/**
* 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);
}
@Test
/** Tests the present value. */
public void presentValueNoNotional() {
final MultipleCurrencyAmount pv = METHOD.presentValue(ZERO_COUPON_CAP, BLACK_INFLATION);
final double timeToMaturity =
ZERO_COUPON_CAP.getReferenceEndTime() - ZERO_COUPON_CAP.getLastKnownFixingTime();
final double df =
MARKET
.getCurve(ZERO_COUPON_CAP.getCurrency())
.getDiscountFactor(ZERO_COUPON_CAP.getPaymentTime());
final double finalIndex =
MARKET.getCurve(PRICE_INDEX_EUR).getPriceIndex(ZERO_COUPON_CAP.getReferenceEndTime());
final double forward = finalIndex / INDEX_1MAY_2008;
final EuropeanVanillaOption option =
new EuropeanVanillaOption(
Math.pow(1 + ZERO_COUPON_CAP.getStrike(), ZERO_COUPON_CAP.getMaturity()),
timeToMaturity,
ZERO_COUPON_CAP.isCap());
final double volatility =
BLACK_INFLATION
.getBlackParameters()
.getVolatility(ZERO_COUPON_CAP.getReferenceEndTime(), ZERO_COUPON_CAP.getStrike());
final BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatility);
final Function1D<BlackFunctionData, Double> func = BLACK_FUNCTION.getPriceFunction(option);
final double pvExpected =
df
* func.evaluate(dataBlack)
* ZERO_COUPON_CAP.getNotional()
* ZERO_COUPON_CAP.getPaymentYearFraction();
assertEquals(
"Zero-coupon inflation DiscountingMethod: Present value",
pvExpected,
pv.getAmount(ZERO_COUPON_CAP.getCurrency()),
TOLERANCE_PV);
}
public void delta() {
final double priceFutures =
METHOD_FUTURE.price(CALL_JB_147.getUnderlyingFuture(), ISSUER_SPECIFIC_MULTICURVES);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(
STRIKE_147, CALL_JB_147.getExpirationTime(), CALL_JB_147.isCall());
final double expiry = CALL_JB_147.getExpirationTime();
final double volatility = BLACK_SURFACE_EXP_STRIKE.getZValue(expiry, STRIKE_147);
double df =
ISSUER_SPECIFIC_MULTICURVES
.getMulticurveProvider()
.getDiscountFactor(JBM5_DEFINITION.getCurrency(), CALL_JB_147.getExpirationTime());
final BlackFunctionData dataBlack = new BlackFunctionData(priceFutures, df, volatility);
final double[] priceAD = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
final double deltaCallExpected = priceAD[1];
final double deltaCallComputed = METHOD_OPT.delta(CALL_JB_147, BLACK_EXP_STRIKE_BNDFUT);
assertEquals(
"BondFuturesOptionPremiumSecurityBlackBondFuturesMethod: delta",
deltaCallExpected,
deltaCallComputed,
TOLERANCE_DELTA);
final double deltaPutComputed = METHOD_OPT.delta(PUT_JB_147, BLACK_EXP_STRIKE_BNDFUT);
assertEquals(
"BondFuturesOptionPremiumSecurityBlackBondFuturesMethod: delta",
deltaCallExpected - deltaPutComputed,
df,
TOLERANCE_DELTA);
}
@Test
public void presentValue() {
final MultipleCurrencyAmount pvMethod =
METHOD_BLACK.presentValue(SWAPTION_LONG_REC, BLACK_MULTICURVES);
final double forward = SWAPTION_LONG_REC.getUnderlyingSwap().accept(PRDC, MULTICURVES);
final double pvbp =
METHOD_SWAP.presentValueBasisPoint(SWAPTION_LONG_REC.getUnderlyingSwap(), MULTICURVES);
final double volatility =
BLACK.getVolatility(
SWAPTION_LONG_REC.getTimeToExpiry(), SWAPTION_LONG_REC.getMaturityTime());
final BlackPriceFunction blackFunction = new BlackPriceFunction();
final BlackFunctionData dataBlack = new BlackFunctionData(forward, pvbp, volatility);
final Function1D<BlackFunctionData, Double> func =
blackFunction.getPriceFunction(SWAPTION_LONG_REC);
final double pvExpected = func.evaluate(dataBlack);
assertEquals(
"Swaption Black method: present value", pvExpected, pvMethod.getAmount(EUR), TOLERANCE_PV);
}
/**
* 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;
}
public void priceFromFuturesPrice() {
final double price = 1.465;
final EuropeanVanillaOption option =
new EuropeanVanillaOption(
STRIKE_147, CALL_JB_147.getExpirationTime(), CALL_JB_147.isCall());
final double logmoney = Math.log(STRIKE_147 / price);
final double expiry = CALL_JB_147.getExpirationTime();
final double volatility = BLACK_SURFACE_EXP_STRIKE.getZValue(expiry, logmoney);
double df =
ISSUER_SPECIFIC_MULTICURVES
.getMulticurveProvider()
.getDiscountFactor(JBM5_DEFINITION.getCurrency(), expiry);
final BlackFunctionData dataBlack = new BlackFunctionData(price, df, volatility);
final double priceExpected = BLACK_FUNCTION.getPriceFunction(option).evaluate(dataBlack);
final double priceComputed =
METHOD_OPT.priceFromUnderlyingPrice(CALL_JB_147, BLACK_EXP_STRIKE_BNDFUT, price);
assertEquals(
"BondFuturesOptionPremiumSecurityBlackBondFuturesMethod: underlying futures price",
priceExpected,
priceComputed,
TOLERANCE_RATE);
}
/**
* Computes the present value of the Physical delivery swaption through approximation..
*
* @param swaption The swaption.
* @param cfe The swaption cash flow equiovalent.
* @param g2Data The G2++ parameters and the curves.
* @return The present value.
*/
public CurrencyAmount presentValue(
final SwaptionPhysicalFixedIbor swaption,
final AnnuityPaymentFixed cfe,
final G2ppPiecewiseConstantDataBundle g2Data) {
YieldAndDiscountCurve dsc =
g2Data.getCurve(swaption.getUnderlyingSwap().getFixedLeg().getDiscountCurve());
int nbCf = cfe.getNumberOfPayments();
double[] cfa = new double[nbCf];
double[] t = new double[nbCf];
for (int loopcf = 0; loopcf < nbCf; loopcf++) {
cfa[loopcf] =
-Math.signum(cfe.getNthPayment(0).getAmount()) * cfe.getNthPayment(loopcf).getAmount();
t[loopcf] = cfe.getNthPayment(loopcf).getPaymentTime();
}
double rhog2pp = g2Data.getG2ppParameter().getCorrelation();
double[][] ht0 = MODEL_G2PP.volatilityMaturityPart(g2Data.getG2ppParameter(), t[0], t);
double[] dfswap = new double[nbCf];
double[] p0 = new double[nbCf];
double[] cP = new double[nbCf];
for (int loopcf = 0; loopcf < nbCf; loopcf++) {
dfswap[loopcf] = dsc.getDiscountFactor(t[loopcf]);
p0[loopcf] = dfswap[loopcf] / dfswap[0];
cP[loopcf] = cfa[loopcf] * p0[loopcf];
}
double k = -cfa[0];
double b0 = 0.0;
for (int loopcf = 1; loopcf < nbCf; loopcf++) {
b0 += cP[loopcf];
}
double[] alpha0 = new double[nbCf - 1];
double[] beta0 = new double[2];
for (int loopcf = 0; loopcf < nbCf - 1; loopcf++) {
alpha0[loopcf] = cfa[loopcf + 1] * p0[loopcf + 1] / b0;
beta0[0] += alpha0[loopcf] * ht0[0][loopcf + 1];
beta0[1] += alpha0[loopcf] * ht0[1][loopcf + 1];
}
double[][] gamma = MODEL_G2PP.gamma(g2Data.getG2ppParameter(), 0, swaption.getTimeToExpiry());
double[] tau = new double[nbCf];
for (int loopcf = 0; loopcf < nbCf; loopcf++) {
tau[loopcf] =
gamma[0][0] * ht0[0][loopcf] * ht0[0][loopcf]
+ gamma[1][1] * ht0[1][loopcf] * ht0[1][loopcf]
+ 2 * rhog2pp * gamma[0][1] * ht0[0][loopcf] * ht0[1][loopcf];
}
double xbarnum = 0.0;
double xbarde = 0.0;
for (int loopcf = 0; loopcf < nbCf; loopcf++) {
xbarnum += cP[loopcf] - cP[loopcf] * tau[loopcf] * tau[loopcf] / 2.0;
xbarde += cP[loopcf] * tau[loopcf];
}
double xbar = xbarnum / xbarde;
double[] pK = new double[nbCf];
for (int loopcf = 0; loopcf < nbCf; loopcf++) {
pK[loopcf] = p0[loopcf] * (1.0 - tau[loopcf] * xbar - tau[loopcf] * tau[loopcf] / 2.0);
}
double[] alphaK = new double[nbCf - 1];
double[] betaK = new double[2];
for (int loopcf = 0; loopcf < nbCf - 1; loopcf++) {
alphaK[loopcf] = cfa[loopcf + 1] * pK[loopcf + 1] / k;
betaK[0] += alphaK[loopcf] * ht0[0][loopcf + 1];
betaK[1] += alphaK[loopcf] * ht0[1][loopcf + 1];
}
double[] betaBar = new double[] {(beta0[0] + betaK[0]) / 2.0, (beta0[1] + betaK[1]) / 2.0};
double sigmaBar2 =
gamma[0][0] * betaBar[0] * betaBar[0]
+ gamma[1][1] * betaBar[1] * betaBar[1]
+ 2 * rhog2pp * gamma[0][1] * betaBar[0] * betaBar[1];
double sigmaBar = Math.sqrt(sigmaBar2);
EuropeanVanillaOption option = new EuropeanVanillaOption(k, 1, !swaption.isCall());
final BlackPriceFunction blackFunction = new BlackPriceFunction();
final BlackFunctionData dataBlack = new BlackFunctionData(b0, dfswap[0], sigmaBar);
final Function1D<BlackFunctionData, Double> func = blackFunction.getPriceFunction(option);
final double price = func.evaluate(dataBlack) * (swaption.isLong() ? 1.0 : -1.0);
return CurrencyAmount.of(swaption.getCurrency(), price);
}