/**
* 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 org.threeten.bp.ZonedDateTime;
import com.opengamma.analytics.financial.model.option.definition.FadeInOptionDefinition;
import com.opengamma.analytics.financial.model.option.definition.StandardOptionWithSpotTimeSeriesDataBundle;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.statistics.distribution.BivariateNormalDistribution;
import com.opengamma.analytics.math.statistics.distribution.ProbabilityDistribution;
/**
*
*/
public class FadeInOptionModel extends AnalyticOptionModel<FadeInOptionDefinition, StandardOptionWithSpotTimeSeriesDataBundle> {
private static final ProbabilityDistribution<double[]> BIVARIATE_NORMAL = new BivariateNormalDistribution();
@Override
public Function1D<StandardOptionWithSpotTimeSeriesDataBundle, Double> getPricingFunction(final FadeInOptionDefinition definition) {
Validate.notNull(definition, "definition");
return new Function1D<StandardOptionWithSpotTimeSeriesDataBundle, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final StandardOptionWithSpotTimeSeriesDataBundle data) {
Validate.notNull(data, "data");
final double s = data.getSpot();
final double k = definition.getStrike();
final double b = data.getCostOfCarry();
final ZonedDateTime date = data.getDate();
final double t = definition.getTimeToExpiry(date);
final double r = data.getInterestRate(t);
final double sigma = data.getVolatility(t, k);
final double l = definition.getLowerBound();
final double u = definition.getUpperBound();
final double n = data.getSpotTimeSeries().size();
final double df1 = Math.exp(t * (b - r));
final double df2 = Math.exp(-r * t);
final int sign = definition.isCall() ? 1 : -1;
double rho, tI, d1, d2, d3, d4, d5, d6;
double price = 0;
for (int i = 0; i < n; i++) {
tI = i * t / n;
rho = -sign * Math.sqrt(tI / t);
d1 = getD1(s, k, t, sigma, b);
d2 = getD2(d1, sigma, t);
d3 = getD1(s, l, tI, sigma, b);
d4 = getD2(d3, sigma, tI);
d5 = getD1(s, u, tI, sigma, b);
d6 = getD2(d5, sigma, tI);
price += sign
* (s * df1 * (BIVARIATE_NORMAL.getCDF(new double[] {-d5, sign * d1, rho}) - BIVARIATE_NORMAL.getCDF(new double[] {-d3, sign * d1, rho})) - k * df2
* (BIVARIATE_NORMAL.getCDF(new double[] {-d6, sign * d2, rho}) - BIVARIATE_NORMAL.getCDF(new double[] {-d4, sign * d2, rho})));
}
return price / n;
}
};
}
}