/**
* Copyright (C) 2011 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.interestrate.payments.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.payments.derivative.CapFloorIbor;
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.option.pricing.analytic.formula.SABRExtrapolationRightFunction;
import com.opengamma.analytics.financial.model.volatility.smile.function.SABRFormulaData;
import com.opengamma.analytics.financial.provider.description.interestrate.MulticurveProviderInterface;
import com.opengamma.analytics.financial.provider.description.interestrate.SABRCapProviderInterface;
import com.opengamma.analytics.financial.provider.method.CapFloorIborSABRCapMethodInterface;
import com.opengamma.analytics.financial.provider.sensitivity.multicurve.ForwardSensitivity;
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.MultipleCurrencyAmount;
import com.opengamma.util.tuple.DoublesPair;
/**
* Class used to compute the price and sensitivity of a Ibor cap/floor with SABR model and extrapolation for high strikes.
* No convexity adjustment is done for payment at non-standard dates.
*/
public class CapFloorIborSABRCapExtrapolationRightMethod implements CapFloorIborSABRCapMethodInterface {
/**
* The cut-off strike. The smile is extrapolated above that level.
*/
private final double _cutOffStrike;
/**
* The tail thickness parameter.
*/
private final double _mu;
/**
* The Black function used in the pricing.
*/
private static final BlackPriceFunction BLACK_FUNCTION = new BlackPriceFunction();
/**
* Constructor from cut-off strike and tail parameter.
* @param cutOffStrike The cut-off strike.
* @param mu The tail thickness parameter.
*/
public CapFloorIborSABRCapExtrapolationRightMethod(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 cap The cap/floor.
* @param sabr The SABR cap and multi-curves provider. The SABR function need to be the Hagan function.
* @return The present value.
*/
@Override
public MultipleCurrencyAmount presentValue(final CapFloorIbor cap, final SABRCapProviderInterface sabr) {
ArgumentChecker.notNull(cap, "The cap/floor shoud not be null");
ArgumentChecker.notNull(sabr, "SABR cap provider");
final EuropeanVanillaOption option = new EuropeanVanillaOption(cap.getStrike(), cap.getFixingTime(), cap.isCap());
final double forward = sabr.getMulticurveProvider().getForwardRate(cap.getIndex(), cap.getFixingPeriodStartTime(), cap.getFixingPeriodEndTime(), cap.getFixingAccrualFactor());
final double df = sabr.getMulticurveProvider().getDiscountFactor(cap.getCurrency(), cap.getPaymentTime());
final double maturity = cap.getFixingPeriodEndTime() - cap.getFixingPeriodStartTime();
double price;
if (cap.getStrike() <= _cutOffStrike) { // No extrapolation
final double volatility = sabr.getSABRParameter().getVolatility(cap.getFixingTime(), maturity, cap.getStrike(), forward);
final BlackFunctionData dataBlack = new BlackFunctionData(forward, df, volatility);
final Function1D<BlackFunctionData, Double> func = BLACK_FUNCTION.getPriceFunction(option);
price = func.evaluate(dataBlack) * cap.getNotional() * cap.getPaymentYearFraction();
} else { // With extrapolation
SABRExtrapolationRightFunction sabrExtrapolation;
final DoublesPair expiryMaturity = new DoublesPair(cap.getFixingTime(), maturity);
final double alpha = sabr.getSABRParameter().getAlpha(expiryMaturity);
final double beta = sabr.getSABRParameter().getBeta(expiryMaturity);
final double rho = sabr.getSABRParameter().getRho(expiryMaturity);
final double nu = sabr.getSABRParameter().getNu(expiryMaturity);
final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, cap.getFixingTime(), _mu);
price = df * sabrExtrapolation.price(option) * cap.getNotional() * cap.getPaymentYearFraction();
}
return MultipleCurrencyAmount.of(cap.getCurrency(), price);
}
/**
* Computes the present value sensitivity to the yield curves of a Ibor cap/floor in the SABR framework with extrapolation on the right.
* @param cap The cap/floor.
* @param sabr The SABR cap and multi-curves provider. The SABR function need to be the Hagan function.
* @return The present value sensitivity to curves.
*/
public MultipleCurrencyMulticurveSensitivity presentValueCurveSensitivity(final CapFloorIbor cap, final SABRCapProviderInterface sabr) {
ArgumentChecker.notNull(cap, "The cap/floor shoud not be null");
ArgumentChecker.notNull(sabr, "SABR cap provider");
final MulticurveProviderInterface multicurve = sabr.getMulticurveProvider();
final EuropeanVanillaOption option = new EuropeanVanillaOption(cap.getStrike(), cap.getFixingTime(), cap.isCap());
final double forward = multicurve.getForwardRate(cap.getIndex(), cap.getFixingPeriodStartTime(), cap.getFixingPeriodEndTime(), cap.getFixingAccrualFactor());
final double df = multicurve.getDiscountFactor(cap.getCurrency(), cap.getPaymentTime());
final MulticurveSensitivity forwardDr = MulticurveSensitivity.ofForward(sabr.getMulticurveProvider().getName(cap.getIndex()),
new ForwardSensitivity(cap.getFixingPeriodStartTime(), cap.getFixingPeriodEndTime(), cap.getFixingAccrualFactor(), 1.0));
final double dfDr = -cap.getPaymentTime() * df;
final double maturity = cap.getFixingPeriodEndTime() - cap.getFixingPeriodStartTime();
final List<DoublesPair> list = new ArrayList<>();
list.add(new DoublesPair(cap.getPaymentTime(), dfDr));
final Map<String, List<DoublesPair>> resultMap = new HashMap<>();
resultMap.put(multicurve.getName(cap.getCurrency()), list);
MulticurveSensitivity result = MulticurveSensitivity.ofYieldDiscounting(resultMap);
double bsPrice;
double bsDforward;
if (cap.getStrike() <= _cutOffStrike) { // No extrapolation
final double[] volatilityAdjoint = sabr.getSABRParameter().getVolatilityAdjoint(cap.getFixingTime(), maturity, cap.getStrike(), forward);
final BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatilityAdjoint[0]);
final double[] bsAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
bsPrice = bsAdjoint[0];
bsDforward = df * (bsAdjoint[1] + bsAdjoint[2] * volatilityAdjoint[1]);
} else { // With extrapolation
final DoublesPair expiryMaturity = new DoublesPair(cap.getFixingTime(), maturity);
final double alpha = sabr.getSABRParameter().getAlpha(expiryMaturity);
final double beta = sabr.getSABRParameter().getBeta(expiryMaturity);
final double rho = sabr.getSABRParameter().getRho(expiryMaturity);
final double nu = sabr.getSABRParameter().getNu(expiryMaturity);
final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, cap.getFixingTime(), _mu);
bsPrice = sabrExtrapolation.price(option);
bsDforward = sabrExtrapolation.priceDerivativeForward(option);
}
result = result.multipliedBy(bsPrice);
result = result.plus(forwardDr.multipliedBy(bsDforward));
result = result.multipliedBy(cap.getNotional() * cap.getPaymentYearFraction());
return MultipleCurrencyMulticurveSensitivity.of(cap.getCurrency(), result);
}
/**
* Computes the present value SABR sensitivity of a cap/floor in the SABR framework with extrapolation on the right.
* @param cap The cap/floor.
* @param sabr The SABR cap and multi-curves provider. The SABR function need to be the Hagan function.
* @return The present value SABR sensitivity.
*/
public PresentValueSABRSensitivityDataBundle presentValueSABRSensitivity(final CapFloorIbor cap, final SABRCapProviderInterface sabr) {
ArgumentChecker.notNull(cap, "The cap/floor shoud not be null");
ArgumentChecker.notNull(sabr, "SABR cap provider");
final EuropeanVanillaOption option = new EuropeanVanillaOption(cap.getStrike(), cap.getFixingTime(), cap.isCap());
final double forward = sabr.getMulticurveProvider().getForwardRate(cap.getIndex(), cap.getFixingPeriodStartTime(), cap.getFixingPeriodEndTime(), cap.getFixingAccrualFactor());
final double df = sabr.getMulticurveProvider().getDiscountFactor(cap.getCurrency(), cap.getPaymentTime());
final double maturity = cap.getFixingPeriodEndTime() - cap.getFixingPeriodStartTime();
final double[] bsDsabr = new double[4];
if (cap.getStrike() <= _cutOffStrike) { // No extrapolation
final double[] volatilityAdjoint = sabr.getSABRParameter().getVolatilityAdjoint(cap.getFixingTime(), maturity, cap.getStrike(), forward);
final BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatilityAdjoint[0]);
final double[] bsAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
bsDsabr[0] = bsAdjoint[2] * volatilityAdjoint[3];
bsDsabr[1] = bsAdjoint[2] * volatilityAdjoint[4];
bsDsabr[2] = bsAdjoint[2] * volatilityAdjoint[5];
bsDsabr[3] = bsAdjoint[2] * volatilityAdjoint[6];
} else { // With extrapolation
final DoublesPair expiryMaturity = new DoublesPair(cap.getFixingTime(), maturity);
final double alpha = sabr.getSABRParameter().getAlpha(expiryMaturity);
final double beta = sabr.getSABRParameter().getBeta(expiryMaturity);
final double rho = sabr.getSABRParameter().getRho(expiryMaturity);
final double nu = sabr.getSABRParameter().getNu(expiryMaturity);
final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, cap.getFixingTime(), _mu);
sabrExtrapolation.priceAdjointSABR(option, bsDsabr);
}
final PresentValueSABRSensitivityDataBundle sensi = new PresentValueSABRSensitivityDataBundle();
final DoublesPair expiryMaturity = new DoublesPair(cap.getFixingTime(), maturity);
sensi.addAlpha(expiryMaturity, cap.getNotional() * cap.getPaymentYearFraction() * df * bsDsabr[0]);
sensi.addBeta(expiryMaturity, cap.getNotional() * cap.getPaymentYearFraction() * df * bsDsabr[1]);
sensi.addRho(expiryMaturity, cap.getNotional() * cap.getPaymentYearFraction() * df * bsDsabr[2]);
sensi.addNu(expiryMaturity, cap.getNotional() * cap.getPaymentYearFraction() * df * bsDsabr[3]);
return sensi;
}
}