DigitalOptionDeltaLikelihood.java

package net.finmath.montecarlo.assetderivativevaluation.products;
/*
 * (c) Copyright Christian P. Fries, Germany. Contact: email@christian-fries.de.
 *
 * Created on 12.02.2013
 */


import net.finmath.exception.CalculationException;
import net.finmath.montecarlo.assetderivativevaluation.AssetModelMonteCarloSimulationModel;
import net.finmath.montecarlo.assetderivativevaluation.MonteCarloAssetModel;
import net.finmath.montecarlo.assetderivativevaluation.MonteCarloBlackScholesModel;
import net.finmath.montecarlo.assetderivativevaluation.models.BlackScholesModel;
import net.finmath.stochastic.RandomVariable;
import net.finmath.stochastic.Scalar;

/**
 * Implements calculation of the delta of a digital option.
 *
 * @author Christian Fries
 * @version 1.0
 * @since finmath-lib 3.6.0
 */
public class DigitalOptionDeltaLikelihood extends AbstractAssetMonteCarloProduct {

	private final double	maturity;
	private final double	strike;

	/**
	 * Construct a product representing an European option on an asset S (where S the asset with index 0 from the model - single asset case).
	 *
	 * @param strike The strike K in the option payoff max(S(T)-K,0).
	 * @param maturity The maturity T in the option payoff max(S(T)-K,0)
	 */
	public DigitalOptionDeltaLikelihood(final double maturity, final double strike) {
		super();
		this.maturity = maturity;
		this.strike = strike;
	}

	/**
	 * This method returns the value random variable of the product within the specified model, evaluated at a given evalutationTime.
	 * Note: For a lattice this is often the value conditional to evalutationTime, for a Monte-Carlo simulation this is the (sum of) value discounted to evaluation time.
	 * Cashflows prior evaluationTime are not considered.
	 *
	 * @param evaluationTime The time on which this products value should be observed.
	 * @param model The model used to price the product.
	 * @return The random variable representing the value of the product discounted to evaluation time
	 * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the <code>cause()</code> method.
	 */
	@Override
	public RandomVariable getValue(final double evaluationTime, final AssetModelMonteCarloSimulationModel model) throws CalculationException {

		/*
		 * The following valuation code requires in-depth knowledge of the model to calculate the denstiy analytically.
		 */
		BlackScholesModel blackScholesModel = null;
		if(model instanceof MonteCarloAssetModel) {
			try {
				blackScholesModel = (BlackScholesModel)((MonteCarloAssetModel)model).getModel();
			}
			catch(final Exception e) {}
		}
		else if(model instanceof MonteCarloBlackScholesModel) {
			blackScholesModel = ((MonteCarloBlackScholesModel)model).getModel();
		}
		if(model == null) {
			throw new ClassCastException("This method requires a Black-Scholes type model (MonteCarloBlackScholesModel).");
		}

		// Get underlying and numeraire
		final RandomVariable underlyingAtMaturity	= model.getAssetValue(maturity,0);
		final RandomVariable underlyingAtToday		= model.getAssetValue(0.0,0);

		// Get some model parameters
		final double T		= maturity-evaluationTime;
		final double r		= blackScholesModel.getRiskFreeRate().doubleValue();
		final double sigma	= blackScholesModel.getVolatility().doubleValue();

		final RandomVariable lr = underlyingAtMaturity.log().sub(underlyingAtToday.log()).sub(r * T - 0.5 * sigma*sigma * T).div(sigma * sigma * T).div(underlyingAtToday);

		final RandomVariable payoff = underlyingAtMaturity.sub(strike).choose(new Scalar(1.0), new Scalar(0.0));

		final RandomVariable modifiedPayoff = payoff.mult(lr);

		final RandomVariable numeraireAtMaturity	= model.getNumeraire(maturity);
		final RandomVariable numeraireAtEvalTime	= model.getNumeraire(evaluationTime);
		final RandomVariable monteCarloWeightsAtMaturity	= model.getMonteCarloWeights(maturity);
		final RandomVariable monteCarloWeightsAtEvalTime	= model.getMonteCarloWeights(evaluationTime);

		return modifiedPayoff.div(numeraireAtMaturity).mult(numeraireAtEvalTime).mult(monteCarloWeightsAtMaturity).div(monteCarloWeightsAtEvalTime);
	}
}