Java tutorial
/** * 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); } }; } }