/**
* Create an analytic swaption approximation product for log normal forward rate model.
*
* <p>Note: It is implicitly assumed that swapTenor.getTime(0) is the exercise date (no forward
* starting).
*
* @param swaprate The strike swap rate of the swaption.
* @param swapTenor The swap tenor in doubles.
*/
public SwaptionAnalyticApproximation(double swaprate, TimeDiscretizationInterface swapTenor) {
this(swaprate, swapTenor.getAsDoubleArray(), ValueUnit.VALUE);
}
/**
* This function calculate the partial derivative <i>d log(S) / d log(L<sub>k</sub>)</i> for a
* given swap rate with respect to a vector of forward rates (on a given forward rate tenor).
*
* <p>It also returns some useful other quantities like the corresponding discout factors and swap
* annuities.
*
* @param liborPeriodDiscretization The libor period discretization.
* @param discountCurveInterface The discount curve. If this parameter is null, the discount curve
* will be calculated from the forward curve.
* @param forwardCurveInterface The forward curve.
* @return A map containing the partial derivatives (key "value"), the discount factors (key
* "discountFactors") and the annuities (key "annuities") as vectors of double[] (indexed by
* forward rate tenor index starting at swap start)
*/
public Map<String, double[]> getLogSwaprateDerivative(
TimeDiscretizationInterface liborPeriodDiscretization,
DiscountCurveInterface discountCurveInterface,
ForwardCurveInterface forwardCurveInterface) {
/*
* We cache the calculation of the log swaprate derivative. In a calibration this method might be called quite often with the same arguments.
*/
synchronized (cachedLogSwaprateDerivativeLock) {
if (cachedLogSwaprateDerivative != null
&& liborPeriodDiscretization == cachedLogSwaprateDerivativeTimeDiscretization.get()
&& discountCurveInterface == cachedLogSwaprateDerivativeDiscountCurve.get()
&& forwardCurveInterface == cachedLogSwaprateDerivativeForwardCurve.get()) {
return cachedLogSwaprateDerivative;
}
cachedLogSwaprateDerivativeTimeDiscretization =
new WeakReference<TimeDiscretizationInterface>(liborPeriodDiscretization);
cachedLogSwaprateDerivativeDiscountCurve =
new WeakReference<DiscountCurveInterface>(discountCurveInterface);
cachedLogSwaprateDerivativeForwardCurve =
new WeakReference<ForwardCurveInterface>(forwardCurveInterface);
/*
* Small workaround for the case that the discount curve is not set. This part will be removed later.
*/
AnalyticModel model = null;
if (discountCurveInterface == null) {
discountCurveInterface = new DiscountCurveFromForwardCurve(forwardCurveInterface.getName());
model =
new AnalyticModel(new CurveInterface[] {forwardCurveInterface, discountCurveInterface});
}
double swapStart = swapTenor[0];
double swapEnd = swapTenor[swapTenor.length - 1];
// Get the indices of the swap start and end on the forward rate tenor
int swapStartIndex = liborPeriodDiscretization.getTimeIndex(swapStart);
int swapEndIndex = liborPeriodDiscretization.getTimeIndex(swapEnd);
// Precalculate forward rates and discount factors. Note: the swap contains
// swapEndIndex-swapStartIndex forward rates
double[] forwardRates = new double[swapEndIndex - swapStartIndex + 1];
double[] discountFactors = new double[swapEndIndex - swapStartIndex + 1];
// Calculate discount factor at swap start
discountFactors[0] = discountCurveInterface.getDiscountFactor(model, swapStart);
// Calculate discount factors for swap period ends (used for swap annuity)
for (int liborPeriodIndex = swapStartIndex;
liborPeriodIndex < swapEndIndex;
liborPeriodIndex++) {
double libor =
forwardCurveInterface.getForward(
null, liborPeriodDiscretization.getTime(liborPeriodIndex));
forwardRates[liborPeriodIndex - swapStartIndex] = libor;
discountFactors[liborPeriodIndex - swapStartIndex + 1] =
discountCurveInterface.getDiscountFactor(
model, liborPeriodDiscretization.getTime(liborPeriodIndex + 1));
}
// Precalculate swap annuities
double[] swapAnnuities = new double[swapTenor.length - 1];
double swapAnnuity = 0.0;
for (int swapPeriodIndex = swapTenor.length - 2; swapPeriodIndex >= 0; swapPeriodIndex--) {
int periodEndIndex = liborPeriodDiscretization.getTimeIndex(swapTenor[swapPeriodIndex + 1]);
swapAnnuity +=
discountFactors[periodEndIndex - swapStartIndex]
* (swapTenor[swapPeriodIndex + 1] - swapTenor[swapPeriodIndex]);
swapAnnuities[swapPeriodIndex] = swapAnnuity;
}
// Precalculate weights: The formula is take from ISBN 0470047224
double[] swapCovarianceWeights = new double[swapEndIndex - swapStartIndex];
double valueFloatLeg = 0.0;
for (int liborPeriodIndex = swapStartIndex;
liborPeriodIndex < swapEndIndex;
liborPeriodIndex++) {
double liborPeriodLength = liborPeriodDiscretization.getTimeStep(liborPeriodIndex);
valueFloatLeg +=
forwardRates[liborPeriodIndex - swapStartIndex]
* discountFactors[liborPeriodIndex - swapStartIndex + 1]
* liborPeriodLength;
}
int swapPeriodIndex = 0;
double valueFloatLegUpToSwapStart = 0.0;
for (int liborPeriodIndex = swapStartIndex;
liborPeriodIndex < swapEndIndex;
liborPeriodIndex++) {
if (liborPeriodDiscretization.getTime(liborPeriodIndex) >= swapTenor[swapPeriodIndex + 1])
swapPeriodIndex++;
double libor = forwardRates[liborPeriodIndex - swapStartIndex];
double liborPeriodLength = liborPeriodDiscretization.getTimeStep(liborPeriodIndex);
valueFloatLegUpToSwapStart +=
forwardRates[liborPeriodIndex - swapStartIndex]
* discountFactors[liborPeriodIndex - swapStartIndex + 1]
* liborPeriodLength;
double discountFactorAtPeriodEnd =
discountCurveInterface.getDiscountFactor(
model, liborPeriodDiscretization.getTime(liborPeriodIndex + 1));
double derivativeFloatLeg =
(discountFactorAtPeriodEnd + valueFloatLegUpToSwapStart - valueFloatLeg)
* liborPeriodLength
/ (1.0 + libor * liborPeriodLength)
/ valueFloatLeg;
double derivativeFixLeg =
-swapAnnuities[swapPeriodIndex]
/ swapAnnuity
* liborPeriodLength
/ (1.0 + libor * liborPeriodLength);
swapCovarianceWeights[liborPeriodIndex - swapStartIndex] =
(derivativeFloatLeg - derivativeFixLeg) * libor;
}
// Return results
Map<String, double[]> results = new HashMap<String, double[]>();
results.put("values", swapCovarianceWeights);
results.put("discountFactors", discountFactors);
results.put("swapAnnuities", swapAnnuities);
cachedLogSwaprateDerivative = results;
return results;
}
}
