters, 0, jointParameters, 0, covarianceParameters.length);
jointParameters[covarianceParameters.length+0] = nu;
jointParameters[covarianceParameters.length+1] = rho;
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-2];
System.arraycopy(parameter, 0, covarianceParameters, 0, covarianceParameters.length);
covarianceModel = covarianceModel.getCloneWithModifiedParameters(covarianceParameters);
nu = parameter[covarianceParameters.length + 0];
rho = parameter[covarianceParameters.length + 1];
stochasticVolatilityScalings = null;
}
@Override
public Object clone() {
final LIBORCovarianceModelStochasticVolatility newModel = new LIBORCovarianceModelStochasticVolatility((AbstractLIBORCovarianceModelParametric) covarianceModel.clone(), brownianMotion, nu, rho, isCalibrateable);
return newModel;
}
@Override
public AbstractLIBORCovarianceModelParametric getCloneWithModifiedParameters(final RandomVariable[] parameters) {
final LIBORCovarianceModelStochasticVolatility model = (LIBORCovarianceModelStochasticVolatility)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 {
BrownianMotion brownianMotion = this.brownianMotion;
RandomVariable nu = this.nu;
RandomVariable rho = this.rho;
boolean isCalibrateable = this.isCalibrateable;
AbstractLIBORCovarianceModelParametric covarianceModel = this.covarianceModel;
RandomVariableFactory randomVariableFactory = null;
if(dataModified != null) {
if(dataModified.containsKey("randomVariableFactory")) {
randomVariableFactory = (RandomVariableFactory)dataModified.get("randomVariableFactory");
nu = randomVariableFactory.createRandomVariable(nu.doubleValue());
rho = randomVariableFactory.createRandomVariable(rho.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("nu", nu) instanceof RandomVariable) {
nu = (RandomVariable)dataModified.getOrDefault("nu", nu);
}else if(randomVariableFactory == null){
nu = new Scalar((double)dataModified.get("nu"));
}else {
nu = randomVariableFactory.createRandomVariable((double)dataModified.get("nu"));
}
if(dataModified.getOrDefault("rho", rho) instanceof RandomVariable) {
rho = (RandomVariable)dataModified.getOrDefault("rho", rho);
}else if(randomVariableFactory == null){
rho = new Scalar((double)dataModified.get("rho"));
}else {
rho = randomVariableFactory.createRandomVariable((double)dataModified.get("rho"));
}
}
final AbstractLIBORCovarianceModelParametric newModel = new LIBORCovarianceModelStochasticVolatility(covarianceModel, brownianMotion, nu, rho, isCalibrateable);
return newModel;
}
}
