net.finmath.fouriermethod.models

Class HestonModel

java.lang.Object

net.finmath.fouriermethod.models.HestonModel

All Implemented Interfaces:

ProcessCharacteristicFunctionInterface

public class HestonModel
extends Object
implements ProcessCharacteristicFunctionInterface

Implements the characteristic function of a Heston model. The model is \[ dS(t) = r^{\text{c}} S(t) dt + \sqrt{V(t)} S(t) dW_{1}(t), \quad S(0) = S_{0}, \] \[ dV(t) = \kappa ( \theta - V(t) ) dt + \xi \sqrt{V(t)} dW_{2}(t), \quad V(0) = \sigma^2, \] \[ dW_{1} dW_{2} = \rho dt \] \[ dN(t) = r^{\text{d}} N(t) dt, \quad N(0) = N_{0}, \] where \( W \) is a Brownian motion. The free parameters of this model are:

\( S_{0} \)

spot - initial value of S

\( r \)

the risk free rate

\( \sigma \)

the initial volatility level

\( \xi \)

the volatility of volatility

\( \theta \)

the mean reversion level of the stochastic volatility

\( \kappa \)

the mean reversion speed of the stochastic volatility

\( \rho \)

the correlation of the Brownian drivers

Author:

Christian Fries, Andy Graf, Lorenzo Toricelli

Constructor Summary

Constructors

Constructor and Description
HestonModel(double initialValue, double riskFreeRate, double volatility, double theta, double kappa, double xi, double rho)

Method Summary

Modifier and Type	Method and Description
CharacteristicFunctionInterface	apply(double time) Returns the characteristic function of X(t), where X is this stochastic process.

Methods inherited from class java.lang.Object

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

Constructor Detail

HestonModel

public HestonModel(double initialValue,
                   double riskFreeRate,
                   double volatility,
                   double theta,
                   double kappa,
                   double xi,
                   double rho)

Method Detail

apply

public CharacteristicFunctionInterface apply(double time)

Description copied from interface: ProcessCharacteristicFunctionInterface

Returns the characteristic function of X(t), where X is this stochastic process.

Specified by:

apply in interface ProcessCharacteristicFunctionInterface

Parameters:

time - The time at which the stochastic process is observed.

Returns:

The characteristic function of X(t).