LocalVolatilityForwardPDESpotGreeksGridCalculator.java example

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/**
 * 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;
    }
  }

}