/**
* Copyright (C) 2012 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.interestrate.payments.provider;
import com.opengamma.analytics.financial.interestrate.annuity.derivative.AnnuityPaymentFixed;
import com.opengamma.analytics.financial.interestrate.payments.derivative.CapFloorCMS;
import com.opengamma.analytics.financial.interestrate.payments.derivative.Payment;
import com.opengamma.analytics.financial.interestrate.swap.derivative.SwapFixedCoupon;
import com.opengamma.analytics.financial.model.interestrate.HullWhiteOneFactorPiecewiseConstantInterestRateModel;
import com.opengamma.analytics.financial.model.interestrate.definition.HullWhiteOneFactorPiecewiseConstantParameters;
import com.opengamma.analytics.financial.provider.calculator.discounting.CashFlowEquivalentCalculator;
import com.opengamma.analytics.financial.provider.description.interestrate.HullWhiteOneFactorProviderInterface;
import com.opengamma.analytics.financial.provider.description.interestrate.MulticurveProviderInterface;
import com.opengamma.analytics.math.MathException;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.integration.RungeKuttaIntegrator1D;
import com.opengamma.util.ArgumentChecker;
import com.opengamma.util.money.Currency;
import com.opengamma.util.money.MultipleCurrencyAmount;
/**
* Pricing method of a CMS cap/floor in the Hull-White (extended Vasicek) model by approximation.
* <P> Reference: M. Henrard. CMS Swaps and Caps in One-Factor Gaussian Models, SSRN working paper 985551, February 2008.
* Available at http://ssrn.com/abstract=985551
*/
public final class CapFloorCMSHullWhiteNumericalIntegrationMethod {
/**
* The method unique instance.
*/
private static final CapFloorCMSHullWhiteNumericalIntegrationMethod INSTANCE = new CapFloorCMSHullWhiteNumericalIntegrationMethod();
/**
* Return the unique instance of the class.
* @return The instance.
*/
public static CapFloorCMSHullWhiteNumericalIntegrationMethod getInstance() {
return INSTANCE;
}
/**
* Private constructor.
*/
private CapFloorCMSHullWhiteNumericalIntegrationMethod() {
}
/**
* The model used in computations.
*/
private static final HullWhiteOneFactorPiecewiseConstantInterestRateModel MODEL = new HullWhiteOneFactorPiecewiseConstantInterestRateModel();
/**
* The cash flow equivalent calculator used in computations.
*/
private static final CashFlowEquivalentCalculator CFEC = CashFlowEquivalentCalculator.getInstance();
/**
* Minimal number of integration steps.
*/
private static final int NB_INTEGRATION = 100;
public MultipleCurrencyAmount presentValue(final CapFloorCMS cms, final HullWhiteOneFactorProviderInterface hullWhite) {
ArgumentChecker.notNull(cms, "CMS");
ArgumentChecker.notNull(hullWhite, "Hull-White provider");
final Currency ccy = cms.getCurrency();
final HullWhiteOneFactorPiecewiseConstantParameters parameters = hullWhite.getHullWhiteParameters();
final MulticurveProviderInterface multicurves = hullWhite.getMulticurveProvider();
final double expiryTime = cms.getFixingTime();
final SwapFixedCoupon<? extends Payment> swap = cms.getUnderlyingSwap();
final int nbFixed = cms.getUnderlyingSwap().getFixedLeg().getNumberOfPayments();
final double[] alphaFixed = new double[nbFixed];
final double[] dfFixed = new double[nbFixed];
final double[] discountedCashFlowFixed = new double[nbFixed];
for (int loopcf = 0; loopcf < nbFixed; loopcf++) {
alphaFixed[loopcf] = MODEL.alpha(parameters, 0.0, expiryTime, expiryTime, swap.getFixedLeg().getNthPayment(loopcf).getPaymentTime());
dfFixed[loopcf] = multicurves.getDiscountFactor(ccy, swap.getFixedLeg().getNthPayment(loopcf).getPaymentTime());
discountedCashFlowFixed[loopcf] = dfFixed[loopcf] * swap.getFixedLeg().getNthPayment(loopcf).getPaymentYearFraction() * swap.getFixedLeg().getNthPayment(loopcf).getNotional();
}
final AnnuityPaymentFixed cfeIbor = swap.getSecondLeg().accept(CFEC, multicurves);
final double[] alphaIbor = new double[cfeIbor.getNumberOfPayments()];
final double[] dfIbor = new double[cfeIbor.getNumberOfPayments()];
final double[] discountedCashFlowIbor = new double[cfeIbor.getNumberOfPayments()];
for (int loopcf = 0; loopcf < cfeIbor.getNumberOfPayments(); loopcf++) {
alphaIbor[loopcf] = MODEL.alpha(parameters, 0.0, expiryTime, expiryTime, cfeIbor.getNthPayment(loopcf).getPaymentTime());
dfIbor[loopcf] = multicurves.getDiscountFactor(ccy, cfeIbor.getNthPayment(loopcf).getPaymentTime());
discountedCashFlowIbor[loopcf] = dfIbor[loopcf] * cfeIbor.getNthPayment(loopcf).getAmount();
}
final double alphaPayment = MODEL.alpha(parameters, 0.0, expiryTime, expiryTime, cms.getPaymentTime());
final double dfPayment = multicurves.getDiscountFactor(ccy, cms.getPaymentTime());
// Integration
final CMSIntegrant integrant = new CMSIntegrant(discountedCashFlowFixed, alphaFixed, discountedCashFlowIbor, alphaIbor, alphaPayment, cms.getStrike(), (cms.isCap() ? 1.0 : -1.0));
final double limit = 10.0;
final double absoluteTolerance = 1.0E-8;
final double relativeTolerance = 1.0E-9;
final RungeKuttaIntegrator1D integrator = new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, NB_INTEGRATION);
double pv = 0.0;
try {
pv = 1.0 / Math.sqrt(2.0 * Math.PI) * integrator.integrate(integrant, -limit, limit) * dfPayment * cms.getNotional() * cms.getPaymentYearFraction();
} catch (final Exception e) {
throw new MathException(e);
}
return MultipleCurrencyAmount.of(cms.getCurrency(), pv);
}
/**
* Inner class to implement the integration used in price computation.
*/
private static final class CMSIntegrant extends Function1D<Double, Double> {
private final double[] _discountedCashFlowFixed;
private final double[] _alphaFixed;
private final double[] _discountedCashFlowIbor;
private final double[] _alphaIbor;
private final double _alphaPayment;
private final double _strike;
private final double _omega;
/**
* Constructor to the integrant function.
* @param discountedCashFlowFixed The discounted cash flows of the underlying swap fixed leg.
* @param alphaFixed The bond volatilities of the underlying swap fixed leg.
* @param discountedCashFlowIbor The discounted cash flows of the underlying swap Ibor leg.
* @param alphaIbor The bond volatilities of the underlying swap Ibor leg.
* @param alphaPayment The bond volatilities of the payment discount factor.
* @param strike The strike.
* @param omega The factor.
*/
public CMSIntegrant(final double[] discountedCashFlowFixed, final double[] alphaFixed, final double[] discountedCashFlowIbor, final double[] alphaIbor, final double alphaPayment,
final double strike, final double omega) {
_discountedCashFlowFixed = discountedCashFlowFixed;
_alphaFixed = alphaFixed;
_discountedCashFlowIbor = discountedCashFlowIbor;
_alphaIbor = alphaIbor;
_alphaPayment = alphaPayment;
_strike = strike;
_omega = omega;
}
@Override
public Double evaluate(final Double x) {
@SuppressWarnings("synthetic-access")
final double swapRate = MODEL.swapRate(x, _discountedCashFlowFixed, _alphaFixed, _discountedCashFlowIbor, _alphaIbor);
final double dfDensity = Math.exp(-(x + _alphaPayment) * (x + _alphaPayment) / 2.0);
final double result = dfDensity * Math.max(_omega * (swapRate - _strike), 0.0);
return result;
}
}
}