/**
* 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 org.apache.commons.lang.Validate;
import com.opengamma.analytics.financial.model.option.definition.GapOptionDefinition;
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;
/**
* Class for pricing gap options (see {@link com.opengamma.analytics.financial.model.option.definition.GapOptionDefinition}).
* <p>
* The price is calculated using the Reiner-Rubenstein formula:
* $$
* \begin{align*}
* c &= S e^{(b-r)T}N(d_1) - K_2 e^{-rT}N(d_2)\\
* p &= K_2 e^{-rT}N(-d_2) - S e^{(b-r)T}N(-d_1)
* \end{align*}
* $$
* where
* $$
* \begin{align*}
* d_1 = \frac{\ln{\frac{S}{K_1}} + (b + \frac{\sigma^2}{2})T}{\sigma\sqrt{T}}
* \end{align*}
* $$
* and
* $$
* \begin{align*}
* d_2 = d_1 - \sigma\sqrt{T}
* \end{align*}
* $$
*
*/
public class GapOptionModel extends AnalyticOptionModel<GapOptionDefinition, StandardOptionDataBundle> {
private static final ProbabilityDistribution<Double> NORMAL = new NormalDistribution(0, 1);
/**
* {@inheritDoc}
*/
@Override
public Function1D<StandardOptionDataBundle, Double> getPricingFunction(final GapOptionDefinition 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 double k = definition.getStrike();
final double t = definition.getTimeToExpiry(data.getDate());
final double r = data.getInterestRate(t);
final double sigma = data.getVolatility(t, k);
final double b = data.getCostOfCarry();
final double payoffStrike = definition.getPayoffStrike();
final int sign = definition.isCall() ? 1 : -1;
final double d1 = getD1(s, k, t, sigma, b);
final double d2 = getD2(d1, sigma, t);
return sign * (s * Math.exp(t * (b - r)) * NORMAL.getCDF(sign * d1) - payoffStrike * Math.exp(-r * t) * NORMAL.getCDF(sign * d2));
}
};
}
}