/**
* 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 PresentValueSensitivity priceCurveSensitivity(
final InterestRateFutureOptionMarginSecurity security,
final SABRInterestRateDataBundle sabrData) {
// Forward sweep
double priceFuture = METHOD_FUTURE.priceFromCurves(security.getUnderlyingFuture(), sabrData);
double rateStrike = 1.0 - security.getStrike();
EuropeanVanillaOption option =
new EuropeanVanillaOption(rateStrike, security.getExpirationTime(), !security.isCall());
double forward = 1 - priceFuture;
double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
double[] volatilityAdjoint =
sabrData
.getSABRParameter()
.getVolatilityAdjoint(security.getExpirationTime(), delay, rateStrike, forward);
BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatilityAdjoint[0]);
double[] priceAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
// Backward sweep
double priceBar = 1.0;
double volatilityBar = priceAdjoint[2] * priceBar;
double forwardBar = priceAdjoint[1] * priceBar + volatilityAdjoint[1] * volatilityBar;
double priceFutureBar = -forwardBar;
PresentValueSensitivity priceFutureDerivative =
METHOD_FUTURE.priceCurveSensitivity(security.getUnderlyingFuture(), sabrData);
return priceFutureDerivative.multiply(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
double priceFuture = METHOD_FUTURE.priceFromCurves(security.getUnderlyingFuture(), sabrData);
double rateStrike = 1.0 - security.getStrike();
EuropeanVanillaOption option =
new EuropeanVanillaOption(rateStrike, security.getExpirationTime(), !security.isCall());
double forward = 1 - priceFuture;
double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
double[] volatilityAdjoint =
sabrData
.getSABRParameter()
.getVolatilityAdjoint(security.getExpirationTime(), delay, rateStrike, forward);
BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatilityAdjoint[0]);
double[] priceAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
// Backward sweep
double priceBar = 1.0;
double volatilityBar = priceAdjoint[2] * priceBar;
final DoublesPair expiryDelay = new DoublesPair(security.getExpirationTime(), delay);
sensi.addAlpha(expiryDelay, volatilityAdjoint[3] * volatilityBar);
sensi.addRho(expiryDelay, volatilityAdjoint[4] * volatilityBar);
sensi.addNu(expiryDelay, volatilityAdjoint[5] * volatilityBar);
return sensi;
}
@Test
/** Test the option price from the future price. Mid-curve one year option. */
public void priceFromFuturePriceMidCurve() {
final double priceFuture = 0.9905;
final double priceOption =
METHOD.optionPriceFromFuturePrice(OPTION_EDU2, SABR_BUNDLE, priceFuture);
final double delay = EDU2.getLastTradingTime() - EXPIRATION_TIME;
final double volatility =
SABR_PARAMETER.getVolatility(EXPIRATION_TIME, delay, 1 - STRIKE, 1 - priceFuture);
final BlackPriceFunction blackFunction = new BlackPriceFunction();
final BlackFunctionData dataBlack = new BlackFunctionData(1 - priceFuture, 1.0, volatility);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(1 - STRIKE, EXPIRATION_TIME, !IS_CALL);
final double priceOptionExpected = blackFunction.getPriceFunction(option).evaluate(dataBlack);
assertEquals(
"Future option with SABR volatilities: option price from future price",
priceOptionExpected,
priceOption);
}
@Test
/** Test the option price from the future price. Standard option. */
public void priceFromFuturePriceStandard() {
final double expirationTime = ACT_ACT.getDayCountFraction(REFERENCE_DATE, LAST_TRADING_DATE);
final InterestRateFutureOptionMarginSecurity optionEDU2Standard =
new InterestRateFutureOptionMarginSecurity(EDU2, expirationTime, STRIKE, IS_CALL);
final double priceFuture = 0.9905;
final double priceOption =
METHOD.optionPriceFromFuturePrice(optionEDU2Standard, SABR_BUNDLE, priceFuture);
final double delay = 0.0;
final double volatility =
SABR_PARAMETER.getVolatility(expirationTime, delay, 1 - STRIKE, 1 - priceFuture);
final BlackPriceFunction blackFunction = new BlackPriceFunction();
final BlackFunctionData dataBlack = new BlackFunctionData(1 - priceFuture, 1.0, volatility);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(1 - STRIKE, expirationTime, !IS_CALL);
final double priceOptionExpected = blackFunction.getPriceFunction(option).evaluate(dataBlack);
assertEquals(
"Future option with SABR volatilities: option price from future price",
priceOptionExpected,
priceOption);
}
/**
* 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;
}