/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.option.pricing.analytic;
import java.util.Set;
import org.apache.commons.lang.NotImplementedException;
import org.apache.commons.lang.Validate;
import org.threeten.bp.ZonedDateTime;
import com.google.common.collect.Sets;
import com.opengamma.analytics.financial.greeks.Greek;
import com.opengamma.analytics.financial.greeks.GreekResultCollection;
import com.opengamma.analytics.financial.model.option.definition.EuropeanOptionOnEuropeanVanillaOptionDefinition;
import com.opengamma.analytics.financial.model.option.definition.EuropeanVanillaOptionDefinition;
import com.opengamma.analytics.financial.model.option.definition.OptionDefinition;
import com.opengamma.analytics.financial.model.option.definition.StandardOptionDataBundle;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.statistics.distribution.NormalDistribution;
import com.opengamma.analytics.math.statistics.distribution.ProbabilityDistribution;
/**
* This model can be used to approximate the value of call-on-call or
* put-on-call options. It is most accurate for at- and in-the-money options.
* <p>
* The value of a call-on-call option can be approximated by:
* $$
* \begin{align*}
* c_{call} \approx c_{BSM}N(d_1) - K_2e^{-rT_2}N(d2)
* \end{align*}
* $$
* where
* $$
* \begin{align*}
* d1 &= \frac{\ln(\frac{c_{BSM}}{K_2}) + (b + \frac{\hat{\sigma^2}}{2})T_2}{\hat{\sigma}\sqrt{T_2}}\\
* \hat{\sigma} &= \frac{\sigma|\Delta_{BSM}|S}{c_{BSM}}\\
* c_{BSM} &= c_{BSM}(S, K_1, T_1, r, b, \sigma)\\
* \Delta_{BSM} &= \Delta_{BSM}(S, K_1, T_1, r, b, \sigma)
* \end{align*}
* $$
* where $K_1$ is the strike on the underlying option, $T_1$ is the expiry of
* the underlying option, $K_2$ is the strike of the option-on-option, $T_2$ is
* the expiry of the option-on-option, and $BSM$ is the standard
* Black-Scholes-Merton pricing model ({@link BlackScholesMertonModel}).
* <p>
* The value of a put-on-call can be approximated by:
* $$
* \begin{align*}
* p_{call} \approx K_2e^{-eT_2}N(d_2) - c_{BSM}N(d_1)
* \end{align*}
* $$
*/
public class BensoussanCrouhyGalaiOptionOnOptionModel extends AnalyticOptionModel<EuropeanOptionOnEuropeanVanillaOptionDefinition, StandardOptionDataBundle> {
private static final ProbabilityDistribution<Double> NORMAL = new NormalDistribution(0, 1);
private static final BlackScholesMertonModel BSM = new BlackScholesMertonModel();
private static final Set<Greek> REQUIRED_GREEKS = Sets.newHashSet(Greek.FAIR_PRICE, Greek.DELTA);
/**
* {@inheritDoc}
*/
@Override
public Function1D<StandardOptionDataBundle, Double> getPricingFunction(final EuropeanOptionOnEuropeanVanillaOptionDefinition definition) {
Validate.notNull(definition, "definition");
return new Function1D<StandardOptionDataBundle, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final StandardOptionDataBundle data) {
Validate.notNull(data, "data");
final double s = data.getSpot();
final OptionDefinition underlying = definition.getUnderlyingOption();
final double k1 = definition.getStrike();
final double k2 = underlying.getStrike();
final ZonedDateTime date = data.getDate();
final double t1 = definition.getTimeToExpiry(date);
final double sigma = data.getVolatility(t1, k1);
final double r = data.getInterestRate(t1);
final double b = data.getCostOfCarry();
final OptionDefinition callDefinition = underlying.isCall() ? underlying : new EuropeanVanillaOptionDefinition(k2, underlying.getExpiry(), true);
final GreekResultCollection result = BSM.getGreeks(callDefinition, data, REQUIRED_GREEKS);
final double callBSM = result.get(Greek.FAIR_PRICE);
final double callDelta = result.get(Greek.DELTA);
final double underlyingSigma = sigma * Math.abs(callDelta) * s / callBSM;
final double d1 = getD1(callBSM, k1, t1, underlyingSigma, b);
final double d2 = getD2(d1, underlyingSigma, t1);
final int sign = definition.isCall() ? 1 : -1;
if (underlying.isCall()) {
return sign * (callBSM * NORMAL.getCDF(sign * d1) - k1 * Math.exp(-r * t1) * NORMAL.getCDF(sign * d2));
}
throw new NotImplementedException("This model can only price call-on-call or put-on-call options");
}
};
}
}