// 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 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);
}
}
}
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);
}
}
// 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);
}
