// node sensitivity function
private System.Func <DoubleArray, DoubleMatrix> createJacobianFunction(SabrIborCapletFloorletVolatilityCalibrationDefinition sabrDefinition, RatesProvider ratesProvider, SabrParametersIborCapletFloorletVolatilities volatilities, IList <ResolvedIborCapFloorLeg> capList, IList <double> priceList, Currency currency)
{
int nCaps = capList.Count;
SabrParameters sabrParams = volatilities.Parameters;
CurveName alphaName = sabrParams.AlphaCurve.Name;
CurveName betaName = sabrParams.BetaCurve.Name;
CurveName rhoName = sabrParams.RhoCurve.Name;
CurveName nuName = sabrParams.NuCurve.Name;
System.Func <DoubleArray, DoubleMatrix> jacobianFunction = (DoubleArray x) =>
{
SabrParametersIborCapletFloorletVolatilities volsNew = updateParameters(sabrDefinition, volatilities, x);
double[][] jacobian = new double[nCaps][];
for (int i = 0; i < nCaps; ++i)
{
PointSensitivities point = sabrPricer.presentValueSensitivityModelParamsSabr(capList[i], ratesProvider, volsNew).build();
CurrencyParameterSensitivities sensi = volsNew.parameterSensitivity(point);
double targetPriceInv = 1d / priceList[i];
DoubleArray sensitivities = sensi.getSensitivity(alphaName, currency).Sensitivity;
if (sabrDefinition.BetaCurve.Present)
{ // beta fixed
sensitivities = sensitivities.concat(sensi.getSensitivity(rhoName, currency).Sensitivity);
}
else
{ // rho fixed
sensitivities = sensitivities.concat(sensi.getSensitivity(betaName, currency).Sensitivity);
}
jacobian[i] = sensitivities.concat(sensi.getSensitivity(nuName, currency).Sensitivity).multipliedBy(targetPriceInv).toArray();
}
return(DoubleMatrix.ofUnsafe(jacobian));
};
return(jacobianFunction);
}
public virtual void recovery_test_black_fixedRho()
{
double rho = 0.15;
SabrIborCapletFloorletVolatilityCalibrationDefinition definition = SabrIborCapletFloorletVolatilityCalibrationDefinition.ofFixedRho(NAME, USD_LIBOR_3M, ACT_ACT_ISDA, rho, ALPHA_KNOTS, BETA_RHO_KNOTS, NU_KNOTS, DOUBLE_QUADRATIC, FLAT, FLAT, HAGAN);
ImmutableList <Period> maturities = createBlackMaturities();
DoubleArray strikes = createBlackStrikes();
DoubleMatrix volData = createFullBlackDataMatrix();
DoubleMatrix error = DoubleMatrix.filled(volData.rowCount(), volData.columnCount(), 1.0e-3);
RawOptionData data = RawOptionData.of(maturities, strikes, ValueType.STRIKE, volData, error, 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 = 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;
assertEquals(priceOrg, priceCalib, Math.Max(priceOrg, 1d) * TOL * 5d);
}
}
assertEquals(resVols.Index, USD_LIBOR_3M);
assertEquals(resVols.Name, definition.Name);
assertEquals(resVols.ValuationDateTime, CALIBRATION_TIME);
assertEquals(resVols.ParameterCount, ALPHA_KNOTS.size() + BETA_RHO_KNOTS.size() + NU_KNOTS.size() + 2); // beta, shift counted
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_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 coverage()
{
SabrParametersIborCapletFloorletVolatilities test1 = SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM);
coverImmutableBean(test1);
SabrParametersIborCapletFloorletVolatilities test2 = SabrParametersIborCapletFloorletVolatilities.of(NAME2, IborIndices.EUR_LIBOR_3M, DATE_TIME.plusDays(1), IborCapletFloorletSabrRateVolatilityDataSet.SABR_PARAM_FLAT);
coverBeanEquals(test1, test2);
}
// price function
private System.Func <DoubleArray, DoubleArray> createPriceFunction(SabrIborCapletFloorletVolatilityCalibrationDefinition sabrDefinition, RatesProvider ratesProvider, SabrParametersIborCapletFloorletVolatilities volatilities, IList <ResolvedIborCapFloorLeg> capList, IList <double> priceList)
{
System.Func <DoubleArray, DoubleArray> priceFunction = (DoubleArray x) =>
{
SabrParametersIborCapletFloorletVolatilities volsNew = updateParameters(sabrDefinition, volatilities, x);
return(DoubleArray.of(capList.Count, n => sabrPricer.presentValue(capList[n], ratesProvider, volsNew).Amount / priceList[n]));
};
return(priceFunction);
}
public virtual void test_calc()
{
SabrParametersIborCapletFloorletVolatilities test = SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM);
assertEquals(test.alpha(1.56), PARAM.alpha(1.56));
assertEquals(test.beta(1.56), PARAM.beta(1.56));
assertEquals(test.rho(1.56), PARAM.rho(1.56));
assertEquals(test.nu(1.56), PARAM.nu(1.56));
assertEquals(test.shift(1.56), PARAM.shift(1.56));
}
// price function
private System.Func <DoubleArray, DoubleArray> createPriceFunction(RatesProvider ratesProvider, SabrParametersIborCapletFloorletVolatilities volatilities, ZonedDateTime prevExpiry, IList <ResolvedIborCapFloorLeg> capList, IList <double> priceList, int[] startIndex, int nExpiries, int timeIndex, int nCaplets, bool betaFixed)
{
int currentStart = startIndex[timeIndex];
System.Func <DoubleArray, DoubleArray> priceFunction = (DoubleArray x) =>
{
SabrParametersIborCapletFloorletVolatilities volsNew = updateParameters(volatilities, nExpiries, timeIndex, betaFixed, x);
return(DoubleArray.of(nCaplets, n => capList[currentStart + n].CapletFloorletPeriods.Where(p => p.FixingDateTime.isAfter(prevExpiry)).Select(p => sabrPeriodPricer.presentValue(p, ratesProvider, volsNew).Amount).Sum() / priceList[currentStart + n]));
};
return(priceFunction);
}
public virtual void test_relativeTime()
{
SabrParametersIborCapletFloorletVolatilities prov = SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM);
double test1 = prov.relativeTime(DATE_TIME);
assertEquals(test1, 0d);
double test2 = prov.relativeTime(DATE_TIME.plusYears(2));
double test3 = prov.relativeTime(DATE_TIME.minusYears(2));
assertEquals(test2, -test3, 1e-2);
}
public virtual void test_findData()
{
SabrParametersIborCapletFloorletVolatilities test = SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM);
assertEquals(test.findData(PARAM.AlphaCurve.Name), PARAM.AlphaCurve);
assertEquals(test.findData(PARAM.BetaCurve.Name), PARAM.BetaCurve);
assertEquals(test.findData(PARAM.RhoCurve.Name), PARAM.RhoCurve);
assertEquals(test.findData(PARAM.NuCurve.Name), PARAM.NuCurve);
assertEquals(test.findData(PARAM.ShiftCurve.Name), PARAM.ShiftCurve);
assertEquals(test.findData(SurfaceName.of("Rubbish")), null);
}
//-------------------------------------------------------------------------
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 SabrIborCapletFloorletVolatilityCalibrationDefinition, "definition should be SabrIborCapletFloorletVolatilityCalibrationDefinition");
SabrIborCapletFloorletVolatilityCalibrationDefinition sabrDefinition = (SabrIborCapletFloorletVolatilityCalibrationDefinition)definition;
// unpack cap data, create node caps
IborIndex index = sabrDefinition.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(sabrDefinition, calibrationDateTime, capFloorData);
SurfaceMetadata metadata = sabrDefinition.createMetadata(capFloorData);
IList <Period> expiries = capFloorData.Expiries;
DoubleArray strikes = capFloorData.Strikes;
int nExpiries = expiries.Count;
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>();
DoubleMatrix errorMatrix = capFloorData.Error.orElse(DoubleMatrix.filled(nExpiries, strikes.size(), 1d));
int[] startIndex = new int[nExpiries + 1];
for (int i = 0; i < nExpiries; ++i)
{
LocalDate endDate = baseDate.plus(expiries[i]);
DoubleArray volatilityForTime = capFloorData.Data.row(i);
DoubleArray errorForTime = errorMatrix.row(i);
reduceRawData(sabrDefinition, ratesProvider, capFloorData.Strikes, volatilityForTime, errorForTime, 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]);
}
// create initial caplet vol surface
IList <CurveMetadata> metadataList = sabrDefinition.createSabrParameterMetadata();
DoubleArray initialValues = sabrDefinition.createFullInitialValues();
IList <Curve> curveList = sabrDefinition.createSabrParameterCurve(metadataList, initialValues);
SabrParameters sabrParamsInitial = SabrParameters.of(curveList[0], curveList[1], curveList[2], curveList[3], sabrDefinition.ShiftCurve, sabrDefinition.SabrVolatilityFormula);
SabrParametersIborCapletFloorletVolatilities vols = SabrParametersIborCapletFloorletVolatilities.of(sabrDefinition.Name, index, calibrationDateTime, sabrParamsInitial);
// solve least square
UncoupledParameterTransforms transform = new UncoupledParameterTransforms(initialValues, sabrDefinition.createFullTransform(TRANSFORMS), new BitArray());
System.Func <DoubleArray, DoubleArray> valueFunction = createPriceFunction(sabrDefinition, ratesProvider, vols, capList, priceList);
System.Func <DoubleArray, DoubleMatrix> jacobianFunction = createJacobianFunction(sabrDefinition, ratesProvider, vols, capList, priceList, index.Currency);
NonLinearTransformFunction transFunc = new NonLinearTransformFunction(valueFunction, jacobianFunction, transform);
LeastSquareResults res = solver.solve(DoubleArray.filled(priceList.Count, 1d), DoubleArray.copyOf(errorList), transFunc.FittingFunction, transFunc.FittingJacobian, transform.transform(initialValues));
LeastSquareResultsWithTransform resTransform = new LeastSquareResultsWithTransform(res, transform);
vols = updateParameters(sabrDefinition, vols, resTransform.ModelParameters);
return(IborCapletFloorletVolatilityCalibrationResult.ofLeastSquare(vols, res.ChiSq));
}
public virtual void test_parameterSensitivity()
{
double alphaSensi = 2.24, betaSensi = 3.45, rhoSensi = -2.12, nuSensi = -0.56, shiftSensi = 2.5;
SabrParametersIborCapletFloorletVolatilities prov = SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM);
for (int i = 0; i < NB_TEST; i++)
{
double expiryTime = prov.relativeTime(TEST_OPTION_EXPIRY[i]);
PointSensitivities point = PointSensitivities.of(IborCapletFloorletSabrSensitivity.of(NAME, expiryTime, ALPHA, EUR, alphaSensi), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime, BETA, EUR, betaSensi), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime, RHO, EUR, rhoSensi), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime, NU, EUR, nuSensi), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime, SHIFT, EUR, shiftSensi));
CurrencyParameterSensitivities sensiComputed = prov.parameterSensitivity(point);
UnitParameterSensitivity alphaSensitivities = prov.Parameters.AlphaCurve.yValueParameterSensitivity(expiryTime);
UnitParameterSensitivity betaSensitivities = prov.Parameters.BetaCurve.yValueParameterSensitivity(expiryTime);
UnitParameterSensitivity rhoSensitivities = prov.Parameters.RhoCurve.yValueParameterSensitivity(expiryTime);
UnitParameterSensitivity nuSensitivities = prov.Parameters.NuCurve.yValueParameterSensitivity(expiryTime);
UnitParameterSensitivity shiftSensitivities = prov.Parameters.ShiftCurve.yValueParameterSensitivity(expiryTime);
CurrencyParameterSensitivity alphaSensiObj = sensiComputed.getSensitivity(IborCapletFloorletSabrRateVolatilityDataSet.META_ALPHA.CurveName, EUR);
CurrencyParameterSensitivity betaSensiObj = sensiComputed.getSensitivity(IborCapletFloorletSabrRateVolatilityDataSet.META_BETA.CurveName, EUR);
CurrencyParameterSensitivity rhoSensiObj = sensiComputed.getSensitivity(IborCapletFloorletSabrRateVolatilityDataSet.META_RHO.CurveName, EUR);
CurrencyParameterSensitivity nuSensiObj = sensiComputed.getSensitivity(IborCapletFloorletSabrRateVolatilityDataSet.META_NU.CurveName, EUR);
CurrencyParameterSensitivity shiftSensiObj = sensiComputed.getSensitivity(IborCapletFloorletSabrRateVolatilityDataSet.META_SHIFT.CurveName, EUR);
DoubleArray alphaNodeSensiComputed = alphaSensiObj.Sensitivity;
DoubleArray betaNodeSensiComputed = betaSensiObj.Sensitivity;
DoubleArray rhoNodeSensiComputed = rhoSensiObj.Sensitivity;
DoubleArray nuNodeSensiComputed = nuSensiObj.Sensitivity;
DoubleArray shiftNodeSensiComputed = shiftSensiObj.Sensitivity;
assertEquals(alphaSensitivities.Sensitivity.size(), alphaNodeSensiComputed.size());
assertEquals(betaSensitivities.Sensitivity.size(), betaNodeSensiComputed.size());
assertEquals(rhoSensitivities.Sensitivity.size(), rhoNodeSensiComputed.size());
assertEquals(nuSensitivities.Sensitivity.size(), nuNodeSensiComputed.size());
assertEquals(shiftSensitivities.Sensitivity.size(), shiftNodeSensiComputed.size());
for (int k = 0; k < alphaNodeSensiComputed.size(); ++k)
{
assertEquals(alphaNodeSensiComputed.get(k), alphaSensitivities.Sensitivity.get(k) * alphaSensi, TOLERANCE_VOL);
}
for (int k = 0; k < betaNodeSensiComputed.size(); ++k)
{
assertEquals(betaNodeSensiComputed.get(k), betaSensitivities.Sensitivity.get(k) * betaSensi, TOLERANCE_VOL);
}
for (int k = 0; k < rhoNodeSensiComputed.size(); ++k)
{
assertEquals(rhoNodeSensiComputed.get(k), rhoSensitivities.Sensitivity.get(k) * rhoSensi, TOLERANCE_VOL);
}
for (int k = 0; k < nuNodeSensiComputed.size(); ++k)
{
assertEquals(nuNodeSensiComputed.get(k), nuSensitivities.Sensitivity.get(k) * nuSensi, TOLERANCE_VOL);
}
for (int k = 0; k < shiftNodeSensiComputed.size(); ++k)
{
assertEquals(shiftNodeSensiComputed.get(k), shiftSensitivities.Sensitivity.get(k) * shiftSensi, TOLERANCE_VOL);
}
}
}
// update vols
private SabrParametersIborCapletFloorletVolatilities updateParameters(SabrIborCapletFloorletVolatilityCalibrationDefinition sabrDefinition, SabrParametersIborCapletFloorletVolatilities volatilities, DoubleArray newValues)
{
SabrParameters sabrParams = volatilities.Parameters;
CurveMetadata alphaMetadata = sabrParams.AlphaCurve.Metadata;
CurveMetadata betaMetadata = sabrParams.BetaCurve.Metadata;
CurveMetadata rhoMetadata = sabrParams.RhoCurve.Metadata;
CurveMetadata nuMetadata = sabrParams.NuCurve.Metadata;
IList <Curve> newCurveList = sabrDefinition.createSabrParameterCurve(ImmutableList.of(alphaMetadata, betaMetadata, rhoMetadata, nuMetadata), newValues);
SabrParameters newSabrParams = SabrParameters.of(newCurveList[0], newCurveList[1], newCurveList[2], newCurveList[3], sabrDefinition.ShiftCurve, sabrDefinition.SabrVolatilityFormula);
SabrParametersIborCapletFloorletVolatilities newVols = SabrParametersIborCapletFloorletVolatilities.of(volatilities.Name, volatilities.Index, volatilities.ValuationDateTime, newSabrParams);
return(newVols);
}
// update vols
private SabrParametersIborCapletFloorletVolatilities updateParameters(SabrParametersIborCapletFloorletVolatilities volatilities, int nExpiries, int timeIndex, bool betaFixed, DoubleArray newParameters)
{
int nBetaParams = volatilities.Parameters.BetaCurve.ParameterCount;
int nRhoParams = volatilities.Parameters.RhoCurve.ParameterCount;
SabrParametersIborCapletFloorletVolatilities newVols = volatilities.withParameter(timeIndex, newParameters.get(0)).withParameter(timeIndex + nExpiries + nBetaParams + nRhoParams, newParameters.get(3));
if (betaFixed)
{
newVols = newVols.withParameter(timeIndex + nExpiries + nBetaParams, newParameters.get(2));
return(newVols);
}
newVols = newVols.withParameter(timeIndex + nExpiries, newParameters.get(1));
return(newVols);
}
public virtual void test_volatility()
{
SabrParametersIborCapletFloorletVolatilities prov = SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM);
for (int i = 0; i < NB_TEST; i++)
{
for (int j = 0; j < NB_STRIKE; ++j)
{
double expiryTime = prov.relativeTime(TEST_OPTION_EXPIRY[i]);
double volExpected = PARAM.volatility(expiryTime, TEST_STRIKE[j], TEST_FORWARD);
double volComputed = prov.volatility(TEST_OPTION_EXPIRY[i], TEST_STRIKE[j], TEST_FORWARD);
assertEquals(volComputed, volExpected, TOLERANCE_VOL);
ValueDerivatives volAdjExpected = PARAM.volatilityAdjoint(expiryTime, TEST_STRIKE[j], TEST_FORWARD);
ValueDerivatives volAdjComputed = prov.volatilityAdjoint(expiryTime, TEST_STRIKE[j], TEST_FORWARD);
assertEquals(volAdjComputed.Value, volExpected, TOLERANCE_VOL);
assertTrue(DoubleArrayMath.fuzzyEquals(volAdjComputed.Derivatives.toArray(), volAdjExpected.Derivatives.toArray(), TOLERANCE_VOL));
}
}
}
public virtual void test_of()
{
SabrParametersIborCapletFloorletVolatilities test = SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM);
assertEquals(test.Index, EUR_EURIBOR_3M);
assertEquals(test.DayCount, ACT_ACT_ISDA);
assertEquals(test.Parameters, PARAM);
assertEquals(test.ValuationDateTime, DATE_TIME);
assertEquals(test.ParameterCount, PARAM.ParameterCount);
int nParams = PARAM.ParameterCount;
double newValue = 152d;
for (int i = 0; i < nParams; ++i)
{
assertEquals(test.getParameter(i), PARAM.getParameter(i));
assertEquals(test.getParameterMetadata(i), PARAM.getParameterMetadata(i));
assertEquals(test.withParameter(i, newValue), SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM.withParameter(i, newValue)));
assertEquals(test.withPerturbation((n, v, m) => 2d * v), SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM.withPerturbation((n, v, m) => 2d * v)));
}
}
public virtual void test_parameterSensitivity_multi()
{
double[] points1 = new double[] { 2.24, 3.45, -2.12, -0.56 };
double[] points2 = new double[] { -0.145, 1.01, -5.0, -11.0 };
double[] points3 = new double[] { 1.3, -4.32, 2.1, -7.18 };
SabrParametersIborCapletFloorletVolatilities prov = SabrParametersIborCapletFloorletVolatilities.of(NAME, EUR_EURIBOR_3M, DATE_TIME, PARAM);
double expiryTime0 = prov.relativeTime(TEST_OPTION_EXPIRY[0]);
double expiryTime3 = prov.relativeTime(TEST_OPTION_EXPIRY[3]);
for (int i = 0; i < NB_TEST; i++)
{
PointSensitivities sensi1 = PointSensitivities.of(IborCapletFloorletSabrSensitivity.of(NAME, expiryTime0, ALPHA, EUR, points1[0]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime0, BETA, EUR, points1[1]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime0, RHO, EUR, points1[2]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime0, NU, EUR, points1[3]));
PointSensitivities sensi2 = PointSensitivities.of(IborCapletFloorletSabrSensitivity.of(NAME, expiryTime0, ALPHA, EUR, points2[0]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime0, BETA, EUR, points2[1]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime0, RHO, EUR, points2[2]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime0, NU, EUR, points2[3]));
PointSensitivities sensi3 = PointSensitivities.of(IborCapletFloorletSabrSensitivity.of(NAME, expiryTime3, ALPHA, EUR, points3[0]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime3, BETA, EUR, points3[1]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime3, RHO, EUR, points3[2]), IborCapletFloorletSabrSensitivity.of(NAME, expiryTime3, NU, EUR, points3[3]));
PointSensitivities sensis = sensi1.combinedWith(sensi2).combinedWith(sensi3).normalized();
CurrencyParameterSensitivities computed = prov.parameterSensitivity(sensis);
CurrencyParameterSensitivities expected = prov.parameterSensitivity(sensi1).combinedWith(prov.parameterSensitivity(sensi2)).combinedWith(prov.parameterSensitivity(sensi3));
DoubleArrayMath.fuzzyEquals(computed.getSensitivity(PARAM.AlphaCurve.Name, EUR).Sensitivity.toArray(), expected.getSensitivity(PARAM.AlphaCurve.Name, EUR).Sensitivity.toArray(), TOLERANCE_VOL);
DoubleArrayMath.fuzzyEquals(computed.getSensitivity(PARAM.BetaCurve.Name, EUR).Sensitivity.toArray(), expected.getSensitivity(PARAM.BetaCurve.Name, EUR).Sensitivity.toArray(), TOLERANCE_VOL);
DoubleArrayMath.fuzzyEquals(computed.getSensitivity(PARAM.RhoCurve.Name, EUR).Sensitivity.toArray(), expected.getSensitivity(PARAM.RhoCurve.Name, EUR).Sensitivity.toArray(), TOLERANCE_VOL);
DoubleArrayMath.fuzzyEquals(computed.getSensitivity(PARAM.NuCurve.Name, EUR).Sensitivity.toArray(), expected.getSensitivity(PARAM.NuCurve.Name, EUR).Sensitivity.toArray(), TOLERANCE_VOL);
}
}
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);
}
}
}
// node sensitivity function
private System.Func <DoubleArray, DoubleMatrix> createJacobianFunction(RatesProvider ratesProvider, SabrParametersIborCapletFloorletVolatilities volatilities, ZonedDateTime prevExpiry, IList <ResolvedIborCapFloorLeg> capList, IList <double> priceList, Currency currency, int[] startIndex, int nExpiries, int timeIndex, int nCaplets, bool betaFixed)
{
Curve alphaCurve = volatilities.Parameters.AlphaCurve;
Curve betaCurve = volatilities.Parameters.BetaCurve;
Curve rhoCurve = volatilities.Parameters.RhoCurve;
Curve nuCurve = volatilities.Parameters.NuCurve;
int currentStart = startIndex[timeIndex];
System.Func <DoubleArray, DoubleMatrix> jacobianFunction = (DoubleArray x) =>
{
SabrParametersIborCapletFloorletVolatilities volsNew = updateParameters(volatilities, nExpiries, timeIndex, betaFixed, x);
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] jacobian = new double[nCaplets][4];
double[][] jacobian = RectangularArrays.ReturnRectangularDoubleArray(nCaplets, 4);
for (int i = 0; i < nCaplets; ++i)
{
PointSensitivities point = capList[currentStart + i].CapletFloorletPeriods.Where(p => p.FixingDateTime.isAfter(prevExpiry)).Select(p => sabrPeriodPricer.presentValueSensitivityModelParamsSabr(p, ratesProvider, volsNew)).Aggregate((c1, c2) => c1.combinedWith(c2)).get().build();
double targetPrice = priceList[currentStart + i];
CurrencyParameterSensitivities sensi = volsNew.parameterSensitivity(point);
jacobian[i][0] = sensi.getSensitivity(alphaCurve.Name, currency).Sensitivity.get(timeIndex) / targetPrice;
if (betaFixed)
{
jacobian[i][1] = 0d;
jacobian[i][2] = sensi.getSensitivity(rhoCurve.Name, currency).Sensitivity.get(timeIndex) / targetPrice;
}
else
{
jacobian[i][1] = sensi.getSensitivity(betaCurve.Name, currency).Sensitivity.get(timeIndex) / targetPrice;
jacobian[i][2] = 0d;
}
jacobian[i][3] = sensi.getSensitivity(nuCurve.Name, currency).Sensitivity.get(timeIndex) / targetPrice;
}
return(DoubleMatrix.ofUnsafe(jacobian));
};
return(jacobianFunction);
}
/// <summary>
/// Obtains {@code SabrParametersIborCapletFloorletVolatilities} with constant shift for specified valuation date.
/// </summary>
/// <param name="dateTime"> the valuation date time </param>
/// <param name="index"> the index </param>
/// <returns> the volatility provider </returns>
public static SabrParametersIborCapletFloorletVolatilities getVolatilities(ZonedDateTime dateTime, IborIndex index)
{
return(SabrParametersIborCapletFloorletVolatilities.of(NAME, index, dateTime, SABR_PARAM_CONST_SHIFT));
}
/// <summary>
/// Obtains {@code SabrParametersIborCapletFloorletVolatilities} with constant SABR parameters for specified valuation date.
/// </summary>
/// <param name="valuationDate"> the valuation date </param>
/// <param name="index"> the index </param>
/// <returns> the volatility provider </returns>
public static SabrParametersIborCapletFloorletVolatilities getVolatilitiesFlatParameters(LocalDate valuationDate, IborIndex index)
{
ZonedDateTime dateTime = valuationDate.atStartOfDay(ZoneOffset.UTC);
return(SabrParametersIborCapletFloorletVolatilities.of(NAME, index, dateTime, SABR_PARAM_FLAT));
}
//-------------------------------------------------------------------------
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));
}
