Module net.finmath.lib

Package net.finmath.montecarlo.assetderivativevaluation.products

Class BermudanDigitalOption

java.lang.Object

net.finmath.montecarlo.AbstractMonteCarloProduct

net.finmath.montecarlo.assetderivativevaluation.products.AbstractAssetMonteCarloProduct

net.finmath.montecarlo.assetderivativevaluation.products.BermudanDigitalOption

All Implemented Interfaces:

Product, AssetMonteCarloProduct, MonteCarloProduct

public class BermudanDigitalOption
extends AbstractAssetMonteCarloProduct

This class implements the valuation of a Bermudan digital option paying
\( N_{i} \cdot \mathbb{1}(S(T_{i}) - K_{i}) \) at \( T_{i} \),
when exercised in \( T_{i} \), where \( N_{i} \) is the notional, \( \mathbb{1} \) is the indicator function, \( S \) is the underlying, \( K_{i} \) is the strike and \( T_{i} \) the exercise date. The code "demos" the two prominent methods for the valuation of Bermudan (American) products:

• The valuation may be performed using an estimation of the conditional expectation to determine the exercise criteria. Apart from a possible foresight bias induced by the Monte-Carlo errors, this give a lower bound for the Bermudan value.
• The valuation may be performed using the dual method based on a minimization problem, which gives an upper bound.

Version:

1.4

Author:

Christian Fries

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	BermudanDigitalOption.ExerciseMethod

Constructor Summary

Constructors

Constructor	Description
BermudanDigitalOption(double[] exerciseDates, double[] notionals, double[] strikes, BermudanDigitalOption.ExerciseMethod exerciseMethod, Map<String,Object> properties)	Create a Bermudan option paying N(i) * (S(T(i)) - K(i)) at T(i), when exercised in T(i), where N(i) is the notional, S is the underlying, K(i) is the strike and T(i) the exercise date.

Method Summary

Modifier and Type	Method	Description
RandomVariable	getValue(double evaluationTime, AssetModelMonteCarloSimulationModel model)	This method returns the value random variable of the product within the specified model, evaluated at a given evalutationTime.

Methods inherited from class net.finmath.montecarlo.assetderivativevaluation.products.AbstractAssetMonteCarloProduct

getValue

Methods inherited from class net.finmath.montecarlo.AbstractMonteCarloProduct

getCurrency, getValue, getValue, getValues, getValues, getValues, getValuesForModifiedData, getValuesForModifiedData, getValuesForModifiedData, getValuesForModifiedData, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Details

BermudanDigitalOption

public BermudanDigitalOption(double[] exerciseDates,
 double[] notionals,
 double[] strikes,
 BermudanDigitalOption.ExerciseMethod exerciseMethod,
 Map<String,Object> properties)

Create a Bermudan option paying N(i) * (S(T(i)) - K(i)) at T(i), when exercised in T(i), where N(i) is the notional, S is the underlying, K(i) is the strike and T(i) the exercise date.

Parameters:

exerciseDates - The exercise dates (T(i)), given as doubles.

notionals - The notionals (N(i)) for each exercise date.

strikes - The strikes (K(i)) for each exercise date.

exerciseMethod - The exercise method to be used for the estimation of the exercise boundary.

properties - Use this map to specify special product parameters, e.g. "orderOfRegressionPolynomial" (Integer).

Method Details

getValue

public RandomVariable getValue(double evaluationTime,
 AssetModelMonteCarloSimulationModel model)
                        throws CalculationException

This method returns the value random variable of the product within the specified model, evaluated at a given evalutationTime. Cash-flows prior evaluationTime are not considered.

Specified by:

getValue in interface AssetMonteCarloProduct

Specified by:

getValue in class AbstractAssetMonteCarloProduct

Parameters:

evaluationTime - The time on which this products value should be observed.

model - The model used to price the product.

Returns:

The random variable representing the value of the product discounted to evaluation time.

Throws:

CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.