@Test
/** Test the present value. */
public void presentValueExplicit() {
final MultipleCurrencyAmount pv = METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final double timeToExpiry = SWAPTION_LONG_PAYER.getTimeToExpiry();
final AnnuityPaymentFixed cfe =
CFEC.visitSwap(SWAPTION_LONG_PAYER.getUnderlyingSwap(), MULTICURVES);
final int numberOfPayments = cfe.getNumberOfPayments();
final double alpha[] = new double[numberOfPayments];
final double disccf[] = new double[numberOfPayments];
for (int loopcf = 0; loopcf < numberOfPayments; loopcf++) {
alpha[loopcf] =
MODEL.alpha(
HW_PARAMETERS,
0.0,
timeToExpiry,
timeToExpiry,
cfe.getNthPayment(loopcf).getPaymentTime());
disccf[loopcf] =
MULTICURVES.getDiscountFactor(EUR, cfe.getNthPayment(loopcf).getPaymentTime())
* cfe.getNthPayment(loopcf).getAmount();
}
final double kappa = MODEL.kappa(disccf, alpha);
double pvExpected = 0.0;
for (int loopcf = 0; loopcf < numberOfPayments; loopcf++) {
pvExpected += disccf[loopcf] * NORMAL.getCDF(-kappa - alpha[loopcf]);
}
assertEquals(
"Swaption physical - Hull-White - present value", pvExpected, pv.getAmount(EUR), 1E-2);
final MultipleCurrencyAmount pv2 =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, cfe, HW_MULTICURVES);
assertEquals("Swaption physical - Hull-White - present value", pv, pv2);
}
@Test
/** Tests long/short parity. */
public void longShortParityExplicit() {
final MultipleCurrencyAmount pvLong =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvShort =
METHOD_HW.presentValue(SWAPTION_SHORT_PAYER, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - present value - long/short parity",
pvLong.getAmount(EUR),
-pvShort.getAmount(EUR),
TOLERANCE_PV);
}
@Test
/** Tests payer/receiver/swap parity. */
public void payerReceiverParityExplicit() {
final MultipleCurrencyAmount pvReceiverLong =
METHOD_HW.presentValue(SWAPTION_LONG_RECEIVER, HW_MULTICURVES);
final MultipleCurrencyAmount pvPayerShort =
METHOD_HW.presentValue(SWAPTION_SHORT_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvSwap = SWAP_RECEIVER.accept(PVDC, MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - present value - payer/receiver/swap parity",
pvReceiverLong.getAmount(EUR) + pvPayerShort.getAmount(EUR),
pvSwap.getAmount(EUR),
TOLERANCE_PV);
}
@Test
/** Tests the method against the present value calculator. */
public void presentValueMethodVsCalculator() {
final MultipleCurrencyAmount pvMethod =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvCalculator = SWAPTION_LONG_PAYER.accept(PVHWC, HW_MULTICURVES);
assertEquals(
"SwaptionPhysicalFixedIborSABRMethod: present value : method and calculator",
pvMethod,
pvCalculator);
}
@Test
/** Compare explicit formula with approximated formula. */
public void presentValueApproximation() {
final BlackImpliedVolatilityFormula implied = new BlackImpliedVolatilityFormula();
final double forward =
SWAPTION_LONG_PAYER
.getUnderlyingSwap()
.accept(ParRateDiscountingCalculator.getInstance(), MULTICURVES);
final double pvbp =
METHOD_SWAP.presentValueBasisPoint(SWAPTION_LONG_PAYER.getUnderlyingSwap(), MULTICURVES);
final MultipleCurrencyAmount pvPayerLongExplicit =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvPayerLongApproximation =
METHOD_HW_APPROXIMATION.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final BlackFunctionData data = new BlackFunctionData(forward, pvbp, 0.20);
final double volExplicit =
implied.getImpliedVolatility(data, SWAPTION_LONG_PAYER, pvPayerLongExplicit.getAmount(EUR));
final double volApprox =
implied.getImpliedVolatility(
data, SWAPTION_LONG_PAYER, pvPayerLongApproximation.getAmount(EUR));
assertEquals(
"Swaption physical - Hull-White - present value - explicit/approximation",
pvPayerLongExplicit.getAmount(EUR),
pvPayerLongApproximation.getAmount(EUR),
5.0E+2);
assertEquals(
"Swaption physical - Hull-White - present value - explicit/approximation",
volExplicit,
volApprox,
2.5E-4); // 0.025%
final MultipleCurrencyAmount pvReceiverLongExplicit =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvReceiverLongApproximation =
METHOD_HW_APPROXIMATION.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - present value - explicit/numerical integration",
pvReceiverLongExplicit.getAmount(EUR),
pvReceiverLongApproximation.getAmount(EUR),
5.0E+2);
}
@Test
/** Compare explicit formula with numerical integration. */
public void presentValueNumericalIntegration() {
final MultipleCurrencyAmount pvPayerLongExplicit =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvPayerLongIntegration =
METHOD_HW_INTEGRATION.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - present value - explicit/numerical integration",
pvPayerLongExplicit.getAmount(EUR),
pvPayerLongIntegration.getAmount(EUR),
TOLERANCE_PV);
final MultipleCurrencyAmount pvPayerShortExplicit =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvPayerShortIntegration =
METHOD_HW_INTEGRATION.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - present value - explicit/numerical integration",
pvPayerShortExplicit.getAmount(EUR),
pvPayerShortIntegration.getAmount(EUR),
TOLERANCE_PV);
final MultipleCurrencyAmount pvReceiverLongExplicit =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvReceiverLongIntegration =
METHOD_HW_INTEGRATION.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - present value - explicit/numerical integration",
pvReceiverLongExplicit.getAmount(EUR),
pvReceiverLongIntegration.getAmount(EUR),
TOLERANCE_PV);
final MultipleCurrencyAmount pvReceiverShortExplicit =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvReceiverShortIntegration =
METHOD_HW_INTEGRATION.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - present value - explicit/numerical integration",
pvReceiverShortExplicit.getAmount(EUR),
pvReceiverShortIntegration.getAmount(EUR),
TOLERANCE_PV);
}
@Test
/** Tests the Hull-White parameters sensitivity for the explicit formula. */
public void presentValueHullWhiteSensitivityExplicit() {
final double[] hwSensitivity =
METHOD_HW.presentValueHullWhiteSensitivity(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final int nbVolatility = HW_PARAMETERS.getVolatility().length;
final double shiftVol = 1.0E-6;
final double[] volatilityBumped = new double[nbVolatility];
System.arraycopy(HW_PARAMETERS.getVolatility(), 0, volatilityBumped, 0, nbVolatility);
final double[] volatilityTime = new double[nbVolatility - 1];
System.arraycopy(HW_PARAMETERS.getVolatilityTime(), 1, volatilityTime, 0, nbVolatility - 1);
final double[] pvBumpedPlus = new double[nbVolatility];
final double[] pvBumpedMinus = new double[nbVolatility];
final HullWhiteOneFactorPiecewiseConstantParameters parametersBumped =
new HullWhiteOneFactorPiecewiseConstantParameters(
HW_PARAMETERS.getMeanReversion(), volatilityBumped, volatilityTime);
final HullWhiteOneFactorProviderDiscount bundleBumped =
new HullWhiteOneFactorProviderDiscount(MULTICURVES, parametersBumped, EUR);
for (int loopvol = 0; loopvol < nbVolatility; loopvol++) {
volatilityBumped[loopvol] += shiftVol;
parametersBumped.setVolatility(volatilityBumped);
pvBumpedPlus[loopvol] =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, bundleBumped).getAmount(EUR);
volatilityBumped[loopvol] -= 2 * shiftVol;
parametersBumped.setVolatility(volatilityBumped);
pvBumpedMinus[loopvol] =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, bundleBumped).getAmount(EUR);
assertEquals(
"Swaption - Hull-White sensitivity adjoint: derivative "
+ loopvol
+ " - difference:"
+ ((pvBumpedPlus[loopvol] - pvBumpedMinus[loopvol]) / (2 * shiftVol)
- hwSensitivity[loopvol]),
(pvBumpedPlus[loopvol] - pvBumpedMinus[loopvol]) / (2 * shiftVol),
hwSensitivity[loopvol],
TOLERANCE_PV_DELTA);
volatilityBumped[loopvol] = HW_PARAMETERS.getVolatility()[loopvol];
}
}
@Test
/** Approximation analysis. */
public void presentValueApproximationAnalysis() {
final NormalImpliedVolatilityFormula implied = new NormalImpliedVolatilityFormula();
final int nbStrike = 20;
final double[] pvExplicit = new double[nbStrike + 1];
final double[] pvApproximation = new double[nbStrike + 1];
final double[] strike = new double[nbStrike + 1];
final double[] volExplicit = new double[nbStrike + 1];
final double[] volApprox = new double[nbStrike + 1];
final double strikeRange = 0.010;
final SwapFixedCoupon<Coupon> swap = SWAP_PAYER_DEFINITION.toDerivative(REFERENCE_DATE);
final double forward = swap.accept(PRDC, MULTICURVES);
final double pvbp = METHOD_SWAP.presentValueBasisPoint(swap, MULTICURVES);
for (int loopstrike = 0; loopstrike <= nbStrike; loopstrike++) {
strike[loopstrike] =
forward
- strikeRange
+ 3
* strikeRange
* loopstrike
/ nbStrike; // From forward-strikeRange to forward+2*strikeRange
final SwapFixedIborDefinition swapDefinition =
SwapFixedIborDefinition.from(
SETTLEMENT_DATE,
SWAP_TENOR,
EUR1YEURIBOR6M,
NOTIONAL,
strike[loopstrike],
FIXED_IS_PAYER);
final SwaptionPhysicalFixedIborDefinition swaptionDefinition =
SwaptionPhysicalFixedIborDefinition.from(EXPIRY_DATE, swapDefinition, IS_LONG);
final SwaptionPhysicalFixedIbor swaption = swaptionDefinition.toDerivative(REFERENCE_DATE);
pvExplicit[loopstrike] = METHOD_HW.presentValue(swaption, HW_MULTICURVES).getAmount(EUR);
pvApproximation[loopstrike] =
METHOD_HW_APPROXIMATION.presentValue(swaption, HW_MULTICURVES).getAmount(EUR);
final NormalFunctionData data = new NormalFunctionData(forward, pvbp, 0.01);
volExplicit[loopstrike] =
implied.getImpliedVolatility(data, swaption, pvExplicit[loopstrike]);
volApprox[loopstrike] =
implied.getImpliedVolatility(data, swaption, pvApproximation[loopstrike]);
assertEquals(
"Swaption physical - Hull-White - implied volatility - explicit/approximation",
volExplicit[loopstrike],
volApprox[loopstrike],
1.0E-3); // 0.10%
}
}
@Test(enabled = true)
/** Compare explicit formula with Monte-Carlo and long/short and payer/receiver parities. */
public void presentValueMonteCarlo() {
HullWhiteMonteCarloMethod methodMC;
methodMC =
new HullWhiteMonteCarloMethod(
new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
// Seed fixed to the DEFAULT_SEED for testing purposes.
final MultipleCurrencyAmount pvPayerLongExplicit =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvPayerLongMC =
methodMC.presentValue(SWAPTION_LONG_PAYER, EUR, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - Monte Carlo",
pvPayerLongExplicit.getAmount(EUR),
pvPayerLongMC.getAmount(EUR),
1.0E+4);
final double pvMCPreviousRun = 4221400.891;
assertEquals(
"Swaption physical - Hull-White - Monte Carlo",
pvMCPreviousRun,
pvPayerLongMC.getAmount(EUR),
TOLERANCE_PV);
methodMC =
new HullWhiteMonteCarloMethod(
new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
final MultipleCurrencyAmount pvPayerShortMC =
methodMC.presentValue(SWAPTION_SHORT_PAYER, EUR, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - Monte Carlo",
-pvPayerLongMC.getAmount(EUR),
pvPayerShortMC.getAmount(EUR),
TOLERANCE_PV);
final MultipleCurrencyAmount pvReceiverLongMC =
methodMC.presentValue(SWAPTION_LONG_RECEIVER, EUR, HW_MULTICURVES);
final MultipleCurrencyAmount pvSwap = SWAP_RECEIVER.accept(PVDC, MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - Monte Carlo - payer/receiver/swap parity",
pvReceiverLongMC.getAmount(EUR) + pvPayerShortMC.getAmount(EUR),
pvSwap.getAmount(EUR),
1.0E+5);
}
@Test(enabled = false)
/** Tests of performance. "enabled = false" for the standard testing. */
public void performance() {
long startTime, endTime;
final int nbTest = 1000;
MultipleCurrencyAmount pvPayerLongExplicit = MultipleCurrencyAmount.of(EUR, 0.0);
MultipleCurrencyAmount pvPayerLongIntegration = MultipleCurrencyAmount.of(EUR, 0.0);
MultipleCurrencyAmount pvPayerLongApproximation = MultipleCurrencyAmount.of(EUR, 0.0);
@SuppressWarnings("unused")
MultipleCurrencyAmount pvPayerLongMC = MultipleCurrencyAmount.of(EUR, 0.0);
double[] pvhws =
METHOD_HW.presentValueHullWhiteSensitivity(SWAPTION_LONG_PAYER, HW_MULTICURVES);
MultipleCurrencyMulticurveSensitivity pvcs =
METHOD_HW.presentValueCurveSensitivity(SWAPTION_LONG_PAYER, HW_MULTICURVES);
startTime = System.currentTimeMillis();
for (int looptest = 0; looptest < nbTest; looptest++) {
pvPayerLongExplicit = METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
}
endTime = System.currentTimeMillis();
System.out.println(
nbTest + " pv swaption Hull-White explicit method: " + (endTime - startTime) + " ms");
// Performance note: HW price: 19-Nov-2012: On Mac Pro 3.2 GHz Quad-Core Intel Xeon: 380 ms for
// 10000 swaptions.
startTime = System.currentTimeMillis();
for (int looptest = 0; looptest < nbTest; looptest++) {
pvhws = METHOD_HW.presentValueHullWhiteSensitivity(SWAPTION_LONG_PAYER, HW_MULTICURVES);
}
endTime = System.currentTimeMillis();
System.out.println(
nbTest
+ " HW sensitivity swaption Hull-White explicit method: "
+ (endTime - startTime)
+ " ms");
// Performance note: HW sensitivity (3): 19-Nov-2012: On Mac Pro 3.2 GHz Quad-Core Intel Xeon:
// 430 ms for 10000 swaptions.
startTime = System.currentTimeMillis();
for (int looptest = 0; looptest < nbTest; looptest++) {
pvcs = METHOD_HW.presentValueCurveSensitivity(SWAPTION_LONG_PAYER, HW_MULTICURVES);
}
endTime = System.currentTimeMillis();
System.out.println(
nbTest
+ " curve sensitivity swaption Hull-White explicit method: "
+ (endTime - startTime)
+ " ms");
// Performance note: curve sensitivity (40): 19-Nov-2012: On Mac Pro 3.2 GHz Quad-Core Intel
// Xeon: 855 ms for 10000 swaptions.
startTime = System.currentTimeMillis();
for (int looptest = 0; looptest < nbTest; looptest++) {
pvhws = METHOD_HW.presentValueHullWhiteSensitivity(SWAPTION_LONG_PAYER, HW_MULTICURVES);
pvcs = METHOD_HW.presentValueCurveSensitivity(SWAPTION_LONG_PAYER, HW_MULTICURVES);
pvhws = METHOD_HW.presentValueHullWhiteSensitivity(SWAPTION_LONG_PAYER, HW_MULTICURVES);
}
endTime = System.currentTimeMillis();
System.out.println(
nbTest
+ " price/delta/vega swaption Hull-White explicit method: "
+ (endTime - startTime)
+ " ms");
// Performance note: present value/delta/vega: 19-Nov-2012: On Mac Pro 3.2 GHz Quad-Core Intel
// Xeon: 1730 ms for 10000 swaptions.
startTime = System.currentTimeMillis();
for (int looptest = 0; looptest < nbTest; looptest++) {
pvPayerLongIntegration =
METHOD_HW_INTEGRATION.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
}
endTime = System.currentTimeMillis();
System.out.println(
nbTest
+ " swaption Hull-White numerical integration method: "
+ (endTime - startTime)
+ " ms");
// Performance note: HW numerical integration: 19-Nov-2012: On Mac Pro 3.2 GHz Quad-Core Intel
// Xeon: 1700 ms for 10000 swaptions.
startTime = System.currentTimeMillis();
for (int looptest = 0; looptest < nbTest; looptest++) {
pvPayerLongApproximation =
METHOD_HW_APPROXIMATION.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
}
endTime = System.currentTimeMillis();
System.out.println(
nbTest + " swaption Hull-White approximation method: " + (endTime - startTime) + " ms");
// Performance note: HW approximation: 19-Nov-2012: On Mac Pro 3.2 GHz Quad-Core Intel Xeon: 250
// ms for 10000 swaptions.
startTime = System.currentTimeMillis();
for (int looptest = 0; looptest < nbTest; looptest++) {
pvPayerLongMC = METHOD_HW_MONTECARLO.presentValue(SWAPTION_LONG_PAYER, EUR, HW_MULTICURVES);
}
endTime = System.currentTimeMillis();
System.out.println(
nbTest
+ " swaption Hull-White Monte Carlo method ("
+ NB_PATH
+ " paths): "
+ (endTime - startTime)
+ " ms");
// Performance note: HW approximation: 18-Aug-11: On Mac Pro 3.2 GHz Quad-Core Intel Xeon: 9200
// ms for 1000 swaptions (12500 paths).
final double difference =
pvPayerLongExplicit.getAmount(EUR) - pvPayerLongIntegration.getAmount(EUR);
final double difference2 =
pvPayerLongExplicit.getAmount(EUR) - pvPayerLongApproximation.getAmount(EUR);
// double difference3 = pvPayerLongExplicit.getAmount(CUR) - pvPayerLongMC.getAmount(CUR);
System.out.println("Difference explicit-integration: " + difference);
System.out.println("Difference explicit-approximation: " + difference2);
// System.out.println("Difference explicit-Monte Carlo: " + difference3);
System.out.println("Curve sensitivity: " + pvcs.toString());
System.out.println("HW sensitivity: " + Arrays.toString(pvhws));
}