/**
* Copyright (C) 2012 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.volatility.local;
import com.opengamma.analytics.financial.model.finitedifference.BoundaryCondition;
import com.opengamma.analytics.financial.model.finitedifference.ConvectionDiffusionPDE1DCoefficients;
import com.opengamma.analytics.financial.model.finitedifference.DirichletBoundaryCondition;
import com.opengamma.analytics.financial.model.finitedifference.ExponentialMeshing;
import com.opengamma.analytics.financial.model.finitedifference.HyperbolicMeshing;
import com.opengamma.analytics.financial.model.finitedifference.MeshingFunction;
import com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition;
import com.opengamma.analytics.financial.model.finitedifference.PDE1DDataBundle;
import com.opengamma.analytics.financial.model.finitedifference.PDEGrid1D;
import com.opengamma.analytics.financial.model.finitedifference.PDETerminalResults1D;
import com.opengamma.analytics.financial.model.interestrate.curve.ForwardCurve;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.EuropeanVanillaOption;
import com.opengamma.analytics.math.function.Function1D;
/**
*
*/
public class LocalVolatilityForwardPDECalculator extends LocalVolatilityPDECalculator {
private final int _nTimeSteps;
private final int _nSpaceSteps;
private final double _timeMeshLambda;
private final double _spaceMeshBunching;
private final double _maxProxyDelta;
private final double _centreMoneyness;
public LocalVolatilityForwardPDECalculator(final double theta, final int nTimeSteps, final int nSpaceSteps, final double timeMeshLambda, final double spaceMeshBunching,
final double maxProxyDelta, final double centreMoneyness) {
super(theta);
_nTimeSteps = nTimeSteps;
_nSpaceSteps = nSpaceSteps;
_timeMeshLambda = timeMeshLambda;
_spaceMeshBunching = spaceMeshBunching;
_maxProxyDelta = maxProxyDelta;
_centreMoneyness = centreMoneyness;
}
@Override
public PDETerminalResults1D runPDESolver(final LocalVolatilitySurfaceMoneyness localVolatility, final EuropeanVanillaOption option) {
final boolean isCall = option.isCall();
final double expiry = option.getTimeToExpiry();
final double minMoneyness = Math.exp(-_maxProxyDelta * Math.sqrt(expiry));
final double maxMoneyness = 1.0 / minMoneyness;
final PDEGrid1D grid = getGrid(getTimeMesh(expiry), getSpaceMesh(minMoneyness, maxMoneyness));
final BoundaryCondition lower = getLowerBoundaryCondition(option, minMoneyness);
final BoundaryCondition upper = getUpperBoundaryCondition(option, maxMoneyness);
final ConvectionDiffusionPDE1DCoefficients pde = getPDEProvider().getForwardLocalVol(localVolatility);
final Function1D<Double, Double> intCond = getInitialConditionProvider().getForwardCallPut(isCall);
final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db = new PDE1DDataBundle<>(pde, intCond, lower, upper, grid);
return (PDETerminalResults1D) getSolver().solve(db);
}
@Override
public PDETerminalResults1D runPDESolver(final LocalVolatilitySurfaceStrike localVolatility, final ForwardCurve forwardCurve, final EuropeanVanillaOption option) {
final boolean isCall = option.isCall();
final double expiry = option.getTimeToExpiry();
final double minMoneyness = Math.exp(-_maxProxyDelta * Math.sqrt(expiry));
final double maxMoneyness = 1.0 / minMoneyness;
final PDEGrid1D grid = getGrid(getTimeMesh(expiry), getSpaceMesh(minMoneyness, maxMoneyness));
final BoundaryCondition lower = getLowerBoundaryCondition(option, minMoneyness);
final BoundaryCondition upper = getUpperBoundaryCondition(option, maxMoneyness);
final ConvectionDiffusionPDE1DCoefficients pde = getPDEProvider().getForwardLocalVol(forwardCurve, localVolatility);
final Function1D<Double, Double> intCond = getInitialConditionProvider().getForwardCallPut(isCall);
final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db = new PDE1DDataBundle<>(pde, intCond, lower, upper, grid);
return (PDETerminalResults1D) getSolver().solve(db);
}
public int getNTimeSteps() {
return _nTimeSteps;
}
public int getNSpaceSteps() {
return _nSpaceSteps;
}
public double getTimeMeshLambda() {
return _timeMeshLambda;
}
public double getSpaceMeshBunching() {
return _spaceMeshBunching;
}
public double getMaxProxyDelta() {
return _maxProxyDelta;
}
public double getCentreMoneyness() {
return _centreMoneyness;
}
private MeshingFunction getTimeMesh(final double maxTime) {
return new ExponentialMeshing(0.0, maxTime, _nTimeSteps, _timeMeshLambda);
}
private MeshingFunction getSpaceMesh(final double minMoneyness, final double maxMoneyness) {
return new HyperbolicMeshing(minMoneyness, maxMoneyness, _centreMoneyness, _nSpaceSteps, _spaceMeshBunching);
}
private BoundaryCondition getLowerBoundaryCondition(final EuropeanVanillaOption option, final double minMoneyness) {
//call option with strike zero is worth the forward, while a put is worthless
return option.isCall() ? new DirichletBoundaryCondition(1.0 - minMoneyness, minMoneyness) : new DirichletBoundaryCondition(0.0, minMoneyness);
}
private BoundaryCondition getUpperBoundaryCondition(final EuropeanVanillaOption option, final double maxMoneyness) {
//call option with strike zero is worth the forward, while a put is worthless
return option.isCall() ? new DirichletBoundaryCondition(0.0, maxMoneyness) : new NeumannBoundaryCondition(1.0, maxMoneyness, false);
}
}