com.opengamma.analytics.financial.model.option.pricing.analytic.CappedPowerOptionModel.java Source code

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Here is the source code for com.opengamma.analytics.financial.model.option.pricing.analytic.CappedPowerOptionModel.java

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/**
 * 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.CappedPowerOptionDefinition;
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;

/**
 * Pricing model for capped power options (see {@link com.opengamma.analytics.financial.model.option.definition.CappedPowerOptionDefinition}).
 * <p>
 * The price of this option is given by:
 * $$
 * \begin{align*}
 * c &= S^ie^{[(i-1)(r + \frac{i\sigma^2}{2}) - i(r-b)]T}[N(d_1) - N(d_3)] - e^{-rT}[KN(d_2) - (C + K)N(d_4)]\\
 * p &= e^{-rT}[KN(-d_2) - (C + K)N(-d_4)] - S^ie^{[(i-1)(r + \frac{i\sigma^2}{2}) - i(r-b)]T}[N(-d_1) - N(-d_3)]
 * \end{align*}
 * $$
 * where
 * $$
 * \begin{align*}
 * d_1 &= \frac{\ln\left(\frac{S}{K^{\frac{1}{i}}}\right) + (b + (i - \frac{1}{2})\sigma^2)T}{\sigma\sqrt{T}}\\
 * d_2 &= d_1 - \sigma\sqrt{T}\\\\
 * \end{align*}
 * $$
 * and 
 * $$
 * \begin{align*}
 * d_3 &= \frac{\ln\left(\frac{S}{(K + C)^{\frac{1}{i}}}\right) + (b + (i - \frac{1}{2})\sigma^2)T}{\sigma\sqrt{T}}\\
 * d_4 &= d_3 - i\sigma\sqrt{T}
 * \end{align*}
 * $$
 * for a call and 
 * $$
 * \begin{align*}
 * d_3 &= \frac{\ln\left(\frac{S}{(K - C)^{\frac{1}{i}}}\right) + (b + (i - \frac{1}{2})\sigma^2)T}{\sigma\sqrt{T}}\\
 * d_4 &= d_3 - i\sigma\sqrt{T}
 * \end{align*}
 * $$
 */
public class CappedPowerOptionModel
        extends AnalyticOptionModel<CappedPowerOptionDefinition, StandardOptionDataBundle> {
    private static final ProbabilityDistribution<Double> NORMAL = new NormalDistribution(0, 1);

    /**
     * {@inheritDoc}
     */
    @Override
    public Function1D<StandardOptionDataBundle, Double> getPricingFunction(
            final CappedPowerOptionDefinition definition) {
        Validate.notNull(definition);
        final Function1D<StandardOptionDataBundle, Double> pricingFunction = new Function1D<StandardOptionDataBundle, Double>() {

            @SuppressWarnings("synthetic-access")
            @Override
            public Double evaluate(final StandardOptionDataBundle data) {
                Validate.notNull(data);
                final double s = data.getSpot();
                final double k = definition.getStrike();
                final double t = definition.getTimeToExpiry(data.getDate());
                final double sigma = data.getVolatility(t, k);
                final double r = data.getInterestRate(t);
                final double b = data.getCostOfCarry();
                final double power = definition.getPower();
                final double inv = 1. / power;
                final double cap = definition.getCap();
                final boolean isCall = definition.isCall();
                final double sigmaT = sigma * Math.sqrt(t);
                final double x = t * (b + sigma * sigma * (power - 0.5));
                final double d1 = getD(s / Math.pow(k, 1. / power), x, sigmaT);
                final double d2 = d1 - power * sigmaT;
                final double d3 = getD(isCall ? s / Math.pow(k + cap, inv) : s / Math.pow(k - cap, inv), x, sigmaT);
                final double d4 = d3 - power * sigmaT;
                final int sign = isCall ? 1 : -1;
                final double df1 = Math.exp(-r * t);
                final double df2 = Math
                        .exp(t * ((power - 1) * (r + power * sigma * sigma * 0.5) - power * (r - b)));
                final double term1 = Math.pow(s, power) * df2
                        * (NORMAL.getCDF(sign * d1) - NORMAL.getCDF(sign * d3));
                final double term2 = df1
                        * (k * NORMAL.getCDF(sign * d2) - (k + sign * cap) * NORMAL.getCDF(sign * d4));
                return sign * (term1 - term2);
            }

        };
        return pricingFunction;
    }

    double getD(final double x, final double y, final double z) {
        return (Math.log(x) + y) / z;
    }
}