AsymmetricPowerOptionModel.java

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

  /**
   * {@inheritDoc}
   */
  @Override
  public Function1D<StandardOptionDataBundle, Double> getPricingFunction(final AsymmetricPowerOptionDefinition 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 sigmaT = sigma * Math.sqrt(t);
        final double d1 = (Math.log(s / Math.pow(k, 1. / power)) + t * (b + sigma * sigma * (power - 0.5))) / sigmaT;
        final double d2 = d1 - power * sigmaT;
        final int sign = definition.isCall() ? 1 : -1;
        final double df1 = Math.exp(((power - 1) * (r + power * sigma * sigma * 0.5) - power * (r - b)) * t);
        final double df2 = Math.exp(-r * t);
        return sign * (Math.pow(s, power) * df1 * NORMAL.getCDF(sign * d1) - df2 * k * NORMAL.getCDF(sign * d2));
      }
    };
    return pricingFunction;
  }

}