/**
* Tests present value in the region where there is extrapolation. Test a hard-coded value. Tests
* long/short parity. Test payer/receiver/swap parity.
*/
@Test
public void testPresentValueExtra() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final SABRInterestRateParameters sabrParameter = TestsDataSetsSABR.createSABR1();
final SABRInterestRateDataBundle sabrBundle =
new SABRInterestRateDataBundle(sabrParameter, curves);
final double highStrike = 0.10;
final SwapFixedIborDefinition swapDefinitionPayerHighStrike =
SwapFixedIborDefinition.from(
SETTLEMENT_DATE, CMS_INDEX, NOTIONAL, highStrike, FIXED_IS_PAYER);
final SwapFixedIborDefinition swapDefinitionReceiverHighStrike =
SwapFixedIborDefinition.from(
SETTLEMENT_DATE, CMS_INDEX, NOTIONAL, highStrike, !FIXED_IS_PAYER);
final SwaptionCashFixedIborDefinition swaptionDefinitionLongPayerHighStrike =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, swapDefinitionPayerHighStrike, IS_LONG);
final SwaptionCashFixedIborDefinition swaptionDefinitionShortPayerHighStrike =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, swapDefinitionPayerHighStrike, !IS_LONG);
final SwaptionCashFixedIborDefinition swaptionDefinitionLongReceiverHighStrike =
SwaptionCashFixedIborDefinition.from(
EXPIRY_DATE, swapDefinitionReceiverHighStrike, IS_LONG);
final SwaptionCashFixedIbor swaptionLongPayerHighStrike =
swaptionDefinitionLongPayerHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
final SwaptionCashFixedIbor swaptionShortPayerHighStrike =
swaptionDefinitionShortPayerHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
final SwaptionCashFixedIbor swaptionLongReceiverHighStrike =
swaptionDefinitionLongReceiverHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
final SwaptionCashFixedIborSABRExtrapolationRightMethod method =
new SwaptionCashFixedIborSABRExtrapolationRightMethod(CUT_OFF_STRIKE, MU);
final double priceLongPayer = method.presentValue(swaptionLongPayerHighStrike, sabrBundle);
final double priceShortPayer = method.presentValue(swaptionShortPayerHighStrike, sabrBundle);
final double priceLongReceiver =
method.presentValue(swaptionLongReceiverHighStrike, sabrBundle);
final double priceLongPayerExpected = 557829.033; // Value from previous run
final double priceLongReceiverExpected = 20759354.082; // Value from previous run
assertEquals(
"Swaption cash SABR extrapolation: fixed value",
priceLongPayerExpected,
priceLongPayer,
1E-2);
assertEquals(
"Swaption cash SABR extrapolation: fixed value",
priceLongReceiverExpected,
priceLongReceiver,
1E-2);
assertEquals(
"Swaption cash SABR extrapolation: long/short parity",
priceLongPayer,
-priceShortPayer,
1E-2);
}
@Test
/**
* Test the present value sensitivity to SABR parameters for a swaption with strike above the
* cut-off strike.
*/
public void testPresentValueSABRSensitivity() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final SABRInterestRateParameters sabrParameter = TestsDataSetsSABR.createSABR1();
final SABRInterestRateDataBundle sabrBundle =
new SABRInterestRateDataBundle(sabrParameter, curves);
final double highStrike = 0.10;
final SwapFixedIborDefinition swapDefinitionPayerHighStrike =
SwapFixedIborDefinition.from(
SETTLEMENT_DATE, CMS_INDEX, NOTIONAL, highStrike, FIXED_IS_PAYER);
final SwaptionCashFixedIborDefinition swaptionDefinitionLongPayerHighStrike =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, swapDefinitionPayerHighStrike, IS_LONG);
final SwaptionCashFixedIborDefinition swaptionDefinitionShortPayerHighStrike =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, swapDefinitionPayerHighStrike, !IS_LONG);
final SwaptionCashFixedIbor swaptionLongPayerHighStrike =
swaptionDefinitionLongPayerHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
final SwaptionCashFixedIbor swaptionShortPayerHighStrike =
swaptionDefinitionShortPayerHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
// SwaptionCashFixedIborSABRExtrapolationRightMethod methodExtra = new
// SwaptionCashFixedIborSABRExtrapolationRightMethod(CUT_OFF_STRIKE, MU);
// Swaption sensitivity
final PresentValueSABRSensitivityDataBundle pvsLongPayer =
METHOD_EXTRAPOLATION.presentValueSABRSensitivity(swaptionLongPayerHighStrike, sabrBundle);
PresentValueSABRSensitivityDataBundle pvsShortPayer =
METHOD_EXTRAPOLATION.presentValueSABRSensitivity(swaptionShortPayerHighStrike, sabrBundle);
// Long/short parity
pvsShortPayer = PresentValueSABRSensitivityDataBundle.multiplyBy(pvsShortPayer, -1.0);
assertEquals(pvsLongPayer.getAlpha(), pvsShortPayer.getAlpha());
// SABR sensitivity vs finite difference
final double pvLongPayer =
METHOD_EXTRAPOLATION.presentValue(swaptionLongPayerHighStrike, sabrBundle);
final DoublesPair expectedExpiryTenor =
new DoublesPair(swaptionLongPayerHighStrike.getTimeToExpiry(), ANNUITY_TENOR_YEAR);
final double shift = 0.000005;
// Alpha sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterAlphaBumped =
TestsDataSetsSABR.createSABR1AlphaBumped(shift);
final SABRInterestRateDataBundle sabrBundleAlphaBumped =
new SABRInterestRateDataBundle(sabrParameterAlphaBumped, curves);
final double pvLongPayerAlphaBumped =
METHOD_EXTRAPOLATION.presentValue(swaptionLongPayerHighStrike, sabrBundleAlphaBumped);
final double expectedAlphaSensi = (pvLongPayerAlphaBumped - pvLongPayer) / shift;
assertEquals(
"Number of alpha sensitivity", pvsLongPayer.getAlpha().getMap().keySet().size(), 1);
assertEquals(
"Alpha sensitivity expiry/tenor",
pvsLongPayer.getAlpha().getMap().keySet().contains(expectedExpiryTenor),
true);
assertEquals(
"Alpha sensitivity value",
expectedAlphaSensi,
pvsLongPayer.getAlpha().getMap().get(expectedExpiryTenor),
2.0E+3);
// Rho sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterRhoBumped =
TestsDataSetsSABR.createSABR1RhoBumped(shift);
final SABRInterestRateDataBundle sabrBundleRhoBumped =
new SABRInterestRateDataBundle(sabrParameterRhoBumped, curves);
final double pvLongPayerRhoBumped =
METHOD_EXTRAPOLATION.presentValue(swaptionLongPayerHighStrike, sabrBundleRhoBumped);
final double expectedRhoSensi = (pvLongPayerRhoBumped - pvLongPayer) / shift;
assertEquals("Number of rho sensitivity", pvsLongPayer.getRho().getMap().keySet().size(), 1);
assertEquals(
"Rho sensitivity expiry/tenor",
pvsLongPayer.getRho().getMap().keySet().contains(expectedExpiryTenor),
true);
assertEquals(
"Rho sensitivity value",
expectedRhoSensi,
pvsLongPayer.getRho().getMap().get(expectedExpiryTenor),
1.0E+0);
// Alpha sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterNuBumped =
TestsDataSetsSABR.createSABR1NuBumped(shift);
final SABRInterestRateDataBundle sabrBundleNuBumped =
new SABRInterestRateDataBundle(sabrParameterNuBumped, curves);
final double pvLongPayerNuBumped =
METHOD_EXTRAPOLATION.presentValue(swaptionLongPayerHighStrike, sabrBundleNuBumped);
final double expectedNuSensi = (pvLongPayerNuBumped - pvLongPayer) / shift;
assertEquals("Number of nu sensitivity", pvsLongPayer.getNu().getMap().keySet().size(), 1);
assertEquals(
"Nu sensitivity expiry/tenor",
pvsLongPayer.getNu().getMap().keySet().contains(expectedExpiryTenor),
true);
assertEquals(
"Nu sensitivity value",
expectedNuSensi,
pvsLongPayer.getNu().getMap().get(expectedExpiryTenor),
5.0E+1);
}
@Test
/**
* Test the present value sensitivity to rate for a swaption with strike above the cut-off strike.
*/
public void testPresentValueSensitivityExtra() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final SABRInterestRateParameters sabrParameter = TestsDataSetsSABR.createSABR1();
final SABRInterestRateDataBundle sabrBundle =
new SABRInterestRateDataBundle(sabrParameter, curves);
final double highStrike = 0.10;
final SwapFixedIborDefinition swapDefinitionPayerHighStrike =
SwapFixedIborDefinition.from(
SETTLEMENT_DATE, CMS_INDEX, NOTIONAL, highStrike, FIXED_IS_PAYER);
final SwaptionCashFixedIborDefinition swaptionDefinitionLongPayerHighStrike =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, swapDefinitionPayerHighStrike, IS_LONG);
final SwaptionCashFixedIborDefinition swaptionDefinitionShortPayerHighStrike =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, swapDefinitionPayerHighStrike, !IS_LONG);
final SwaptionCashFixedIbor swaptionLongPayerHighStrike =
swaptionDefinitionLongPayerHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
final SwaptionCashFixedIbor swaptionShortPayerHighStrike =
swaptionDefinitionShortPayerHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
final SwaptionCashFixedIborSABRExtrapolationRightMethod methodExtra =
new SwaptionCashFixedIborSABRExtrapolationRightMethod(CUT_OFF_STRIKE, MU);
// Swaption sensitivity
InterestRateCurveSensitivity pvsLongPayerExtra =
methodExtra.presentValueSensitivity(swaptionLongPayerHighStrike, sabrBundle);
final InterestRateCurveSensitivity pvsShortPayerExtra =
methodExtra.presentValueSensitivity(swaptionShortPayerHighStrike, sabrBundle);
// Long/short parity
final InterestRateCurveSensitivity pvsShortPayer_1 = pvsShortPayerExtra.multiply(-1);
assertEquals(pvsLongPayerExtra.getSensitivities(), pvsShortPayer_1.getSensitivities());
// Present value sensitivity comparison with finite difference.
final double deltaTolerance = 5.0E+4;
// Testing note: Sensitivity is for a movement of 1. 1E+2 = 1 cent for a 1 bp move. Tolerance
// increased to cope with numerical imprecision of finite difference.
final double deltaShift = 1.0E-5;
pvsLongPayerExtra = pvsLongPayerExtra.clean();
final double pv = methodExtra.presentValue(swaptionLongPayerHighStrike, sabrBundle);
// 1. Forward curve sensitivity
final String bumpedCurveName = "Bumped Curve";
final String[] bumpedCurvesForwardName = {FUNDING_CURVE_NAME, bumpedCurveName};
final SwaptionCashFixedIbor swaptionBumpedForward =
swaptionDefinitionLongPayerHighStrike.toDerivative(REFERENCE_DATE, bumpedCurvesForwardName);
final YieldAndDiscountCurve curveForward = curves.getCurve(FORWARD_CURVE_NAME);
final Set<Double> timeForwardSet = new TreeSet<Double>();
for (final Payment pay :
swaptionLongPayerHighStrike.getUnderlyingSwap().getSecondLeg().getPayments()) {
final CouponIbor coupon = (CouponIbor) pay;
timeForwardSet.add(coupon.getFixingPeriodStartTime());
timeForwardSet.add(coupon.getFixingPeriodEndTime());
}
final int nbForwardDate = timeForwardSet.size();
final List<Double> timeForwardList = new ArrayList<Double>(timeForwardSet);
Double[] timeForwardArray = new Double[nbForwardDate];
timeForwardArray = timeForwardList.toArray(timeForwardArray);
final double[] yieldsForward = new double[nbForwardDate + 1];
final double[] nodeTimesForward = new double[nbForwardDate + 1];
yieldsForward[0] = curveForward.getInterestRate(0.0);
for (int i = 0; i < nbForwardDate; i++) {
nodeTimesForward[i + 1] = timeForwardArray[i];
yieldsForward[i + 1] = curveForward.getInterestRate(nodeTimesForward[i + 1]);
}
final YieldAndDiscountCurve tempCurveForward =
new YieldCurve(
InterpolatedDoublesCurve.fromSorted(
nodeTimesForward, yieldsForward, new LinearInterpolator1D()));
final List<DoublesPair> tempForward =
pvsLongPayerExtra.getSensitivities().get(FORWARD_CURVE_NAME);
final double[] resFwd = new double[nbForwardDate];
for (int i = 0; i < nbForwardDate; i++) {
final YieldAndDiscountCurve bumpedCurveForward =
tempCurveForward.withSingleShift(nodeTimesForward[i + 1], deltaShift);
final YieldCurveBundle curvesBumpedForward = new YieldCurveBundle();
curvesBumpedForward.addAll(curves);
curvesBumpedForward.setCurve("Bumped Curve", bumpedCurveForward);
final SABRInterestRateDataBundle sabrBundleBumped =
new SABRInterestRateDataBundle(sabrParameter, curvesBumpedForward);
final double bumpedpv = methodExtra.presentValue(swaptionBumpedForward, sabrBundleBumped);
resFwd[i] = (bumpedpv - pv) / deltaShift;
final DoublesPair pair = tempForward.get(i);
assertEquals(
"Sensitivity to forward curve: Node " + i,
nodeTimesForward[i + 1],
pair.getFirst(),
1E-8);
assertEquals(
"Sensitivity to forward curve: Node " + i, resFwd[i], pair.getSecond(), deltaTolerance);
}
// 2. Funding curve sensitivity
final String[] bumpedCurvesFundingName = {bumpedCurveName, FORWARD_CURVE_NAME};
final SwaptionCashFixedIbor swaptionBumpedFunding =
swaptionDefinitionLongPayerHighStrike.toDerivative(REFERENCE_DATE, bumpedCurvesFundingName);
final int nbPayDate =
swaptionDefinitionLongPayerHighStrike.getUnderlyingSwap().getIborLeg().getPayments().length;
final YieldAndDiscountCurve curveFunding = curves.getCurve(FUNDING_CURVE_NAME);
final double[] yieldsFunding = new double[nbPayDate + 2];
final double[] nodeTimesFunding = new double[nbPayDate + 2];
yieldsFunding[0] = curveFunding.getInterestRate(0.0);
nodeTimesFunding[1] = swaptionLongPayerHighStrike.getSettlementTime();
yieldsFunding[1] = curveFunding.getInterestRate(nodeTimesFunding[1]);
for (int i = 0; i < nbPayDate; i++) {
nodeTimesFunding[i + 2] =
swaptionLongPayerHighStrike
.getUnderlyingSwap()
.getSecondLeg()
.getNthPayment(i)
.getPaymentTime();
yieldsFunding[i + 2] = curveFunding.getInterestRate(nodeTimesFunding[i + 2]);
}
final YieldAndDiscountCurve tempCurveFunding =
new YieldCurve(
InterpolatedDoublesCurve.fromSorted(
nodeTimesFunding, yieldsFunding, new LinearInterpolator1D()));
final List<DoublesPair> tempFunding =
pvsLongPayerExtra.getSensitivities().get(FUNDING_CURVE_NAME);
final double[] resDsc = new double[nbPayDate];
for (int i = 0; i < nbPayDate; i++) {
final YieldAndDiscountCurve bumpedCurve =
tempCurveFunding.withSingleShift(nodeTimesFunding[i + 1], deltaShift);
final YieldCurveBundle curvesBumped = new YieldCurveBundle();
curvesBumped.addAll(curves);
curvesBumped.setCurve("Bumped Curve", bumpedCurve);
final SABRInterestRateDataBundle sabrBundleBumped =
new SABRInterestRateDataBundle(sabrParameter, curvesBumped);
final double bumpedpv = methodExtra.presentValue(swaptionBumpedFunding, sabrBundleBumped);
resDsc[i] = (bumpedpv - pv) / deltaShift;
final DoublesPair pair = tempFunding.get(i);
assertEquals(
"Sensitivity to discounting curve: Node " + i,
nodeTimesFunding[i + 1],
pair.getFirst(),
1E-8);
assertEquals(
"Sensitivity to discounting curve: Node " + i,
resDsc[i],
pair.getSecond(),
deltaTolerance);
}
}