/**
* Interpolates and returns the option's implied volatility The future price is computed without
* convexity adjustment.
*
* @param security The future option security.
* @param normalData The normal volatility and multi-curves provider.
* @return Lognormal Implied Volatility.
*/
public double impliedVolatility(
final InterestRateFutureOptionMarginSecurity security,
final NormalSTIRFuturesSmileProviderInterface normalData) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(normalData, "Normal data");
final double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
return normalData.getVolatility(security.getExpirationTime(), security.getStrike(), delay);
}
/**
* Computes the option security price volatility sensitivity. The future price is computed without
* convexity adjustment.
*
* @param security The future option security.
* @param normalData The normal volatility and multi-curves provider.
* @return The security price Black volatility sensitivity.
*/
public SurfaceValue priceNormalSensitivity(
final InterestRateFutureOptionMarginSecurity security,
final NormalSTIRFuturesSmileProviderInterface normalData) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(normalData, "Normal data");
// Forward sweep
final double priceFuture =
METHOD_FUTURE.price(security.getUnderlyingFuture(), normalData.getMulticurveProvider());
final double strike = security.getStrike();
final EuropeanVanillaOption option =
new EuropeanVanillaOption(strike, security.getExpirationTime(), security.isCall());
final double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
final double volatility =
normalData.getVolatility(security.getExpirationTime(), security.getStrike(), delay);
final NormalFunctionData normalPoint = new NormalFunctionData(priceFuture, 1.0, volatility);
// Backward sweep
final double[] priceAdjoint = new double[3];
NORMAL_FUNCTION.getPriceAdjoint(option, normalPoint, priceAdjoint);
final double priceBar = 1.0;
final double volatilityBar = priceAdjoint[1] * priceBar;
final DoublesPair expiryStrikeDelay = new DoublesPair(security.getExpirationTime(), strike);
final SurfaceValue sensi = SurfaceValue.from(expiryStrikeDelay, volatilityBar);
return sensi;
}
/**
* Computes the option security price curve sensitivity. The future price is computed without
* convexity adjustment. It is supposed that for a given strike the volatility does not change
* with the curves (sticky strike).
*
* @param security The future option security.
* @param normalData The normal volatility and multi-curves provider.
* @return The security price curve sensitivity.
*/
@Override
public MulticurveSensitivity priceCurveSensitivity(
final InterestRateFutureOptionMarginSecurity security,
final NormalSTIRFuturesSmileProviderInterface normalData) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(normalData, "Normal data");
// Forward sweep
final double priceFuture =
METHOD_FUTURE.price(security.getUnderlyingFuture(), normalData.getMulticurveProvider());
final EuropeanVanillaOption option =
new EuropeanVanillaOption(
security.getStrike(), security.getExpirationTime(), security.isCall());
final double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
final double volatility =
normalData.getVolatility(security.getExpirationTime(), security.getStrike(), delay);
final NormalFunctionData normalPoint = new NormalFunctionData(priceFuture, 1.0, volatility);
// Backward sweep
final double[] priceAdjoint = new double[3];
NORMAL_FUNCTION.getPriceAdjoint(option, normalPoint, priceAdjoint);
final double priceBar = 1.0;
final double priceFutureBar = priceAdjoint[0] * priceBar;
final MulticurveSensitivity priceFutureDerivative =
METHOD_FUTURE.priceCurveSensitivity(
security.getUnderlyingFuture(), normalData.getMulticurveProvider());
return priceFutureDerivative.multipliedBy(priceFutureBar);
}
/**
* Computes the option security price curve sensitivity. The future price is computed without
* convexity adjustment.
*
* @param security The future option security.
* @param sabrData The SABR data bundle.
* @return The security price curve sensitivity.
*/
public PresentValueSABRSensitivityDataBundle priceSABRSensitivity(
final InterestRateFutureOptionMarginSecurity security,
final SABRInterestRateDataBundle sabrData) {
final PresentValueSABRSensitivityDataBundle sensi = new PresentValueSABRSensitivityDataBundle();
// Forward sweep
final double priceFuture = METHOD_FUTURE.price(security.getUnderlyingFuture(), sabrData);
final double rateStrike = 1.0 - security.getStrike();
final EuropeanVanillaOption option =
new EuropeanVanillaOption(rateStrike, security.getExpirationTime(), !security.isCall());
final double forward = 1 - priceFuture;
final double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
final double[] volatilityAdjoint =
sabrData
.getSABRParameter()
.getVolatilityAdjoint(security.getExpirationTime(), delay, rateStrike, forward);
final BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatilityAdjoint[0]);
final double[] priceAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
// Backward sweep
final double priceBar = 1.0;
final double volatilityBar = priceAdjoint[2] * priceBar;
final DoublesPair expiryDelay = new DoublesPair(security.getExpirationTime(), delay);
sensi.addAlpha(expiryDelay, volatilityAdjoint[3] * volatilityBar);
sensi.addBeta(expiryDelay, volatilityAdjoint[4] * volatilityBar);
sensi.addRho(expiryDelay, volatilityAdjoint[5] * volatilityBar);
sensi.addNu(expiryDelay, volatilityAdjoint[6] * volatilityBar);
return sensi;
}
/**
* Computes the option security price curve sensitivity. The future price is computed without
* convexity adjustment.
*
* @param security The future option security.
* @param sabrData The SABR data bundle.
* @return The security price curve sensitivity.
*/
public InterestRateCurveSensitivity priceCurveSensitivity(
final InterestRateFutureOptionMarginSecurity security,
final SABRInterestRateDataBundle sabrData) {
// Forward sweep
final double priceFuture = METHOD_FUTURE.price(security.getUnderlyingFuture(), sabrData);
final double rateStrike = 1.0 - security.getStrike();
final EuropeanVanillaOption option =
new EuropeanVanillaOption(rateStrike, security.getExpirationTime(), !security.isCall());
final double forward = 1 - priceFuture;
final double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
final double[] volatilityAdjoint =
sabrData
.getSABRParameter()
.getVolatilityAdjoint(security.getExpirationTime(), delay, rateStrike, forward);
final BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatilityAdjoint[0]);
final double[] priceAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
// Backward sweep
final double priceBar = 1.0;
final double volatilityBar = priceAdjoint[2] * priceBar;
final double forwardBar = priceAdjoint[1] * priceBar + volatilityAdjoint[1] * volatilityBar;
final double priceFutureBar = -forwardBar;
final InterestRateCurveSensitivity priceFutureDerivative =
METHOD_FUTURE.priceCurveSensitivity(security.getUnderlyingFuture(), sabrData);
return priceFutureDerivative.multipliedBy(priceFutureBar);
}
/**
* Computes the option security price. The future price is computed without convexity adjustment.
*
* @param security The future option security.
* @param normalData The normal volatility and multi-curves provider.
* @return The security price.
*/
@Override
public double price(
final InterestRateFutureOptionMarginSecurity security,
final NormalSTIRFuturesSmileProviderInterface normalData) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(normalData, "Normal data");
final double priceFuture =
METHOD_FUTURE.price(security.getUnderlyingFuture(), normalData.getMulticurveProvider());
return priceFromFuturePrice(security, normalData, priceFuture);
}
/**
* 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 option security price from future price.
*
* @param security The future option security.
* @param normalData The normal volatility and multi-curves provider.
* @param priceFuture The price of the underlying future.
* @return The security price.
*/
public double priceFromFuturePrice(
final InterestRateFutureOptionMarginSecurity security,
final NormalSTIRFuturesSmileProviderInterface normalData,
final double priceFuture) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(normalData, "Normal data");
final EuropeanVanillaOption option =
new EuropeanVanillaOption(
security.getStrike(), security.getExpirationTime(), security.isCall());
final double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
final double volatility =
normalData.getVolatility(security.getExpirationTime(), security.getStrike(), delay);
final NormalFunctionData normalPoint = new NormalFunctionData(priceFuture, 1.0, volatility);
final double priceSecurity = NORMAL_FUNCTION.getPriceFunction(option).evaluate(normalPoint);
return priceSecurity;
}
/**
* 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;
}
/**
* Computes the option security price from future price.
*
* @param security The future option security.
* @param sabrData The SABR data bundle.
* @param priceFuture The price of the underlying future.
* @return The security price.
*/
public double optionPriceFromFuturePrice(
final InterestRateFutureOptionMarginSecurity security,
final SABRInterestRateDataBundle sabrData,
final double priceFuture) {
final double rateStrike = 1.0 - security.getStrike();
final EuropeanVanillaOption option =
new EuropeanVanillaOption(rateStrike, security.getExpirationTime(), !security.isCall());
final double forward = 1 - priceFuture;
final double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
final double volatility =
sabrData
.getSABRParameter()
.getVolatility(new double[] {security.getExpirationTime(), delay, rateStrike, forward});
final BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatility);
final double priceSecurity = BLACK_FUNCTION.getPriceFunction(option).evaluate(dataBlack);
return priceSecurity;
}
/**
* Computes the underlying future security price. The future price is computed without convexity
* adjustment.
*
* @param security The future option security.
* @param multicurves The multi-curves provider.
* @return The security price.
*/
public double underlyingFuturesPrice(
final InterestRateFutureOptionMarginSecurity security,
final MulticurveProviderInterface multicurves) {
ArgumentChecker.notNull(security, "Option security");
return METHOD_FUTURE.price(security.getUnderlyingFuture(), multicurves);
}
/**
* Computes the option security price. The future price is computed without convexity adjustment.
*
* @param security The future option security.
* @param sabrData The SABR data bundle.
* @return The security price.
*/
public double optionPrice(
final InterestRateFutureOptionMarginSecurity security,
final SABRInterestRateDataBundle sabrData) {
final double priceFuture = METHOD_FUTURE.price(security.getUnderlyingFuture(), sabrData);
return optionPriceFromFuturePrice(security, sabrData, priceFuture);
}
