/**
* 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);
}
/**
* Class to test the present value and present value rate sensitivity of the cash-settled European
* swaption in the SABR with extrapolation method. The SABR smile is extrapolated above a certain
* cut-off strike.
*/
public class SwaptionCashFixedIborSABRExtrapolationRightMethodTest {
// Swaption description
private static final ZonedDateTime EXPIRY_DATE = DateUtils.getUTCDate(2014, 3, 18);
private static final boolean IS_LONG = true;
private static final int SETTLEMENT_DAYS = 2;
// Swap 5Y description
private static final Currency CUR = Currency.USD;
private static final Calendar CALENDAR = new MondayToFridayCalendar("A");
private static final BusinessDayConvention BUSINESS_DAY =
BusinessDayConventionFactory.INSTANCE.getBusinessDayConvention("Modified Following");
private static final boolean IS_EOM = true;
private static final int ANNUITY_TENOR_YEAR = 5;
private static final Period ANNUITY_TENOR = Period.ofYears(ANNUITY_TENOR_YEAR);
private static final ZonedDateTime SETTLEMENT_DATE =
ScheduleCalculator.getAdjustedDate(EXPIRY_DATE, SETTLEMENT_DAYS, CALENDAR);
private static final double NOTIONAL = 100000000; // 100m
// Fixed leg: Semi-annual bond
private static final Period FIXED_PAYMENT_PERIOD = Period.ofMonths(6);
private static final DayCount FIXED_DAY_COUNT = DayCountFactory.INSTANCE.getDayCount("30/360");
private static final double RATE = 0.04;
private static final boolean FIXED_IS_PAYER = true;
// Ibor leg: quarterly money
private static final Period INDEX_TENOR = Period.ofMonths(3);
private static final DayCount DAY_COUNT = DayCountFactory.INSTANCE.getDayCount("Actual/360");
private static final IborIndex IBOR_INDEX =
new IborIndex(CUR, INDEX_TENOR, SETTLEMENT_DAYS, CALENDAR, DAY_COUNT, BUSINESS_DAY, IS_EOM);
// Swaption construction
private static final IndexSwap CMS_INDEX =
new IndexSwap(FIXED_PAYMENT_PERIOD, FIXED_DAY_COUNT, IBOR_INDEX, ANNUITY_TENOR);
private static final SwapFixedIborDefinition SWAP_DEFINITION_PAYER =
SwapFixedIborDefinition.from(SETTLEMENT_DATE, CMS_INDEX, NOTIONAL, RATE, FIXED_IS_PAYER);
private static final SwapFixedIborDefinition SWAP_DEFINITION_RECEIVER =
SwapFixedIborDefinition.from(SETTLEMENT_DATE, CMS_INDEX, NOTIONAL, RATE, !FIXED_IS_PAYER);
private static final SwaptionCashFixedIborDefinition SWAPTION_DEFINITION_LONG_PAYER =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, SWAP_DEFINITION_PAYER, IS_LONG);
private static final SwaptionCashFixedIborDefinition SWAPTION_DEFINITION_LONG_RECEIVER =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, SWAP_DEFINITION_RECEIVER, IS_LONG);
private static final SwaptionCashFixedIborDefinition SWAPTION_DEFINITION_SHORT_PAYER =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, SWAP_DEFINITION_PAYER, !IS_LONG);
private static final SwaptionCashFixedIborDefinition SWAPTION_DEFINITION_SHORT_RECEIVER =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, SWAP_DEFINITION_RECEIVER, !IS_LONG);
// to derivatives
private static final ZonedDateTime REFERENCE_DATE = DateUtils.getUTCDate(2008, 8, 18);
private static final String FUNDING_CURVE_NAME = "Funding";
private static final String FORWARD_CURVE_NAME = "Forward";
private static final String[] CURVES_NAME = {FUNDING_CURVE_NAME, FORWARD_CURVE_NAME};
private static final SwaptionCashFixedIbor SWAPTION_LONG_PAYER =
SWAPTION_DEFINITION_LONG_PAYER.toDerivative(REFERENCE_DATE, CURVES_NAME);
private static final SwaptionCashFixedIbor SWAPTION_LONG_RECEIVER =
SWAPTION_DEFINITION_LONG_RECEIVER.toDerivative(REFERENCE_DATE, CURVES_NAME);
private static final SwaptionCashFixedIbor SWAPTION_SHORT_PAYER =
SWAPTION_DEFINITION_SHORT_PAYER.toDerivative(REFERENCE_DATE, CURVES_NAME);
private static final SwaptionCashFixedIbor SWAPTION_SHORT_RECEIVER =
SWAPTION_DEFINITION_SHORT_RECEIVER.toDerivative(REFERENCE_DATE, CURVES_NAME);
// Extrapolation
private static final double CUT_OFF_STRIKE = 0.08;
private static final double MU = 10.0;
private static final SwaptionCashFixedIborSABRExtrapolationRightMethod METHOD_EXTRAPOLATION =
new SwaptionCashFixedIborSABRExtrapolationRightMethod(CUT_OFF_STRIKE, MU);
// Calculators
private static final PresentValueSABRExtrapolationCalculator PVC =
PresentValueSABRExtrapolationCalculator.getInstance();
/** Tests present value in the region where there is no extrapolation. Tests long/short parity. */
@Test
public void testPresentValueNoExtra() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final SABRInterestRateParameters sabrParameter =
TestsDataSetsSABR.createSABRExtrapolation1(CUT_OFF_STRIKE, MU);
final SABRInterestRateDataBundle sabrBundle =
new SABRInterestRateDataBundle(sabrParameter, curves);
final SwaptionCashFixedIborSABRExtrapolationRightMethod method =
new SwaptionCashFixedIborSABRExtrapolationRightMethod(CUT_OFF_STRIKE, MU);
final double priceLongPayer = method.presentValue(SWAPTION_LONG_PAYER, sabrBundle);
final double priceShortPayer = method.presentValue(SWAPTION_SHORT_PAYER, sabrBundle);
final double priceLongReceiver = method.presentValue(SWAPTION_LONG_RECEIVER, sabrBundle);
final double priceShortReceiver = method.presentValue(SWAPTION_SHORT_RECEIVER, sabrBundle);
final double priceLongPayerNoExtra = PVC.visit(SWAPTION_LONG_PAYER, sabrBundle);
final double priceShortPayerNoExtra = PVC.visit(SWAPTION_SHORT_PAYER, sabrBundle);
final double priceLongReceiverNoExtra = PVC.visit(SWAPTION_LONG_RECEIVER, sabrBundle);
final double priceShortReceiverNoExtra = PVC.visit(SWAPTION_SHORT_RECEIVER, sabrBundle);
assertEquals(
"Swaption cash SABR extrapolation: below cut-off strike",
priceLongPayerNoExtra,
priceLongPayer,
1E-2);
assertEquals(
"Swaption cash SABR extrapolation: below cut-off strike",
priceShortPayerNoExtra,
priceShortPayer,
1E-2);
assertEquals(
"Swaption cash SABR extrapolation: below cut-off strike",
priceLongReceiverNoExtra,
priceLongReceiver,
1E-2);
assertEquals(
"Swaption cash SABR extrapolation: below cut-off strike",
priceShortReceiverNoExtra,
priceShortReceiver,
1E-2);
assertEquals(
"Swaption cash SABR extrapolation: below cut-off strike long/short parity",
priceLongPayer,
-priceShortPayer,
1E-2);
assertEquals(
"Swaption cash SABR extrapolation: below cut-off strike long/short parity",
priceLongReceiver,
-priceShortReceiver,
1E-2);
}
/**
* 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 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);
}
}
@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 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);
}
}