/**
* 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().getTradingLastTime();
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.getSimplyCompoundForwardRate(
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 SimplyCompoundedForwardSensitivity(t1, t2, delta, forwardBar));
mapFwd.put(
hwMulticurves
.getMulticurveProvider()
.getName(security.getUnderlyingFuture().getIborIndex()),
listForward);
return MulticurveSensitivity.ofForward(mapFwd);
}
/**
* 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().getTradingLastTime();
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.getSimplyCompoundForwardRate(
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;
}