/**
* Copyright (C) 2011 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.interestrate.swaption.provider;
import com.opengamma.analytics.financial.interestrate.annuity.derivative.AnnuityCouponFixed;
import com.opengamma.analytics.financial.interestrate.swap.provider.SwapFixedCouponDiscountingMethod;
import com.opengamma.analytics.financial.interestrate.swaption.derivative.SwaptionCashFixedIbor;
import com.opengamma.analytics.financial.model.option.definition.SABRInterestRateParameters;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.BlackFunctionData;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.BlackPriceFunction;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.EuropeanVanillaOption;
import com.opengamma.analytics.financial.model.volatility.smile.function.SABRFormulaData;
import com.opengamma.analytics.financial.model.volatility.smile.function.VolatilityFunctionProvider;
import com.opengamma.analytics.financial.provider.calculator.discounting.ParRateDiscountingCalculator;
import com.opengamma.analytics.financial.provider.description.interestrate.MulticurveProviderInterface;
import com.opengamma.analytics.financial.provider.description.interestrate.SABRSwaptionProviderInterface;
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;
import com.opengamma.util.tuple.DoublesPair;
/**
* Method to compute the present value of cash-settled European swaptions with with the Linear Terminal Swap Rate method.
* The physical swaptions are priced with SABR.
*/
public class SwaptionCashFixedIborLinearTSRMethod {
/**
* The par rate calculator.
*/
private static final ParRateDiscountingCalculator PRDC = ParRateDiscountingCalculator.getInstance();
/**
* Minimal number of integration steps in the replication.
*/
private final int _nbIteration = 6;
/**
* Range of the integral. Used only for caps. Represent the approximation of infinity in the strike dimension.
* The range is [strike, strike+integrationInterval].
*/
private final double _integrationInterval = 1.0;
/**
* The swap method.
*/
private static final SwapFixedCouponDiscountingMethod METHOD_SWAP = SwapFixedCouponDiscountingMethod.getInstance();
/**
* Computes the present value of a cash-settled European swaption in the linear TSR method.
* @param swaption The swaption.
* @param sabrData The SABR data (used for physical swaptions).
* @return The present value.
*/
public MultipleCurrencyAmount presentValue(final SwaptionCashFixedIbor swaption, final SABRSwaptionProviderInterface sabrData) {
ArgumentChecker.notNull(swaption, "Swaption");
ArgumentChecker.notNull(sabrData, "SABR swaption provider");
MulticurveProviderInterface multicurves = sabrData.getMulticurveProvider();
Currency ccy = swaption.getCurrency();
final AnnuityCouponFixed annuityFixed = swaption.getUnderlyingSwap().getFixedLeg();
final double nominal = Math.abs(annuityFixed.getNthPayment(0).getNotional());
final double discountFactorSettle = multicurves.getDiscountFactor(ccy, swaption.getSettlementTime());
final double annuityPhysical = METHOD_SWAP.presentValueBasisPoint(swaption.getUnderlyingSwap(), multicurves) / nominal;
final double strike = swaption.getStrike();
final double forward = swaption.getUnderlyingSwap().accept(PRDC, multicurves);
// Linear approximation
final double[] alpha = new double[2];
for (int loopcpn = 0; loopcpn < annuityFixed.getNumberOfPayments(); loopcpn++) {
alpha[1] += annuityFixed.getNthPayment(loopcpn).getPaymentYearFraction();
}
alpha[1] = 1 / alpha[1];
alpha[0] = (discountFactorSettle / annuityPhysical - alpha[1]) / forward;
final LinearTSRIntegrant integrant = new LinearTSRIntegrant(swaption, sabrData.getSABRParameter(), forward, alpha);
@SuppressWarnings("synthetic-access")
final double strikePart = integrant.k(strike) * integrant.bs(strike);
final double absoluteTolerance = 1.0E-2;
final double relativeTolerance = 1.0E-5;
final RungeKuttaIntegrator1D integrator = new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, _nbIteration);
double integralPart;
try {
if (swaption.isCall()) {
integralPart = integrator.integrate(integrant, strike, strike + _integrationInterval);
} else {
integralPart = integrator.integrate(integrant, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
final double pv = nominal * annuityPhysical * (strikePart + integralPart) * (swaption.isLong() ? 1.0 : -1.0);
return MultipleCurrencyAmount.of(swaption.getCurrency(), pv);
}
/**
* Inner class to implement the integration used in price replication.
*/
private static final class LinearTSRIntegrant extends Function1D<Double, Double> {
private static final double EPS = 1E-10;
private final double[] _linear;
private final int _nbFixedPeriod;
private final int _nbFixedPaymentYear;
private final double _strike;
private final double _forward;
private final double _timeToExpiry;
private final double _maturity;
private final boolean _isCall;
private final SABRFormulaData _sabrData;
private final VolatilityFunctionProvider<SABRFormulaData> _sabrFunction;
private final BlackPriceFunction _blackFunction = new BlackPriceFunction();
/**
* Constructor with the required data.
* @param baseMethod The base method for the pricing of standard cap/floors.
* @param capStandard The standard cap/floor used for replication.
* @param sabrData The SABR data bundle used in the standard cap/floor pricing.
*/
public LinearTSRIntegrant(final SwaptionCashFixedIbor swaption, final SABRInterestRateParameters sabrParameter, final double forward, final double[] linear) {
_forward = forward;
_nbFixedPeriod = swaption.getUnderlyingSwap().getFixedLeg().getPayments().length;
_nbFixedPaymentYear = (int) Math.round(1.0 / swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(0).getPaymentYearFraction());
_timeToExpiry = swaption.getTimeToExpiry();
final AnnuityCouponFixed annuityFixed = swaption.getUnderlyingSwap().getFixedLeg();
_maturity = annuityFixed.getNthPayment(annuityFixed.getNumberOfPayments() - 1).getPaymentTime() - swaption.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(_timeToExpiry, _maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
_sabrData = new SABRFormulaData(alpha, beta, rho, nu);
_sabrFunction = sabrParameter.getSabrFunction();
_isCall = swaption.isCall();
_strike = swaption.getStrike();
_linear = linear;
}
@Override
public Double evaluate(final Double x) {
final double[] kD = kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative of k.
return (kD[1] * (x - _strike) + 2.0 * kD[0]) * bs(x);
}
/**
* The factor used in the strike part and in the integration of the replication.
* @param x The swap rate.
* @return The factor.
*/
private double k(final double x) {
double g;
final double linear = _linear[0] * x + _linear[1];
if (x >= EPS) {
final double periodFactor = 1 + x / _nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -_nbFixedPeriod);
g = 1.0 / x * (1.0 - nPeriodDiscount);
} else {
g = ((double) _nbFixedPeriod) / _nbFixedPaymentYear;
}
return linear * g;
}
/**
* The first and second derivative of the function k.
* @param x The swap rate.
* @return The derivative (first element is the first derivative, second element is second derivative).
*/
private double[] kpkpp(final double x) {
final double periodFactor = 1 + x / _nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -_nbFixedPeriod);
/**
* The value of the annuity and its first and second derivative.
*/
double g, gp, gpp;
if (x >= EPS) {
g = 1.0 / x * (1.0 - nPeriodDiscount);
gp = -g / x + _nbFixedPeriod / x / _nbFixedPaymentYear * nPeriodDiscount / periodFactor;
gpp = 2.0 / (x * x) * g - 2.0 * _nbFixedPeriod / (x * x) / _nbFixedPaymentYear * nPeriodDiscount / periodFactor - (_nbFixedPeriod + 1.0) * _nbFixedPeriod / x
/ (_nbFixedPaymentYear * _nbFixedPaymentYear) * nPeriodDiscount / (periodFactor * periodFactor);
} else {
// Implementation comment: When x is (almost) 0, useful for CMS swaps which are priced as CMS cap of strike 0.
g = ((double) _nbFixedPeriod) / _nbFixedPaymentYear;
gp = -_nbFixedPeriod / 2.0 * (_nbFixedPeriod + 1.0) / (_nbFixedPaymentYear * _nbFixedPaymentYear);
gpp = _nbFixedPeriod / 2.0 * (_nbFixedPeriod + 1.0) * (1.0 + (_nbFixedPeriod + 2.0) / 3.0) / (_nbFixedPaymentYear * _nbFixedPaymentYear * _nbFixedPaymentYear);
}
final double kp = _linear[0] * g + (_linear[0] * x + _linear[1]) * gp;
final double kpp = 2 * _linear[0] * gp + (_linear[0] * x + _linear[1]) * gpp;
return new double[] {kp, kpp};
}
/**
* The Black-Scholes formula with numeraire 1 as function of the strike.
* @param strike The strike.
* @return The Black-Scholes formula.
*/
double bs(final double strike) {
final EuropeanVanillaOption option = new EuropeanVanillaOption(strike, _timeToExpiry, _isCall);
final Function1D<SABRFormulaData, Double> funcSabr = _sabrFunction.getVolatilityFunction(option, _forward);
final double volatility = funcSabr.evaluate(_sabrData);
final BlackFunctionData dataBlack = new BlackFunctionData(_forward, 1.0, volatility);
final Function1D<BlackFunctionData, Double> func = _blackFunction.getPriceFunction(option);
return func.evaluate(dataBlack);
}
}
}