/**
* 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.twoasset;
import org.apache.commons.lang.Validate;
import com.opengamma.analytics.financial.model.option.definition.twoasset.EuropeanExchangeAssetOptionDefinition;
import com.opengamma.analytics.financial.model.option.definition.twoasset.StandardTwoAssetOptionDataBundle;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.statistics.distribution.NormalDistribution;
import com.opengamma.analytics.math.statistics.distribution.ProbabilityDistribution;
/**
* The value of a European-style exchange-asset option is given by:
* $$
* \begin{eqnarray*}
* Q_1 S_1 e^{(b_1 - r)T} N(d_1) - Q_2 S_2 e^{(b_2 - r)T} N(d_2)
* \end{eqnarray*}
* $$
* where
* $$
* \begin{eqnarray*}
* \hat{\sigma} &=& \sqrt{\sigma_1 ^2 + \sigma_2 ^2 - 2 \rho\sigma_1\sigma_2}\\
* d_1 &=& \frac{\ln{\frac{Q_1 S_1}{Q_2 S_2}} + \left(b_1 - b_2 + \frac{\hat{\sigma}^2}{2}\right) T }{\hat{\sigma} \sqrt{T}}\\
* d_2 &=& d_1 - \hat{\sigma}\sqrt{T}
* \end{eqnarray*}
* $$
* and
* <ul>
* <li>$Q_1$ is the quantity of the first asset</li>
* <li>$Q_2$ is the quantity of the second asset</li>
* <li>$S_1$ is the spot value of the first asset</li>
* <li>$S_2$ is the spot value of the second asset</li>
* <li>$b_1$ is the cost-of-carry of the first asset</li>
* <li>$b_2$ is the cost-of-carry of the second asset</li>
* <li>$T$ is the time to expiry of the option</li>
* <li>$r$ is the spot interest rate for time $T$</li>
* <li>$\sigma_1$ is the annualized volatility of the first asset</li>
* <li>$\sigma_2$ is the annualized volatility of the second asset</li>
* <li>$N(x)$ is the CDF of the normal distribution $N(0, 1)$ </li>
* </ul>
*/
public class EuropeanExchangeAssetOptionModel extends TwoAssetAnalyticOptionModel<EuropeanExchangeAssetOptionDefinition, StandardTwoAssetOptionDataBundle> {
private static final ProbabilityDistribution<Double> NORMAL = new NormalDistribution(0, 1);
/**
* Gets the pricing function for a European-style exchange asset option
* @param definition The option definition
* @return The pricing function
* @throws IllegalArgumentException If the definition is null
*/
@Override
public Function1D<StandardTwoAssetOptionDataBundle, Double> getPricingFunction(final EuropeanExchangeAssetOptionDefinition definition) {
Validate.notNull(definition, "definition");
return new Function1D<StandardTwoAssetOptionDataBundle, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final StandardTwoAssetOptionDataBundle data) {
Validate.notNull(data, "data");
final double s1 = data.getFirstSpot();
final double s2 = data.getSecondSpot();
final double b1 = data.getFirstCostOfCarry();
final double b2 = data.getSecondCostOfCarry();
final double t = definition.getTimeToExpiry(data.getDate());
final double r = data.getInterestRate(t);
final double sigma1 = data.getFirstVolatility(t, s1);
final double sigma2 = data.getSecondVolatility(t, s2);
final double rho = data.getCorrelation();
final double q1 = definition.getFirstQuantity();
final double q2 = definition.getSecondQuantity();
final double sigma = Math.sqrt(sigma1 * sigma1 + sigma2 * sigma2 - 2 * rho * sigma1 * sigma2);
final double sigmaT = sigma * Math.sqrt(t);
final double d1 = (Math.log(q1 * s1 / q2 / s2) + t * (b1 - b2 + sigma * sigma / 2)) / sigmaT;
final double d2 = d1 - sigmaT;
return q1 * s1 * Math.exp(t * (b1 - r)) * NORMAL.getCDF(d1) - q2 * s2 * Math.exp(t * (b2 - r)) * NORMAL.getCDF(d2);
}
};
}
}