public static ResolvedIborCapFloorLeg[][] ReturnRectangularResolvedIborCapFloorLegArray(int size1, int size2)
{
ResolvedIborCapFloorLeg[][] newArray = new ResolvedIborCapFloorLeg[size1][];
for (int array1 = 0; array1 < size1; array1++)
{
newArray[array1] = new ResolvedIborCapFloorLeg[size2];
}
return(newArray);
}
//-------------------------------------------------------------------------
// price and vega function
private System.Func <double, double[]> getValueVegaFunction(ResolvedIborCapFloorLeg cap, RatesProvider ratesProvider, IborCapletFloorletVolatilities vols, ZonedDateTime prevExpiry, int nodeIndex)
{
VolatilityIborCapletFloorletPeriodPricer periodPricer = LegPricer.PeriodPricer;
System.Func <double, double[]> priceAndVegaFunction = (double?x) =>
{
IborCapletFloorletVolatilities newVols = vols.withParameter(nodeIndex, x.Value);
double price = cap.CapletFloorletPeriods.Where(p => p.FixingDateTime.isAfter(prevExpiry)).Select(p => periodPricer.presentValue(p, ratesProvider, newVols).Amount).Sum();
PointSensitivities point = cap.CapletFloorletPeriods.Where(p => p.FixingDateTime.isAfter(prevExpiry)).Select(p => periodPricer.presentValueSensitivityModelParamsVolatility(p, ratesProvider, newVols)).Aggregate((c1, c2) => c1.combinedWith(c2)).get().build();
CurrencyParameterSensitivities sensi = newVols.parameterSensitivity(point);
double vega = sensi.Sensitivities.get(0).Sensitivity.get(nodeIndex);
return(new double[] { price, vega });
};
return(priceAndVegaFunction);
}
//-------------------------------------------------------------------------
// create complete lists of caps, volatilities, strikes, expiries
protected internal virtual void reduceRawData(IborCapletFloorletVolatilityDefinition definition, RatesProvider ratesProvider, DoubleArray strikes, DoubleArray volatilityData, DoubleArray errors, LocalDate startDate, LocalDate endDate, SurfaceMetadata metadata, System.Func <Surface, IborCapletFloorletVolatilities> volatilityFunction, IList <double> timeList, IList <double> strikeList, IList <double> volList, IList <ResolvedIborCapFloorLeg> capList, IList <double> priceList, IList <double> errorList)
{
int nStrikes = strikes.size();
for (int i = 0; i < nStrikes; ++i)
{
if (Double.isFinite(volatilityData.get(i)))
{
ResolvedIborCapFloorLeg capFloor = definition.createCap(startDate, endDate, strikes.get(i)).resolve(referenceData);
capList.Add(capFloor);
strikeList.Add(strikes.get(i));
volList.Add(volatilityData.get(i));
ConstantSurface constVolSurface = ConstantSurface.of(metadata, volatilityData.get(i));
IborCapletFloorletVolatilities vols = volatilityFunction(constVolSurface);
timeList.Add(vols.relativeTime(capFloor.FinalFixingDateTime));
priceList.Add(pricer.presentValue(capFloor, ratesProvider, vols).Amount);
errorList.Add(errors.get(i));
}
}
}
//-------------------------------------------------------------------------
// computes initial guess for each time step
private DoubleArray computeInitialValues(RatesProvider ratesProvider, Curve betaCurve, Curve shiftCurve, IList <double> timeList, IList <double> volList, IList <ResolvedIborCapFloorLeg> capList, int[] startIndex, int postion, bool betaFixed, ValueType valueType)
{
IList <double> vols = volList.subList(startIndex[postion], startIndex[postion + 1]);
ResolvedIborCapFloorLeg cap = capList[startIndex[postion]];
double fwd = ratesProvider.iborIndexRates(cap.Index).rate(cap.FinalPeriod.IborRate.Observation);
double shift = shiftCurve.yValue(timeList[startIndex[postion]]);
double factor = valueType.Equals(ValueType.BLACK_VOLATILITY) ? 1d : 1d / (fwd + shift);
IList <double> volsEquiv = vols.Select(v => v * factor).ToList();
double nuFirst;
double betaInitial = betaFixed ? betaCurve.yValue(timeList[startIndex[postion]]) : 0.5d;
double alphaInitial = DoubleArray.copyOf(volsEquiv).min() * Math.Pow(fwd, 1d - betaInitial);
if (alphaInitial == volsEquiv[0] || alphaInitial == volsEquiv[volsEquiv.Count - 1])
{
nuFirst = 0.1d;
alphaInitial *= 0.95d;
}
else
{
nuFirst = 1d;
}
return(DoubleArray.of(alphaInitial, betaInitial, -0.5 * betaInitial + 0.5 * (1d - betaInitial), nuFirst));
}
//-------------------------------------------------------------------------
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 DirectIborCapletFloorletVolatilityDefinition, "definition should be DirectIborCapletFloorletVolatilityDefinition");
DirectIborCapletFloorletVolatilityDefinition directDefinition = (DirectIborCapletFloorletVolatilityDefinition)definition;
// unpack cap data, create node caps
IborIndex index = directDefinition.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(directDefinition, calibrationDateTime, capFloorData);
SurfaceMetadata metadata = directDefinition.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(directDefinition, 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 caplet nodes and initial caplet vol surface
ResolvedIborCapFloorLeg cap = capList[capList.Count - 1];
int nCaplets = cap.CapletFloorletPeriods.size();
DoubleArray capletExpiries = DoubleArray.of(nCaplets, n => directDefinition.DayCount.relativeYearFraction(calibrationDate, cap.CapletFloorletPeriods.get(n).FixingDateTime.toLocalDate()));
Triple <DoubleArray, DoubleArray, DoubleArray> capletNodes;
DoubleArray initialVols = DoubleArray.copyOf(volList);
if (directDefinition.ShiftCurve.Present)
{
metadata = Surfaces.blackVolatilityByExpiryStrike(directDefinition.Name.Name, directDefinition.DayCount);
Curve shiftCurve = directDefinition.ShiftCurve.get();
if (capFloorData.DataType.Equals(NORMAL_VOLATILITY))
{
initialVols = DoubleArray.of(capList.Count, n => volList[n] / (ratesProvider.iborIndexRates(index).rate(capList[n].FinalPeriod.IborRate.Observation) + shiftCurve.yValue(timeList[n])));
}
InterpolatedNodalSurface capVolSurface = InterpolatedNodalSurface.of(metadata, DoubleArray.copyOf(timeList), DoubleArray.copyOf(strikeList), initialVols, INTERPOLATOR);
capletNodes = createCapletNodes(capVolSurface, capletExpiries, strikes, directDefinition.ShiftCurve.get());
volatilitiesFunction = createShiftedBlackVolatilitiesFunction(index, calibrationDateTime, shiftCurve);
}
else
{
InterpolatedNodalSurface capVolSurface = InterpolatedNodalSurface.of(metadata, DoubleArray.copyOf(timeList), DoubleArray.copyOf(strikeList), initialVols, INTERPOLATOR);
capletNodes = createCapletNodes(capVolSurface, capletExpiries, strikes);
}
InterpolatedNodalSurface baseSurface = InterpolatedNodalSurface.of(metadata, capletNodes.First, capletNodes.Second, capletNodes.Third, INTERPOLATOR);
DoubleMatrix penaltyMatrix = directDefinition.computePenaltyMatrix(strikes, capletExpiries);
// solve least square
LeastSquareResults res = solver.solve(DoubleArray.copyOf(priceList), DoubleArray.copyOf(errorList), getPriceFunction(capList, ratesProvider, volatilitiesFunction, baseSurface), getJacobianFunction(capList, ratesProvider, volatilitiesFunction, baseSurface), capletNodes.Third, penaltyMatrix, POSITIVE);
InterpolatedNodalSurface resSurface = InterpolatedNodalSurface.of(metadata, capletNodes.First, capletNodes.Second, res.FitParameters, directDefinition.Interpolator);
return(IborCapletFloorletVolatilityCalibrationResult.ofLeastSquare(volatilitiesFunction(resSurface), res.ChiSq));
}
// sum of caplet prices which are already fixed
private double priceFixed(ResolvedIborCapFloorLeg cap, RatesProvider ratesProvider, IborCapletFloorletVolatilities vols, ZonedDateTime prevExpiry)
{
VolatilityIborCapletFloorletPeriodPricer periodPricer = LegPricer.PeriodPricer;
return(cap.CapletFloorletPeriods.Where(p => !p.FixingDateTime.isAfter(prevExpiry)).Select(p => periodPricer.presentValue(p, ratesProvider, vols).Amount).Sum());
}
