Module net.finmath.lib

Package net.finmath.montecarlo.assetderivativevaluation.products

Class BlackScholesHedgedPortfolio

java.lang.Object

net.finmath.montecarlo.AbstractMonteCarloProduct

net.finmath.montecarlo.assetderivativevaluation.products.AbstractAssetMonteCarloProduct

net.finmath.montecarlo.assetderivativevaluation.products.BlackScholesHedgedPortfolio

All Implemented Interfaces:

Product, AssetMonteCarloProduct, MonteCarloProduct

public class BlackScholesHedgedPortfolio
extends AbstractAssetMonteCarloProduct

This class implements a delta and delta-gamma hedged portfolio of an European option (a hedge simulator). The hedge is done under the assumption of a Black Scholes Model (even if the pricing model is a different one). In case of the gamma hedge and the vega hedge, note that we make the assumption that the market trades these option according to Black-Scholes parameters assumed in hedging. While this is a simple model, it is to some extend reasonable, when we assume that the hedge is done by calculating delta from a calibrated model (where the risk free rate and the volatility are "market implied"). That said, this class evaluates the hedge portfolio given that the market implies a given risk free rate and volatility, while the underlying follows a given (possibly different) stochastic process. The getValue-method returns the random variable \( \Pi(t) \) representing the value of the replication portfolio \( \Pi(t) = \phi_0(t) N(t) + \phi_1(t) S(t) + \psi_0(t) C(t) \).

Version:

1.4

Author:

Christian Fries

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	BlackScholesHedgedPortfolio.HedgeStrategy

Constructor Summary

Constructors

Constructor	Description
BlackScholesHedgedPortfolio(double maturity, double strike, double riskFreeRate, double volatility)	Construction of a hedge portfolio assuming a Black-Scholes model for the hedge ratios.
BlackScholesHedgedPortfolio(double maturity, double strike, double riskFreeRate, double volatility, double hedgeOptionMaturity, double hedgeOptionStrike, BlackScholesHedgedPortfolio.HedgeStrategy hedgeStrategy)	Construction of a delta-gamma hedge portfolio assuming a Black-Scholes model.

Method Summary

Modifier and Type	Method	Description
RandomVariable	getValue(double evaluationTime, AssetModelMonteCarloSimulationModel model)

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 Detail

BlackScholesHedgedPortfolio

public BlackScholesHedgedPortfolio(double maturity,
                                   double strike,
                                   double riskFreeRate,
                                   double volatility,
                                   double hedgeOptionMaturity,
                                   double hedgeOptionStrike,
                                   BlackScholesHedgedPortfolio.HedgeStrategy hedgeStrategy)

Construction of a delta-gamma hedge portfolio assuming a Black-Scholes model.

Parameters:

maturity - Maturity of the option we wish to replicate.

strike - Strike of the option we wish to replicate.

riskFreeRate - Model riskFreeRate assumption for our delta hedge.

volatility - Model volatility assumption for our delta hedge.

hedgeOptionMaturity - Maturity of the option used in the hedge portfolio (to hedge gamma).

hedgeOptionStrike - Strike of the option used in the hedge portfolio (to hedge gamma).

hedgeStrategy - Specification of the hedge strategy to be used (delta, delta-gamma, etc.).

BlackScholesHedgedPortfolio

public BlackScholesHedgedPortfolio(double maturity,
                                   double strike,
                                   double riskFreeRate,
                                   double volatility)

Construction of a hedge portfolio assuming a Black-Scholes model for the hedge ratios.

Parameters:

maturity - Maturity of the option we wish to replicate.

strike - Strike of the option we wish to replicate.

riskFreeRate - Model riskFreeRate assumption for our delta hedge.

volatility - Model volatility assumption for our delta hedge.

Method Detail

getValue

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

Specified by:

getValue in interface AssetMonteCarloProduct

Specified by:

getValue in class AbstractAssetMonteCarloProduct

Throws:

CalculationException