public virtual void test_recovery_black_fixedRho()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition definition = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedRho(IborCapletFloorletVolatilitiesName.of("test"), USD_LIBOR_3M, ACT_ACT_ISDA, 0.0, CurveInterpolators.STEP_UPPER, CurveExtrapolators.FLAT, CurveExtrapolators.FLAT, SabrHaganVolatilityFunctionProvider.DEFAULT);
DoubleMatrix volData = createFullBlackDataMatrix();
double errorValue = 1.0e-3;
DoubleMatrix error = DoubleMatrix.filled(volData.rowCount(), volData.columnCount(), errorValue);
RawOptionData data = RawOptionData.of(createBlackMaturities(), createBlackStrikes(), ValueType.STRIKE, volData, error, ValueType.BLACK_VOLATILITY);
IborCapletFloorletVolatilityCalibrationResult res = CALIBRATOR.calibrate(definition, CALIBRATION_TIME, data, RATES_PROVIDER);
SabrParametersIborCapletFloorletVolatilities resVols = (SabrParametersIborCapletFloorletVolatilities)res.Volatilities;
double expSq = 0d;
for (int i = 0; i < NUM_BLACK_STRIKES; ++i)
{
Pair <IList <ResolvedIborCapFloorLeg>, IList <double> > capsAndVols = getCapsBlackVols(i);
IList <ResolvedIborCapFloorLeg> caps = capsAndVols.First;
IList <double> vols = capsAndVols.Second;
int nCaps = caps.Count;
for (int j = 0; j < nCaps; ++j)
{
ConstantSurface volSurface = ConstantSurface.of(Surfaces.blackVolatilityByExpiryStrike("test", ACT_ACT_ISDA), vols[j]);
BlackIborCapletFloorletExpiryStrikeVolatilities constVol = BlackIborCapletFloorletExpiryStrikeVolatilities.of(USD_LIBOR_3M, CALIBRATION_TIME, volSurface);
double priceOrg = LEG_PRICER_BLACK.presentValue(caps[j], RATES_PROVIDER, constVol).Amount;
double priceCalib = LEG_PRICER_SABR.presentValue(caps[j], RATES_PROVIDER, resVols).Amount;
expSq += Math.Pow((priceOrg - priceCalib) / priceOrg / errorValue, 2);
assertEquals(priceOrg, priceCalib, Math.Max(priceOrg, 1d) * TOL * 3d);
}
}
assertEquals(res.ChiSquare, expSq, expSq * 1.0e-14);
assertEquals(resVols.Index, USD_LIBOR_3M);
assertEquals(resVols.Name, definition.Name);
assertEquals(resVols.ValuationDateTime, CALIBRATION_TIME);
assertEquals(resVols.Parameters.ShiftCurve, definition.ShiftCurve);
assertEquals(resVols.Parameters.RhoCurve, definition.RhoCurve.get());
}
public virtual void test_recovery_normal_fixedRho()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition definition = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedRho(IborCapletFloorletVolatilitiesName.of("test"), USD_LIBOR_3M, ACT_ACT_ISDA, 0.0, CurveInterpolators.LINEAR, CurveExtrapolators.FLAT, CurveExtrapolators.FLAT, SabrHaganVolatilityFunctionProvider.DEFAULT);
RawOptionData data = RawOptionData.of(createNormalEquivMaturities(), createNormalEquivStrikes(), ValueType.STRIKE, createFullNormalEquivDataMatrix(), ValueType.NORMAL_VOLATILITY);
IborCapletFloorletVolatilityCalibrationResult res = CALIBRATOR.calibrate(definition, CALIBRATION_TIME, data, RATES_PROVIDER);
SabrParametersIborCapletFloorletVolatilities resVols = (SabrParametersIborCapletFloorletVolatilities)res.Volatilities;
for (int i = 1; i < NUM_BLACK_STRIKES; ++i)
{
Pair <IList <ResolvedIborCapFloorLeg>, IList <double> > capsAndVols = getCapsNormalEquivVols(i);
IList <ResolvedIborCapFloorLeg> caps = capsAndVols.First;
IList <double> vols = capsAndVols.Second;
int nCaps = caps.Count;
for (int j = 0; j < nCaps; ++j)
{
ConstantSurface volSurface = ConstantSurface.of(Surfaces.normalVolatilityByExpiryStrike("test", ACT_ACT_ISDA), vols[j]);
NormalIborCapletFloorletExpiryStrikeVolatilities constVol = NormalIborCapletFloorletExpiryStrikeVolatilities.of(USD_LIBOR_3M, CALIBRATION_TIME, volSurface);
double priceOrg = LEG_PRICER_NORMAL.presentValue(caps[j], RATES_PROVIDER, constVol).Amount;
double priceCalib = LEG_PRICER_SABR.presentValue(caps[j], RATES_PROVIDER, resVols).Amount;
assertEquals(priceOrg, priceCalib, Math.Max(priceOrg, 1d) * TOL * 3d);
}
}
assertTrue(res.ChiSquare > 0d);
assertEquals(resVols.Index, USD_LIBOR_3M);
assertEquals(resVols.Name, definition.Name);
assertEquals(resVols.ValuationDateTime, CALIBRATION_TIME);
}
public virtual void test_invalid_data()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition definition = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(IborCapletFloorletVolatilitiesName.of("test"), USD_LIBOR_3M, ACT_ACT_ISDA, 0.85, CurveInterpolators.LINEAR, CurveExtrapolators.FLAT, CurveExtrapolators.FLAT, SabrHaganVolatilityFunctionProvider.DEFAULT);
RawOptionData data = RawOptionData.of(createBlackMaturities(), createBlackStrikes(), ValueType.STRIKE, createFullBlackDataMatrixInvalid(), ValueType.BLACK_VOLATILITY);
assertThrowsIllegalArg(() => CALIBRATOR.calibrate(definition, CALIBRATION_TIME, data, RATES_PROVIDER));
}
public virtual void test_createSabrParameterMetadata()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition @base = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, 0.5, LINEAR, FLAT, FLAT, SabrVolatilityFormula.hagan());
ImmutableList <CurveMetadata> expected = ImmutableList.of(Curves.sabrParameterByExpiry(NAME.Name + "-Alpha", ACT_ACT_ISDA, SABR_ALPHA), Curves.sabrParameterByExpiry(NAME.Name + "-Beta", ACT_ACT_ISDA, SABR_BETA), Curves.sabrParameterByExpiry(NAME.Name + "-Rho", ACT_ACT_ISDA, SABR_RHO), Curves.sabrParameterByExpiry(NAME.Name + "-Nu", ACT_ACT_ISDA, SABR_NU));
ImmutableList <CurveMetadata> computed = @base.createSabrParameterMetadata();
assertEquals(computed, expected);
}
//-------------------------------------------------------------------------
public virtual void coverage()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition test1 = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, 0.5, LINEAR, FLAT, FLAT, SabrVolatilityFormula.hagan());
coverImmutableBean(test1);
SabrIborCapletFloorletVolatilityBootstrapDefinition test2 = SabrIborCapletFloorletVolatilityBootstrapDefinition.builder().index(GBP_LIBOR_3M).name(IborCapletFloorletVolatilitiesName.of("other")).interpolator(STEP_UPPER).extrapolatorLeft(FLAT).extrapolatorRight(CurveExtrapolators.LINEAR).rhoCurve(ConstantCurve.of("rho", 0.1d)).shiftCurve(ConstantCurve.of("shift", 0.01d)).dayCount(ACT_365F).sabrVolatilityFormula(SabrVolatilityFormula.hagan()).build();
coverBeanEquals(test1, test2);
}
public virtual void test_createMetadata_wrongValueType()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition @base = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, 0.5, LINEAR, FLAT, FLAT, SabrVolatilityFormula.hagan());
RawOptionData capData = RawOptionData.of(ImmutableList.of(Period.ofYears(1), Period.ofYears(5)), DoubleArray.of(0.005, 0.01, 0.015), ValueType.STRIKE, DoubleMatrix.copyOf(new double[][]
{
new double[] { 0.15, 0.12, 0.13 },
new double[] { 0.1, 0.08, 0.09 }
}), ValueType.PRICE);
assertThrowsIllegalArg(() => @base.createMetadata(capData));
}
public virtual void test_createCap()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition @base = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, 0.5, STEP_UPPER, FLAT, FLAT, SabrVolatilityFormula.hagan());
LocalDate startDate = LocalDate.of(2012, 4, 20);
LocalDate endDate = LocalDate.of(2017, 4, 20);
double strike = 0.01;
IborCapFloorLeg expected = IborCapFloorLeg.builder().calculation(IborRateCalculation.of(USD_LIBOR_3M)).capSchedule(ValueSchedule.of(strike)).currency(USD_LIBOR_3M.Currency).notional(ValueSchedule.ALWAYS_1).paymentDateOffset(DaysAdjustment.NONE).paymentSchedule(PeriodicSchedule.of(startDate, endDate, Frequency.of(USD_LIBOR_3M.Tenor.Period), BusinessDayAdjustment.of(BusinessDayConventions.MODIFIED_FOLLOWING, USD_LIBOR_3M.FixingCalendar), StubConvention.NONE, RollConventions.NONE)).payReceive(PayReceive.RECEIVE).build();
IborCapFloorLeg computed = @base.createCap(startDate, endDate, strike);
assertEquals(computed, expected);
}
public virtual void test_createMetadata_black()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition @base = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, 0.5, LINEAR, FLAT, FLAT, SabrVolatilityFormula.hagan());
RawOptionData capData = RawOptionData.of(ImmutableList.of(Period.ofYears(1), Period.ofYears(5)), DoubleArray.of(0.005, 0.01, 0.015), ValueType.STRIKE, DoubleMatrix.copyOf(new double[][]
{
new double[] { 0.15, 0.12, 0.13 },
new double[] { 0.1, 0.08, 0.09 }
}), ValueType.BLACK_VOLATILITY);
SurfaceMetadata expected = Surfaces.blackVolatilityByExpiryStrike(NAME.Name, ACT_ACT_ISDA);
SurfaceMetadata computed = @base.createMetadata(capData);
assertEquals(computed, expected);
}
public virtual void test_ofFixedBeta_shift()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition test = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, 0.5, 0.01, LINEAR, FLAT, FLAT, SabrVolatilityFormula.hagan());
assertEquals(test.DayCount, ACT_ACT_ISDA);
assertEquals(test.Index, USD_LIBOR_3M);
assertEquals(test.Interpolator, LINEAR);
assertEquals(test.ExtrapolatorLeft, FLAT);
assertEquals(test.ExtrapolatorRight, FLAT);
assertEquals(test.Name, NAME);
assertEquals(test.BetaCurve.get(), ConstantCurve.of(Curves.sabrParameterByExpiry(NAME.Name + "-Beta", ACT_ACT_ISDA, SABR_BETA), 0.5));
assertFalse(test.RhoCurve.Present);
assertEquals(test.SabrVolatilityFormula, SabrVolatilityFormula.hagan());
assertEquals(test.ShiftCurve, ConstantCurve.of("Shift curve", 0.01));
}
public virtual void test_builder()
{
Curve betaCurve = ConstantCurve.of(Curves.sabrParameterByExpiry(NAME.Name + "-Beta", ACT_ACT_ISDA, SABR_BETA), 0.65);
SabrIborCapletFloorletVolatilityBootstrapDefinition test = SabrIborCapletFloorletVolatilityBootstrapDefinition.builder().index(USD_LIBOR_3M).name(NAME).interpolator(LINEAR).extrapolatorLeft(FLAT).extrapolatorRight(CurveExtrapolators.LINEAR).dayCount(ACT_ACT_ISDA).sabrVolatilityFormula(SabrVolatilityFormula.hagan()).betaCurve(betaCurve).build();
assertEquals(test.DayCount, ACT_ACT_ISDA);
assertEquals(test.Index, USD_LIBOR_3M);
assertEquals(test.Interpolator, LINEAR);
assertEquals(test.ExtrapolatorLeft, FLAT);
assertEquals(test.ExtrapolatorRight, CurveExtrapolators.LINEAR);
assertEquals(test.Name, NAME);
assertEquals(test.BetaCurve.get(), betaCurve);
assertFalse(test.RhoCurve.Present);
assertEquals(test.SabrVolatilityFormula, SabrVolatilityFormula.hagan());
assertEquals(test.ShiftCurve, ConstantCurve.of("Zero shift", 0d));
}
public virtual void test_recovery_flatVol()
{
double beta = 0.8;
SabrIborCapletFloorletVolatilityBootstrapDefinition definition = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(IborCapletFloorletVolatilitiesName.of("test"), USD_LIBOR_3M, ACT_ACT_ISDA, beta, CurveInterpolators.STEP_UPPER, CurveExtrapolators.FLAT, CurveExtrapolators.FLAT, SabrHaganVolatilityFunctionProvider.DEFAULT);
RawOptionData data = RawOptionData.of(createBlackMaturities(), createBlackStrikes(), ValueType.STRIKE, createFullFlatBlackDataMatrix(), ValueType.BLACK_VOLATILITY);
IborCapletFloorletVolatilityCalibrationResult res = CALIBRATOR.calibrate(definition, CALIBRATION_TIME, data, RATES_PROVIDER);
SabrParametersIborCapletFloorletVolatilities resVols = (SabrParametersIborCapletFloorletVolatilities)res.Volatilities;
for (int i = 0; i < NUM_BLACK_STRIKES; ++i)
{
Pair <IList <ResolvedIborCapFloorLeg>, IList <double> > capsAndVols = getCapsFlatBlackVols(i);
IList <ResolvedIborCapFloorLeg> caps = capsAndVols.First;
IList <double> vols = capsAndVols.Second;
int nCaps = caps.Count;
for (int j = 0; j < nCaps; ++j)
{
ConstantSurface volSurface = ConstantSurface.of(Surfaces.blackVolatilityByExpiryStrike("test", ACT_ACT_ISDA), vols[j]);
BlackIborCapletFloorletExpiryStrikeVolatilities constVol = BlackIborCapletFloorletExpiryStrikeVolatilities.of(USD_LIBOR_3M, CALIBRATION_TIME, volSurface);
double priceOrg = LEG_PRICER_BLACK.presentValue(caps[j], RATES_PROVIDER, constVol).Amount;
double priceCalib = LEG_PRICER_SABR.presentValue(caps[j], RATES_PROVIDER, resVols).Amount;
assertEquals(priceOrg, priceCalib, Math.Max(priceOrg, 1d) * TOL);
}
}
}
//-------------------------------------------------------------------------
public override IborCapletFloorletVolatilityCalibrationResult calibrate(IborCapletFloorletVolatilityDefinition definition, ZonedDateTime calibrationDateTime, RawOptionData capFloorData, RatesProvider ratesProvider)
{
ArgChecker.isTrue(ratesProvider.ValuationDate.Equals(calibrationDateTime.toLocalDate()), "valuationDate of ratesProvider should be coherent to calibrationDateTime");
ArgChecker.isTrue(definition is SabrIborCapletFloorletVolatilityBootstrapDefinition, "definition should be SabrIborCapletFloorletVolatilityBootstrapDefinition");
SabrIborCapletFloorletVolatilityBootstrapDefinition bsDefinition = (SabrIborCapletFloorletVolatilityBootstrapDefinition)definition;
IborIndex index = bsDefinition.Index;
LocalDate calibrationDate = calibrationDateTime.toLocalDate();
LocalDate baseDate = index.EffectiveDateOffset.adjust(calibrationDate, ReferenceData);
LocalDate startDate = baseDate.plus(index.Tenor);
System.Func <Surface, IborCapletFloorletVolatilities> volatilitiesFunction = this.volatilitiesFunction(bsDefinition, calibrationDateTime, capFloorData);
SurfaceMetadata metaData = bsDefinition.createMetadata(capFloorData);
IList <Period> expiries = capFloorData.Expiries;
int nExpiries = expiries.Count;
DoubleArray strikes = capFloorData.Strikes;
DoubleMatrix errorsMatrix = capFloorData.Error.orElse(DoubleMatrix.filled(nExpiries, strikes.size(), 1d));
IList <double> timeList = new List <double>();
IList <double> strikeList = new List <double>();
IList <double> volList = new List <double>();
IList <ResolvedIborCapFloorLeg> capList = new List <ResolvedIborCapFloorLeg>();
IList <double> priceList = new List <double>();
IList <double> errorList = new List <double>();
int[] startIndex = new int[nExpiries + 1];
for (int i = 0; i < nExpiries; ++i)
{
LocalDate endDate = baseDate.plus(expiries[i]);
DoubleArray volatilityData = capFloorData.Data.row(i);
DoubleArray errors = errorsMatrix.row(i);
reduceRawData(bsDefinition, ratesProvider, strikes, volatilityData, errors, startDate, endDate, metaData, volatilitiesFunction, timeList, strikeList, volList, capList, priceList, errorList);
startIndex[i + 1] = volList.Count;
ArgChecker.isTrue(startIndex[i + 1] > startIndex[i], "no valid option data for {}", expiries[i]);
}
IList <CurveMetadata> metadataList = bsDefinition.createSabrParameterMetadata();
DoubleArray timeToExpiries = DoubleArray.of(nExpiries, i => timeList[startIndex[i]]);
BitArray @fixed = new BitArray();
bool betaFix = false;
Curve betaCurve;
Curve rhoCurve;
if (bsDefinition.BetaCurve.Present)
{
betaFix = true;
@fixed.Set(1, true);
betaCurve = bsDefinition.BetaCurve.get();
rhoCurve = InterpolatedNodalCurve.of(metadataList[2], timeToExpiries, DoubleArray.filled(nExpiries), bsDefinition.Interpolator, bsDefinition.ExtrapolatorLeft, bsDefinition.ExtrapolatorRight);
}
else
{
@fixed.Set(2, true);
betaCurve = InterpolatedNodalCurve.of(metadataList[1], timeToExpiries, DoubleArray.filled(nExpiries), bsDefinition.Interpolator, bsDefinition.ExtrapolatorLeft, bsDefinition.ExtrapolatorRight);
rhoCurve = bsDefinition.RhoCurve.get();
}
InterpolatedNodalCurve alphaCurve = InterpolatedNodalCurve.of(metadataList[0], timeToExpiries, DoubleArray.filled(nExpiries), bsDefinition.Interpolator, bsDefinition.ExtrapolatorLeft, bsDefinition.ExtrapolatorRight);
InterpolatedNodalCurve nuCurve = InterpolatedNodalCurve.of(metadataList[3], timeToExpiries, DoubleArray.filled(nExpiries), bsDefinition.Interpolator, bsDefinition.ExtrapolatorLeft, bsDefinition.ExtrapolatorRight);
Curve shiftCurve = bsDefinition.ShiftCurve;
SabrParameters sabrParams = SabrParameters.of(alphaCurve, betaCurve, rhoCurve, nuCurve, shiftCurve, bsDefinition.SabrVolatilityFormula);
SabrParametersIborCapletFloorletVolatilities vols = SabrParametersIborCapletFloorletVolatilities.of(bsDefinition.Name, index, calibrationDateTime, sabrParams);
double totalChiSq = 0d;
ZonedDateTime prevExpiry = calibrationDateTime.minusDays(1L); // included if calibrationDateTime == fixingDateTime
for (int i = 0; i < nExpiries; ++i)
{
DoubleArray start = computeInitialValues(ratesProvider, betaCurve, shiftCurve, timeList, volList, capList, startIndex, i, betaFix, capFloorData.DataType);
UncoupledParameterTransforms transform = new UncoupledParameterTransforms(start, TRANSFORMS, @fixed);
int nCaplets = startIndex[i + 1] - startIndex[i];
int currentStart = startIndex[i];
System.Func <DoubleArray, DoubleArray> valueFunction = createPriceFunction(ratesProvider, vols, prevExpiry, capList, priceList, startIndex, nExpiries, i, nCaplets, betaFix);
System.Func <DoubleArray, DoubleMatrix> jacobianFunction = createJacobianFunction(ratesProvider, vols, prevExpiry, capList, priceList, index.Currency, startIndex, nExpiries, i, nCaplets, betaFix);
NonLinearTransformFunction transFunc = new NonLinearTransformFunction(valueFunction, jacobianFunction, transform);
DoubleArray adjustedPrices = this.adjustedPrices(ratesProvider, vols, prevExpiry, capList, priceList, startIndex, i, nCaplets);
DoubleArray errors = DoubleArray.of(nCaplets, n => errorList[currentStart + n]);
LeastSquareResults res = solver.solve(adjustedPrices, errors, transFunc.FittingFunction, transFunc.FittingJacobian, transform.transform(start));
LeastSquareResultsWithTransform resTransform = new LeastSquareResultsWithTransform(res, transform);
vols = updateParameters(vols, nExpiries, i, betaFix, resTransform.ModelParameters);
totalChiSq += res.ChiSq;
prevExpiry = capList[startIndex[i + 1] - 1].FinalFixingDateTime;
}
return(IborCapletFloorletVolatilityCalibrationResult.ofLeastSquare(vols, totalChiSq));
}
public virtual void test_serialization()
{
SabrIborCapletFloorletVolatilityBootstrapDefinition test = SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, 0.5, LINEAR, FLAT, FLAT, SabrVolatilityFormula.hagan());
assertSerialization(test);
}
//-------------------------------------------------------------------------
public virtual void test_of_wrongInterpolator()
{
assertThrowsIllegalArg(() => SabrIborCapletFloorletVolatilityBootstrapDefinition.ofFixedBeta(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, 0.5, DOUBLE_QUADRATIC, FLAT, FLAT, SabrVolatilityFormula.hagan()));
}
