/**
* 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.PDETerminalResults1D;
import com.opengamma.analytics.financial.model.interestrate.curve.ForwardCurve;
import com.opengamma.analytics.financial.model.interestrate.curve.YieldAndDiscountCurve;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.EuropeanVanillaOption;
import com.opengamma.analytics.math.interpolation.Interpolator1D;
import com.opengamma.analytics.math.interpolation.data.Interpolator1DDataBundle;
/**
*
*/
public abstract class LocalVolatilityForwardPDESpotGreeksGridCalculator implements PDELocalVolatilityCalculator<Interpolator1DDataBundle> {
private static final double SHIFT = 1e-2;
private final LocalVolatilityForwardPDECalculator _pdeCalculator;
private final Interpolator1D _interpolator;
public LocalVolatilityForwardPDESpotGreeksGridCalculator(final LocalVolatilityForwardPDECalculator pdeCalculator, final Interpolator1D interpolator) {
_pdeCalculator = pdeCalculator;
_interpolator = interpolator;
}
@Override
public Interpolator1DDataBundle getResult(final LocalVolatilitySurfaceMoneyness localVolatility, final ForwardCurve forwardCurve, final EuropeanVanillaOption option,
final YieldAndDiscountCurve discountingCurve) {
final double expiry = option.getTimeToExpiry();
final double forward = forwardCurve.getForward(expiry);
final PDETerminalResults1D pdeGrid = _pdeCalculator.runPDESolver(localVolatility, option);
final PDETerminalResults1D pdeGridUp = _pdeCalculator.runPDESolver(localVolatility, option);
final PDETerminalResults1D pdeGridDown = _pdeCalculator.runPDESolver(localVolatility, option);
final int n = pdeGrid.getNumberSpaceNodes();
final double[] strikes = new double[n];
final double[] greeks = new double[n];
for (int i = 0; i < n; i++) {
final double moneyness = pdeGrid.getSpaceValue(i);
strikes[i] = moneyness * forward;
greeks[i] = getResultForMoneyness(pdeGrid, pdeGridUp, pdeGridDown, i, forward, option);
}
return _interpolator.getDataBundleFromSortedArrays(strikes, greeks);
}
@Override
public Interpolator1DDataBundle getResult(final LocalVolatilitySurfaceStrike localVolatility, final ForwardCurve forwardCurve, final EuropeanVanillaOption option,
final YieldAndDiscountCurve discountingCurve) {
return getResult(LocalVolatilitySurfaceConverter.toMoneynessSurface(localVolatility, forwardCurve), forwardCurve, option, discountingCurve);
}
protected abstract double getResultForMoneyness(final PDETerminalResults1D pdeGrid, final PDETerminalResults1D pdeGridUp, final PDETerminalResults1D pdeGridDown,
final int index, final double forward, final EuropeanVanillaOption option);
public Interpolator1D getInterpolator() {
return _interpolator;
}
/**
* Calculates the delta
*/
public static class DeltaCalculator extends LocalVolatilityForwardPDESpotGreeksGridCalculator {
public DeltaCalculator(final LocalVolatilityForwardPDECalculator pdeCalculator, final Interpolator1D interpolator) {
super(pdeCalculator, interpolator);
}
@Override
protected double getResultForMoneyness(final PDETerminalResults1D pdeGrid, final PDETerminalResults1D pdeGridUp, final PDETerminalResults1D pdeGridDown,
final int index, final double forward, final EuropeanVanillaOption option) {
final double moneyness = option.getStrike() / forward;
final double mPrice = pdeGrid.getFunctionValue(index);
final double modelDD = pdeGrid.getFirstSpatialDerivative(index);
final double fixedSurfaceDelta = mPrice - moneyness * modelDD; //i.e. the delta if the moneyness parameterised local vol surface was invariant to forward
final double surfaceDelta = (pdeGridUp.getFunctionValue(index) - pdeGridDown.getFunctionValue(index)) / 2 / forward / SHIFT;
return fixedSurfaceDelta + forward * surfaceDelta;
}
}
/**
* Calculates the gamma
*/
public static class GammaCalculator extends LocalVolatilityForwardPDESpotGreeksGridCalculator {
public GammaCalculator(final LocalVolatilityForwardPDECalculator pdeCalculator, final Interpolator1D interpolator) {
super(pdeCalculator, interpolator);
}
@Override
protected double getResultForMoneyness(final PDETerminalResults1D pdeGrid, final PDETerminalResults1D pdeGridUp, final PDETerminalResults1D pdeGridDown,
final int index, final double forward, final EuropeanVanillaOption option) {
final double k = option.getStrike();
final double moneyness = k / forward;
final double surfaceDelta = (pdeGridUp.getFunctionValue(index) - pdeGridDown.getFunctionValue(index)) / 2 / forward / SHIFT;
final double modelDG = pdeGrid.getSecondSpatialDerivative(index) / forward;
final double crossGamma = (pdeGridUp.getFirstSpatialDerivative(index) - pdeGridDown.getFirstSpatialDerivative(index)) / 2 / forward / SHIFT;
final double surfaceGamma = (pdeGridUp.getFunctionValue(index) + pdeGridDown.getFunctionValue(index) - 2 * pdeGrid.getFunctionValue(index)) / forward / SHIFT / SHIFT;
return 2 * surfaceDelta + surfaceGamma - 2 * moneyness * crossGamma + moneyness * moneyness * modelDG;
}
}
}