@Test
/** Test the present value using the method with the direct formula with extrapolation. */
public void presentValueAboveCutOff() {
CurrencyAmount methodPrice = METHOD.presentValue(CAP_HIGH_LONG, SABR_BUNDLE);
final double df =
CURVES.getCurve(FUNDING_CURVE_NAME).getDiscountFactor(CAP_HIGH_LONG.getPaymentTime());
final double forward = CAP_HIGH_LONG.accept(PRC, CURVES);
final double maturity =
CAP_HIGH_LONG.getFixingPeriodEndTime() - CAP_LONG.getFixingPeriodStartTime();
final DoublesPair expiryMaturity = new DoublesPair(CAP_HIGH_LONG.getFixingTime(), maturity);
final double alpha = SABR_PARAMETERS.getAlpha(expiryMaturity);
final double beta = SABR_PARAMETERS.getBeta(expiryMaturity);
final double rho = SABR_PARAMETERS.getRho(expiryMaturity);
final double nu = SABR_PARAMETERS.getNu(expiryMaturity);
final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
final SABRExtrapolationRightFunction sabrExtrapolation =
new SABRExtrapolationRightFunction(
forward, sabrParam, CUT_OFF_STRIKE, CAP_HIGH_LONG.getFixingTime(), MU);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(
CAP_HIGH_LONG.getStrike(), CAP_HIGH_LONG.getFixingTime(), CAP_HIGH_LONG.isCap());
final double expectedPrice =
sabrExtrapolation.price(option)
* CAP_HIGH_LONG.getNotional()
* CAP_HIGH_LONG.getPaymentYearFraction()
* df;
assertEquals(
"Cap/floor: SABR with extrapolation pricing", expectedPrice, methodPrice.getAmount(), 1E-2);
methodPrice = METHOD.presentValue(CAP_HIGH_LONG, SABR_BUNDLE);
assertEquals(
"Cap/floor: SABR with extrapolation pricing", expectedPrice, methodPrice.getAmount(), 1E-2);
}
@Test
/** Test the present value using the method with the direct formula with extrapolation. */
public void presentValueLongShortParityAboveCutOff() {
final CurrencyAmount priceLong = METHOD.presentValue(CAP_HIGH_LONG, SABR_BUNDLE);
final CurrencyAmount priceShort = METHOD.presentValue(CAP_HIGH_SHORT, SABR_BUNDLE);
assertEquals(
"Cap/floor: SABR with extrapolation pricing: long/short parity",
priceLong.getAmount(),
-priceShort.getAmount(),
1E-2);
}
@Test
/** Test the cap/floor/forward parity above the cut-off strike. */
public void presentValueCapFloorParityAboveCutOff() {
final CurrencyAmount priceCap = METHOD.presentValue(CAP_HIGH_LONG, SABR_BUNDLE);
final CurrencyAmount priceFloor = METHOD.presentValue(FLOOR_HIGH_SHORT, SABR_BUNDLE);
final double priceCouponStrike = COUPON_STRIKE_HIGH.accept(PVC, CURVES);
final double priceCouponIbor = COUPON_IBOR.accept(PVC, CURVES);
assertEquals(
"Cap/floor: SABR with extrapolation pricing: cap/floor parity",
priceCouponIbor - priceCouponStrike,
priceCap.getAmount() + priceFloor.getAmount(),
1E-2);
}
@Test
/** Test the present value using the method with the direct formula with extrapolation. */
public void presentValueCurveSensitivityMethodVsCalculator() {
final SABRInterestRateDataBundle sabrExtraBundle =
new SABRInterestRateDataBundle(SABR_PARAMETERS, CURVES);
final InterestRateCurveSensitivity pvsMethod =
METHOD.presentValueSensitivity(CAP_HIGH_LONG, SABR_BUNDLE);
final InterestRateCurveSensitivity pvsCalculator =
new InterestRateCurveSensitivity(CAP_HIGH_LONG.accept(PVSC, sabrExtraBundle));
assertEquals(
"Cap/floor: SABR with extrapolation pv curve sensitivity - Method vs Calculator",
pvsMethod,
pvsCalculator);
}
@Test
/** Test the present value using the method with the direct formula with extrapolation. */
public void presentValueMethodVsCalculator() {
final SABRInterestRateDataBundle sabrExtraBundle =
new SABRInterestRateDataBundle(SABR_PARAMETERS, CURVES);
final CurrencyAmount pvMethod = METHOD.presentValue(CAP_LONG, SABR_BUNDLE);
final PresentValueSABRExtrapolationCalculator pvc =
new PresentValueSABRExtrapolationCalculator(CUT_OFF_STRIKE, MU);
final double pvCalculator = CAP_LONG.accept(pvc, sabrExtraBundle);
assertEquals(
"Cap/floor: SABR with extrapolation pricing - Method vs Calculator",
pvMethod.getAmount(),
pvCalculator,
1E-2);
}
@Test
/**
* Test the present value SABR parameters sensitivity against a finite difference computation;
* strike above the cut-off strike.
*/
public void testPresentValueSABRSensitivityAboveCutOff() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final SABRInterestRateParameters sabrParameter = TestsDataSetsSABR.createSABR1();
final SABRInterestRateDataBundle sabrBundle =
new SABRInterestRateDataBundle(sabrParameter, curves);
final CurrencyAmount pv = METHOD.presentValue(CAP_HIGH_LONG, sabrBundle);
final PresentValueSABRSensitivityDataBundle pvsCapLong =
METHOD.presentValueSABRSensitivity(CAP_HIGH_LONG, sabrBundle);
PresentValueSABRSensitivityDataBundle pvsCapShort =
METHOD.presentValueSABRSensitivity(CAP_HIGH_SHORT, sabrBundle);
// Long/short parity
pvsCapShort = pvsCapShort.multiplyBy(-1.0);
assertEquals(pvsCapShort.getAlpha(), pvsCapLong.getAlpha());
// SABR sensitivity vs finite difference
final double shift = 0.0001;
final double shiftAlpha = 0.00001;
final DoublesPair expectedExpiryTenor =
new DoublesPair(
CAP_HIGH_LONG.getFixingTime(),
CAP_HIGH_LONG.getFixingPeriodEndTime() - CAP_HIGH_LONG.getFixingPeriodStartTime());
// Alpha sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterAlphaBumped =
TestsDataSetsSABR.createSABR1AlphaBumped(shiftAlpha);
final SABRInterestRateDataBundle sabrBundleAlphaBumped =
new SABRInterestRateDataBundle(sabrParameterAlphaBumped, curves);
final CurrencyAmount pvLongPayerAlphaBumped =
METHOD.presentValue(CAP_HIGH_LONG, sabrBundleAlphaBumped);
final double expectedAlphaSensi =
(pvLongPayerAlphaBumped.getAmount() - pv.getAmount()) / shiftAlpha;
assertEquals("Number of alpha sensitivity", pvsCapLong.getAlpha().getMap().keySet().size(), 1);
assertEquals(
"Alpha sensitivity expiry/tenor",
pvsCapLong.getAlpha().getMap().keySet().contains(expectedExpiryTenor),
true);
assertEquals(
"Alpha sensitivity value",
expectedAlphaSensi,
pvsCapLong.getAlpha().getMap().get(expectedExpiryTenor),
1.0E-0);
// Rho sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterRhoBumped =
TestsDataSetsSABR.createSABR1RhoBumped();
final SABRInterestRateDataBundle sabrBundleRhoBumped =
new SABRInterestRateDataBundle(sabrParameterRhoBumped, curves);
final CurrencyAmount pvLongPayerRhoBumped =
METHOD.presentValue(CAP_HIGH_LONG, sabrBundleRhoBumped);
final double expectedRhoSensi = (pvLongPayerRhoBumped.getAmount() - pv.getAmount()) / shift;
assertEquals("Number of rho sensitivity", pvsCapLong.getRho().getMap().keySet().size(), 1);
assertEquals(
"Rho sensitivity expiry/tenor",
pvsCapLong.getRho().getMap().keySet().contains(expectedExpiryTenor),
true);
assertEquals(
"Rho sensitivity value",
pvsCapLong.getRho().getMap().get(expectedExpiryTenor),
expectedRhoSensi,
1.0E-1);
// Alpha sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterNuBumped =
TestsDataSetsSABR.createSABR1NuBumped();
final SABRInterestRateDataBundle sabrBundleNuBumped =
new SABRInterestRateDataBundle(sabrParameterNuBumped, curves);
final CurrencyAmount pvLongPayerNuBumped =
METHOD.presentValue(CAP_HIGH_LONG, sabrBundleNuBumped);
final double expectedNuSensi = (pvLongPayerNuBumped.getAmount() - pv.getAmount()) / shift;
assertEquals("Number of nu sensitivity", pvsCapLong.getNu().getMap().keySet().size(), 1);
assertEquals(
"Nu sensitivity expiry/tenor",
pvsCapLong.getNu().getMap().keySet().contains(expectedExpiryTenor),
true);
assertEquals(
"Nu sensitivity value",
pvsCapLong.getNu().getMap().get(expectedExpiryTenor),
expectedNuSensi,
2.0E-1);
}
@Test
/**
* Test the present value rate sensitivity against a finite difference computation; strike above
* the cut-off strike. Test sensitivity long/short parity.
*/
public void testPresentValueSensitivityAboveCutOff() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final SABRInterestRateParameters sabrParameter = TestsDataSetsSABR.createSABR1();
final SABRInterestRateDataBundle sabrBundle =
new SABRInterestRateDataBundle(sabrParameter, curves);
InterestRateCurveSensitivity pvsCapLong =
METHOD.presentValueSensitivity(CAP_HIGH_LONG, sabrBundle);
final InterestRateCurveSensitivity pvsCapShort =
METHOD.presentValueSensitivity(CAP_HIGH_SHORT, sabrBundle);
// Long/short parity
final InterestRateCurveSensitivity pvsCapShort_1 = pvsCapShort.multipliedBy(-1);
assertEquals(pvsCapLong.getSensitivities(), pvsCapShort_1.getSensitivities());
// Present value sensitivity comparison with finite difference.
final double deltaTolerancePrice = 1.0E-1;
// Testing note: Sensitivity is for a movement of 1. 1E+2 = 1 cent for a 1 bp move.
final double deltaShift = 1.0E-7;
pvsCapLong = pvsCapLong.cleaned();
final String bumpedCurveName = "Bumped Curve";
// 1. Forward curve sensitivity
final String[] CurveNameBumpedForward = {FUNDING_CURVE_NAME, bumpedCurveName};
final CapFloorIbor capBumpedForward =
(CapFloorIbor)
CAP_HIGH_LONG_DEFINITION.toDerivative(REFERENCE_DATE, CurveNameBumpedForward);
final double[] nodeTimesForward =
new double[] {
capBumpedForward.getFixingPeriodStartTime(), capBumpedForward.getFixingPeriodEndTime()
};
final double[] sensiForwardMethod =
SensitivityFiniteDifference.curveSensitivity(
capBumpedForward,
SABR_BUNDLE,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForward,
deltaShift,
METHOD);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardMethod.length);
final List<DoublesPair> sensiPvForward = pvsCapLong.getSensitivities().get(FORWARD_CURVE_NAME);
for (int loopnode = 0; loopnode < sensiForwardMethod.length; loopnode++) {
final DoublesPair pairPv = sensiPvForward.get(loopnode);
assertEquals(
"Sensitivity cap/floor pv to forward curve: Node " + loopnode,
nodeTimesForward[loopnode],
pairPv.getFirst(),
1E-8);
// assertEquals("Sensitivity finite difference method: node sensitivity: Node " +
// loopnode, pairPv.second, sensiForwardMethod[loopnode], deltaTolerancePrice);
}
// 2. Discounting curve sensitivity
final String[] CurveNameBumpedDisc = {bumpedCurveName, FORWARD_CURVE_NAME};
final CapFloorIbor capBumpedDisc =
(CapFloorIbor) CAP_HIGH_LONG_DEFINITION.toDerivative(REFERENCE_DATE, CurveNameBumpedDisc);
final double[] nodeTimesDisc = new double[] {capBumpedDisc.getPaymentTime()};
final double[] sensiDiscMethod =
SensitivityFiniteDifference.curveSensitivity(
capBumpedDisc,
SABR_BUNDLE,
FUNDING_CURVE_NAME,
bumpedCurveName,
nodeTimesDisc,
deltaShift,
METHOD);
assertEquals("Sensitivity finite difference method: number of node", 1, sensiDiscMethod.length);
final List<DoublesPair> sensiPvDisc = pvsCapLong.getSensitivities().get(FUNDING_CURVE_NAME);
for (int loopnode = 0; loopnode < sensiDiscMethod.length; loopnode++) {
final DoublesPair pairPv = sensiPvDisc.get(loopnode);
assertEquals(
"Sensitivity cap/floor pv to forward curve: Node " + loopnode,
nodeTimesDisc[loopnode],
pairPv.getFirst(),
1E-8);
assertEquals(
"Sensitivity finite difference method: node sensitivity",
pairPv.second,
sensiDiscMethod[loopnode],
deltaTolerancePrice);
}
}
