/**
* 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 java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import com.opengamma.analytics.financial.interestrate.PresentValueSABRSensitivityDataBundle;
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.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.SABRExtrapolationRightFunction;
import com.opengamma.analytics.financial.model.volatility.smile.function.SABRFormulaData;
import com.opengamma.analytics.financial.provider.calculator.discounting.ParRateCurveSensitivityDiscountingCalculator;
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.financial.provider.sensitivity.multicurve.MulticurveSensitivity;
import com.opengamma.analytics.financial.provider.sensitivity.multicurve.MultipleCurrencyMulticurveSensitivity;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.util.ArgumentChecker;
import com.opengamma.util.money.Currency;
import com.opengamma.util.money.MultipleCurrencyAmount;
import com.opengamma.util.tuple.DoublesPair;
/**
* Class used to compute the price and sensitivity of a cash-settled European swaption with SABR model and extrapolation to the right.
* Implemented only for the SABRHaganVolatilityFunction.
* OpenGamma implementation note for the extrapolation: Smile extrapolation, version 1.2, May 2011.
*/
public class SwaptionCashFixedIborSABRExtrapolationRightMethod {
/**
* The cut-off strike. The smile is extrapolated above that level.
*/
private final double _cutOffStrike;
/**
* The tail thickness parameter.
*/
private final double _mu;
/**
* The par rate sensitivity calculator.
*/
private static final ParRateDiscountingCalculator PRDC = ParRateDiscountingCalculator.getInstance();
private static final ParRateCurveSensitivityDiscountingCalculator PRCSDC = ParRateCurveSensitivityDiscountingCalculator.getInstance();
private static final SwapFixedCouponDiscountingMethod METHOD_SWAP = SwapFixedCouponDiscountingMethod.getInstance();
/**
* Constructor from cut-off strike and tail parameter.
* @param cutOffStrike The cut-off strike.
* @param mu The tail thickness parameter.
*/
public SwaptionCashFixedIborSABRExtrapolationRightMethod(final double cutOffStrike, final double mu) {
_cutOffStrike = cutOffStrike;
_mu = mu;
}
/**
* Computes the present value of a cash-settled European swaption in the SABR model with extrapolation to the right.
* @param swaption The swaption.
* @param sabrData The SABR data.
* @return The present value.
*/
public MultipleCurrencyAmount presentValue(final SwaptionCashFixedIbor swaption, final SABRSwaptionProviderInterface sabrData) {
ArgumentChecker.notNull(swaption, "Swaption");
ArgumentChecker.notNull(sabrData, "SABR swaption provider");
final MulticurveProviderInterface multicurves = sabrData.getMulticurveProvider();
final Currency ccy = swaption.getCurrency();
final AnnuityCouponFixed annuityFixed = swaption.getUnderlyingSwap().getFixedLeg();
final double forward = swaption.getUnderlyingSwap().accept(PRDC, multicurves);
final double pvbp = METHOD_SWAP.getAnnuityCash(swaption.getUnderlyingSwap(), forward);
// Implementation comment: cash-settled swaptions make sense only for constant strike, the computation of coupon equivalent is not required.
final double maturity = annuityFixed.getNthPayment(annuityFixed.getNumberOfPayments() - 1).getPaymentTime() - swaption.getSettlementTime();
final double discountFactorSettle = multicurves.getDiscountFactor(ccy, swaption.getSettlementTime());
double pv;
if (swaption.getStrike() <= _cutOffStrike) { // No extrapolation
final BlackPriceFunction blackFunction = new BlackPriceFunction();
final double volatility = sabrData.getSABRParameter().getVolatility(swaption.getTimeToExpiry(), maturity, swaption.getStrike(), forward);
final BlackFunctionData dataBlack = new BlackFunctionData(forward, discountFactorSettle * pvbp, volatility);
final Function1D<BlackFunctionData, Double> func = blackFunction.getPriceFunction(swaption);
pv = func.evaluate(dataBlack) * (swaption.isLong() ? 1.0 : -1.0);
} else { // With extrapolation
final DoublesPair expiryMaturity = DoublesPair.of(swaption.getTimeToExpiry(), maturity);
final double alpha = sabrData.getSABRParameter().getAlpha(expiryMaturity);
final double beta = sabrData.getSABRParameter().getBeta(expiryMaturity);
final double rho = sabrData.getSABRParameter().getRho(expiryMaturity);
final double nu = sabrData.getSABRParameter().getNu(expiryMaturity);
final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
pv = discountFactorSettle * pvbp * sabrExtrapolation.price(swaption) * (swaption.isLong() ? 1.0 : -1.0);
}
return MultipleCurrencyAmount.of(ccy, pv);
}
/**
* Computes the present value rate sensitivity to rates of a cash-settled European swaption in the SABR model with extrapolation to the right.
* @param swaption The swaption.
* @param sabrData The SABR data. The SABR function need to be the Hagan function.
* @return The present value curve sensitivity.
*/
public MultipleCurrencyMulticurveSensitivity presentValueCurveSensitivity(final SwaptionCashFixedIbor swaption, final SABRSwaptionProviderInterface sabrData) {
ArgumentChecker.notNull(swaption, "Swaption");
ArgumentChecker.notNull(sabrData, "SABR swaption provider");
final MulticurveProviderInterface multicurves = sabrData.getMulticurveProvider();
final Currency ccy = swaption.getCurrency();
final AnnuityCouponFixed annuityFixed = swaption.getUnderlyingSwap().getFixedLeg();
final double forward = swaption.getUnderlyingSwap().accept(PRDC, multicurves);
// Derivative of the forward with respect to the rates.
final MulticurveSensitivity forwardDr = swaption.getUnderlyingSwap().accept(PRCSDC, multicurves);
final double pvbp = METHOD_SWAP.getAnnuityCash(swaption.getUnderlyingSwap(), forward);
// Derivative of the annuity with respect to the forward.
final double pvbpDf = METHOD_SWAP.getAnnuityCashDerivative(swaption.getUnderlyingSwap(), forward);
final double discountFactorSettle = multicurves.getDiscountFactor(ccy, swaption.getSettlementTime());
final double maturity = annuityFixed.getNthPayment(annuityFixed.getNumberOfPayments() - 1).getPaymentTime() - swaption.getSettlementTime();
// Implementation note: option required to pass the strike (in case the swap has non-constant coupon).
final double dfDr = -swaption.getSettlementTime() * discountFactorSettle;
final List<DoublesPair> list = new ArrayList<>();
list.add(DoublesPair.of(swaption.getSettlementTime(), dfDr));
final Map<String, List<DoublesPair>> resultMap = new HashMap<>();
resultMap.put(multicurves.getName(ccy), list);
MulticurveSensitivity result = MulticurveSensitivity.ofYieldDiscounting(resultMap);
final DoublesPair expiryMaturity = DoublesPair.of(swaption.getTimeToExpiry(), maturity);
final double alpha = sabrData.getSABRParameter().getAlpha(expiryMaturity);
final double beta = sabrData.getSABRParameter().getBeta(expiryMaturity);
final double rho = sabrData.getSABRParameter().getRho(expiryMaturity);
final double nu = sabrData.getSABRParameter().getNu(expiryMaturity);
final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
final double price = sabrExtrapolation.price(swaption);
result = result.multipliedBy(pvbp * price);
result = result.plus(forwardDr.multipliedBy(discountFactorSettle * (pvbpDf * price + pvbp * sabrExtrapolation.priceDerivativeForward(swaption))));
if (!swaption.isLong()) {
result = result.multipliedBy(-1);
}
return MultipleCurrencyMulticurveSensitivity.of(ccy, result);
}
/**
* Computes the present value SABR sensitivity of a physical delivery European swaption in the SABR model with extrapolation to the right.
* @param swaption The swaption.
* @param sabrData The SABR data. The SABR function need to be the Hagan function.
* @return The present value SABR sensitivity.
*/
public PresentValueSABRSensitivityDataBundle presentValueSABRSensitivity(final SwaptionCashFixedIbor swaption, final SABRSwaptionProviderInterface sabrData) {
ArgumentChecker.notNull(swaption, "Swaption");
ArgumentChecker.notNull(sabrData, "SABR swaption provider");
final MulticurveProviderInterface multicurves = sabrData.getMulticurveProvider();
final Currency ccy = swaption.getCurrency();
final PresentValueSABRSensitivityDataBundle sensi = new PresentValueSABRSensitivityDataBundle();
final AnnuityCouponFixed annuityFixed = swaption.getUnderlyingSwap().getFixedLeg();
final double forward = swaption.getUnderlyingSwap().accept(PRDC, multicurves);
final double pvbp = METHOD_SWAP.getAnnuityCash(swaption.getUnderlyingSwap(), forward);
final double maturity = annuityFixed.getNthPayment(annuityFixed.getNumberOfPayments() - 1).getPaymentTime() - swaption.getSettlementTime();
final double discountFactorSettle = multicurves.getDiscountFactor(ccy, swaption.getSettlementTime());
final DoublesPair expiryMaturity = DoublesPair.of(swaption.getTimeToExpiry(), maturity);
final double alpha = sabrData.getSABRParameter().getAlpha(expiryMaturity);
final double beta = sabrData.getSABRParameter().getBeta(expiryMaturity);
final double rho = sabrData.getSABRParameter().getRho(expiryMaturity);
final double nu = sabrData.getSABRParameter().getNu(expiryMaturity);
final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
final double[] priceDSabr = new double[4];
sabrExtrapolation.priceAdjointSABR(swaption, priceDSabr);
final double omega = (swaption.isLong() ? 1.0 : -1.0);
sensi.addAlpha(expiryMaturity, omega * discountFactorSettle * pvbp * priceDSabr[0]);
sensi.addBeta(expiryMaturity, omega * discountFactorSettle * pvbp * priceDSabr[1]);
sensi.addRho(expiryMaturity, omega * discountFactorSettle * pvbp * priceDSabr[2]);
sensi.addNu(expiryMaturity, omega * discountFactorSettle * pvbp * priceDSabr[3]);
return sensi;
}
}