/**
* Copyright (C) 2014 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.interestrate.future.provider;
import com.opengamma.analytics.financial.interestrate.future.derivative.InterestRateFutureOptionMarginSecurity;
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.BlackFormulaRepository;
import com.opengamma.analytics.financial.provider.description.interestrate.BlackSTIRFuturesProviderInterface;
import com.opengamma.analytics.financial.provider.description.interestrate.ParameterProviderInterface;
import com.opengamma.util.ArgumentChecker;
/**
* Method for the pricing of STIR future options (with futures-like margin).
* The pricing is done with a Black approach on the future rate (1-price).
* The Black parameters are obtain from implied volatility providers at (expiration-delay-strike-rate) points.
* The delay is the time difference between the underlying futures last trading date and the option expiration.
* The price of the underlying STIR futures is computed by "discounting" (no convexity adjustment).
*/
public final class InterestRateFutureOptionMarginSecurityBlackSTIRFuturesMethod
extends FuturesSecurityBlackSTIRFuturesMethod {
/**
* Creates the method unique instance.
*/
private static final InterestRateFutureOptionMarginSecurityBlackSTIRFuturesMethod INSTANCE =
new InterestRateFutureOptionMarginSecurityBlackSTIRFuturesMethod();
/**
* Constructor.
*/
private InterestRateFutureOptionMarginSecurityBlackSTIRFuturesMethod() {
}
/**
* Return the method unique instance.
* @return The instance.
*/
public static InterestRateFutureOptionMarginSecurityBlackSTIRFuturesMethod getInstance() {
return INSTANCE;
}
/** The method used to compute the future price. It is a method without convexity adjustment. */
private static final InterestRateFutureSecurityDiscountingMethod METHOD_FUTURE =
InterestRateFutureSecurityDiscountingMethod.getInstance();
/** The Black function used in the pricing. */
private static final BlackPriceFunction BLACK_FUNCTION = new BlackPriceFunction();
/**
* Computes the option security price from future price.
* @param security The future option security.
* @param blackData The Black volatility and multi-curves provider.
* @param priceFuture The price of the underlying future.
* @return The security price.
*/
public double price(final InterestRateFutureOptionMarginSecurity security,
final BlackSTIRFuturesProviderInterface blackData, final double priceFuture) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(blackData, "Black data");
final double rateStrike = 1.0 - security.getStrike();
EuropeanVanillaOption option = new EuropeanVanillaOption(rateStrike, security.getExpirationTime(), !security.isCall());
final double rateFutures = 1 - priceFuture;
final double delay = security.getUnderlyingFuture().getTradingLastTime() - security.getExpirationTime();
double volatility = blackData.getVolatility(security.getExpirationTime(), delay, security.getStrike(), priceFuture);
final BlackFunctionData dataBlack = new BlackFunctionData(rateFutures, 1.0, volatility);
final double priceSecurity = BLACK_FUNCTION.getPriceFunction(option).evaluate(dataBlack);
return priceSecurity;
}
/**
* Interpolates and returns the option's implied volatility
* The future price is computed without convexity adjustment.
* @param security The future option security.
* @param blackData The curve and Black volatility data.
* @return Lognormal Implied Volatility.
*/
public double impliedVolatility(final InterestRateFutureOptionMarginSecurity security,
final BlackSTIRFuturesProviderInterface blackData) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(blackData, "Black data");
final double priceFutures = METHOD_FUTURE.price(security.getUnderlyingFuture(), blackData);
final double delay = security.getUnderlyingFuture().getTradingLastTime() - security.getExpirationTime();
return blackData.getVolatility(security.getExpirationTime(), delay, security.getStrike(), priceFutures);
}
/**
* Computes the underlying future security price. The future price is computed without convexity adjustment.
* @param security The future option security.
* @param blackData The curve and Black volatility data.
* @return The security price.
*/
public double underlyingFuturesPrice(final InterestRateFutureOptionMarginSecurity security,
final ParameterProviderInterface blackData) {
return METHOD_FUTURE.price(security.getUnderlyingFuture(), blackData.getMulticurveProvider());
}
/**
* Computes the option security theoretical delta wrt the underlying futures price. The futures price is
* computed without convexity adjustment.
* It is supposed that for a given strike the volatility does not change with the curves.
* @param security The future option security.
* @param blackData The curve and Black volatility data.
* @return The delta.
*/
public double deltaUnderlyingPrice(final InterestRateFutureOptionMarginSecurity security,
final BlackSTIRFuturesProviderInterface blackData) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(blackData, "Black data");
// Forward sweep
final double priceFutures = METHOD_FUTURE.price(security.getUnderlyingFuture(), blackData);
final double rateStrike = 1.0 - security.getStrike();
final EuropeanVanillaOption option = new EuropeanVanillaOption(rateStrike, security.getExpirationTime(),
!security.isCall());
final double rateFutures = 1 - priceFutures;
final double delay = security.getUnderlyingFuture().getTradingLastTime() - security.getExpirationTime();
final double volatility = blackData.getVolatility(security.getExpirationTime(), delay, security.getStrike(),
priceFutures);
final BlackFunctionData dataBlack = new BlackFunctionData(rateFutures, 1.0, volatility);
final double[] priceAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
// Implementation note: the black delta is wrt the rateFutures; the function returns the delta with respect to the priceFutures
return -priceAdjoint[1];
}
/**
* Computes the option's value gamma, the second derivative of the security price wrt underlying futures rate.
* The future price is computed without convexity adjustment.
* @param security The future option security.
* @param blackData The curve and Black volatility data.
* @return The security price.
*/
public double gammaUnderlyingPrice(final InterestRateFutureOptionMarginSecurity security,
final BlackSTIRFuturesProviderInterface blackData) {
ArgumentChecker.notNull(security, "Option security");
ArgumentChecker.notNull(blackData, "Black data");
// Forward sweep
final double priceFutures = METHOD_FUTURE.price(security.getUnderlyingFuture(), blackData.getMulticurveProvider());
final double strike = security.getStrike();
final double rateStrike = 1.0 - strike;
final EuropeanVanillaOption option = new EuropeanVanillaOption(rateStrike, security.getExpirationTime(),
!security.isCall());
final double rateFutures = 1 - priceFutures;
final double delay = security.getUnderlyingFuture().getTradingLastTime() - security.getExpirationTime();
final double volatility = blackData.getVolatility(security.getExpirationTime(), delay, security.getStrike(),
priceFutures);
final BlackFunctionData dataBlack = new BlackFunctionData(rateFutures, 1.0, volatility);
final double[] firstDerivs = new double[3];
final double[][] secondDerivs = new double[3][3];
BLACK_FUNCTION.getPriceAdjoint2(option, dataBlack, firstDerivs, secondDerivs);
return secondDerivs[0][0];
}
/**
* Computes the option security vega. The future price is computed without convexity adjustment.
* @param security The future option security.
* @param blackData The curve and Black volatility data.
* @return Black lognormal vega.
*/
public double vegaUnderlyingPrice(final InterestRateFutureOptionMarginSecurity security,
final BlackSTIRFuturesProviderInterface blackData) {
// Forward sweep
final double priceFutures = METHOD_FUTURE.price(security.getUnderlyingFuture(), blackData);
final double strike = security.getStrike();
final double rateStrike = 1.0 - strike;
final EuropeanVanillaOption option = new EuropeanVanillaOption(rateStrike, security.getExpirationTime(),
!security.isCall());
final double rateFutures = 1 - priceFutures;
final double delay = security.getUnderlyingFuture().getTradingLastTime() - security.getExpirationTime();
final double volatility = blackData.getVolatility(security.getExpirationTime(), delay, security.getStrike(),
priceFutures);
final BlackFunctionData dataBlack = new BlackFunctionData(rateFutures, 1.0, volatility);
final double[] priceAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
return priceAdjoint[2];
}
/**
* Computes the options theta.
* @param security the future option.
* @param black the curve and black volatility data.
* @return the theta.
*/
public double thetaUnderlyingPrice(final InterestRateFutureOptionMarginSecurity security,
final BlackSTIRFuturesProviderInterface black) {
ArgumentChecker.notNull(security, "security");
ArgumentChecker.notNull(black, "black");
final double priceFutures = METHOD_FUTURE.price(security.getUnderlyingFuture(), black);
final double strike = security.getStrike();
final double rateStrike = 1.0 - strike;
final double rateFutures = 1 - priceFutures;
final double delay = security.getUnderlyingFuture().getTradingLastTime() - security.getExpirationTime();
final double volatility = black.getVolatility(security.getExpirationTime(), delay, security.getStrike(),
priceFutures);
final double rate = -Math.log(black.getMulticurveProvider().getDiscountFactor(security.getCurrency(),
security.getExpirationTime())) / security.getExpirationTime();
return BlackFormulaRepository.theta(rateFutures, rateStrike, security.getExpirationTime(), volatility,
!security.isCall(), rate);
}
}