/**
* Copyright (C) 2012 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.interestrate.future.provider;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import com.opengamma.analytics.financial.interestrate.future.derivative.InterestRateFutureOptionMarginSecurity;
import com.opengamma.analytics.financial.model.interestrate.HullWhiteOneFactorPiecewiseConstantInterestRateModel;
import com.opengamma.analytics.financial.model.interestrate.definition.HullWhiteOneFactorPiecewiseConstantParameters;
import com.opengamma.analytics.financial.provider.description.interestrate.HullWhiteOneFactorProviderInterface;
import com.opengamma.analytics.financial.provider.description.interestrate.MulticurveProviderInterface;
import com.opengamma.analytics.financial.provider.sensitivity.multicurve.ForwardSensitivity;
import com.opengamma.analytics.financial.provider.sensitivity.multicurve.MulticurveSensitivity;
import com.opengamma.analytics.math.statistics.distribution.NormalDistribution;
import com.opengamma.analytics.math.statistics.distribution.ProbabilityDistribution;
import com.opengamma.util.ArgumentChecker;
/**
* Method for the pricing of interest rate future options with daily margining.
* The model is the Hull-White one factor model {@link HullWhiteOneFactorPiecewiseConstantInterestRateModel}.
* <p>Reference: Interest Rate Futures and their options: Some Pricing Approaches. OpenGamma Documentation n.6. Version 1.5 - December 2012.
*/
public final class InterestRateFutureOptionMarginSecurityHullWhiteMethod extends InterestRateFutureOptionMarginSecurityGenericMethod<HullWhiteOneFactorProviderInterface> {
/**
* The unique instance of the calculator.
*/
private static final InterestRateFutureOptionMarginSecurityHullWhiteMethod INSTANCE = new InterestRateFutureOptionMarginSecurityHullWhiteMethod();
/**
* Constructor.
*/
private InterestRateFutureOptionMarginSecurityHullWhiteMethod() {
}
/**
* Gets the calculator instance.
* @return The calculator.
*/
public static InterestRateFutureOptionMarginSecurityHullWhiteMethod getInstance() {
return INSTANCE;
}
/**
* The Hull-White model.
*/
private static final HullWhiteOneFactorPiecewiseConstantInterestRateModel MODEL = new HullWhiteOneFactorPiecewiseConstantInterestRateModel();
/**
* The normal distribution implementation.
*/
private static final ProbabilityDistribution<Double> NORMAL = new NormalDistribution(0, 1);
/**
* Computes the price in the Hull-White one factor model.
* @param security The option security.
* @param hwMulticurves The multi-curves provider with Hull-White one factor parameters.
* @return The price.
*/
@Override
public double price(final InterestRateFutureOptionMarginSecurity security, final HullWhiteOneFactorProviderInterface hwMulticurves) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(hwMulticurves, "Hull-White and multi-curves data");
ArgumentChecker.isTrue(security.getCurrency().equals(hwMulticurves.getHullWhiteCurrency()), "Model currency incompatible with security currency");
final MulticurveProviderInterface multicurves = hwMulticurves.getMulticurveProvider();
final HullWhiteOneFactorPiecewiseConstantParameters parameters = hwMulticurves.getHullWhiteParameters();
final double k = security.getStrike();
final double ktilde = 1.0 - k;
final double theta = security.getExpirationTime();
final double delta = security.getUnderlyingFuture().getFixingPeriodAccrualFactor();
final double t0 = security.getUnderlyingFuture().getLastTradingTime();
final double t1 = security.getUnderlyingFuture().getFixingPeriodStartTime();
final double t2 = security.getUnderlyingFuture().getFixingPeriodEndTime();
final double alpha = MODEL.alpha(parameters, 0.0, theta, t1, t2);
final double gamma = MODEL.futuresConvexityFactor(parameters, t0, t1, t2);
final double forward = multicurves.getForwardRate(security.getUnderlyingFuture().getIborIndex(), t1, t2, delta);
final double kappa = -Math.log((1 + delta * ktilde) / (1 + delta * forward) / gamma) / alpha - 0.5 * alpha;
if (security.isCall()) {
final double normalKappa = NORMAL.getCDF(-kappa);
final double normalAlphaKappa = NORMAL.getCDF(-kappa - alpha);
return (1 - k + 1.0 / delta) * normalKappa - (1.0 / delta + forward) * gamma * normalAlphaKappa;
}
final double normalKappa = NORMAL.getCDF(kappa);
final double normalAlphaKappa = NORMAL.getCDF(kappa + alpha);
return (1.0 / delta + forward) * gamma * normalAlphaKappa - (1 - k + 1.0 / delta) * normalKappa;
}
/**
* Computes the price curve sensitivity in the Hull-White one factor model.
* @param security The option security.
* @param hwMulticurves The multi-curves provider with Hull-White one factor parameters.
* @return The curve sensitivity.
*/
@Override
public MulticurveSensitivity priceCurveSensitivity(final InterestRateFutureOptionMarginSecurity security, final HullWhiteOneFactorProviderInterface hwMulticurves) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(hwMulticurves, "Hull-White and multi-curves data");
ArgumentChecker.isTrue(security.getCurrency().equals(hwMulticurves.getHullWhiteCurrency()), "Model currency incompatible with security currency");
final MulticurveProviderInterface multicurves = hwMulticurves.getMulticurveProvider();
final HullWhiteOneFactorPiecewiseConstantParameters parameters = hwMulticurves.getHullWhiteParameters();
final double k = security.getStrike();
final double ktilde = 1.0 - k;
final double theta = security.getExpirationTime();
final double delta = security.getUnderlyingFuture().getFixingPeriodAccrualFactor();
final double t0 = security.getUnderlyingFuture().getLastTradingTime();
final double t1 = security.getUnderlyingFuture().getFixingPeriodStartTime();
final double t2 = security.getUnderlyingFuture().getFixingPeriodEndTime();
// forward sweep
final double alpha = MODEL.alpha(parameters, 0.0, theta, t1, t2);
final double gamma = MODEL.futuresConvexityFactor(parameters, t0, t1, t2);
final double forward = multicurves.getForwardRate(security.getUnderlyingFuture().getIborIndex(), t1, t2, delta);
final double kappa = -Math.log((1 + delta * ktilde) / (1 + delta * forward) / gamma) / alpha - 0.5 * alpha;
// Bakcward sweep
final double priceBar = 1.0;
double forwardBar;
if (security.isCall()) {
final double normalAlphaKappa = NORMAL.getCDF(-kappa - alpha);
forwardBar = -gamma * normalAlphaKappa * priceBar;
} else {
final double normalAlphaKappa = NORMAL.getCDF(kappa + alpha);
forwardBar = gamma * normalAlphaKappa * priceBar;
}
final Map<String, List<ForwardSensitivity>> mapFwd = new HashMap<>();
final List<ForwardSensitivity> listForward = new ArrayList<>();
listForward.add(new ForwardSensitivity(t1, t2, delta, forwardBar));
mapFwd.put(hwMulticurves.getMulticurveProvider().getName(security.getUnderlyingFuture().getIborIndex()), listForward);
return MulticurveSensitivity.ofForward(mapFwd);
}
}