net.finmath.fouriermethod.models

Class HestonModel

java.lang.Object

net.finmath.fouriermethod.models.HestonModel

All Implemented Interfaces:

ProcessCharacteristicFunctionInterface, Model<HestonModelDescriptor>

public class HestonModel
extends Object
implements Model<HestonModelDescriptor>, ProcessCharacteristicFunctionInterface

Implements the characteristic function of a Heston model. The model is \[ dS(t) = r^{\text{c}}(t) S(t) dt + \sqrt{V(t)} S(t) dW_{1}(t), \quad S(0) = S_{0}, \] \[ dV(t) = \kappa ( \theta - V(t) ) dt + \xi \sqrt{V(t)} dW_{2}(t), \quad V(0) = \sigma^2, \] \[ dW_{1} dW_{2} = \rho dt \] \[ dN(t) = r^{\text{d}}(t) N(t) dt, \quad N(0) = N_{0}, \] where \( W \) is a Brownian motion. The model allows to specify two independent rate for forwarding (\( r^{\text{c}} \)) and discounting (\( r^{\text{d}} \)). It thus allow for a simple modelling of a funding / collateral curve (via (\( r^{\text{d}} \)) and/or the specification of a dividend yield. The free parameters of this model are:

\( S_{0} \)

spot - initial value of S

\( r^{\text{c}} \)

the risk free rate (may be provided as a curve or a constant)

\( \sigma \)

the initial volatility level

\( r^{\text{d}} \)

the discount rate (may be provided as a curve or a constant)

\( \xi \)

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, DiscountCurveInterface discountCurveForForwardRate, double volatility, DiscountCurveInterface discountCurveForDiscountRate, double theta, double kappa, double xi, double rho) Create a Heston model (characteristic function)
HestonModel(double initialValue, double riskFreeRate, double volatility, double theta, double kappa, double xi, double rho)
HestonModel(double initialValue, double riskFreeRate, double volatility, double discountRate, double theta, double kappa, double xi, double rho) Create a Heston model (characteristic function)
HestonModel(HestonModelDescriptor descriptor) Create a model from a model desciptor.
HestonModel(LocalDate referenceDate, double initialValue, DiscountCurveInterface discountCurveForForwardRate, double volatility, DiscountCurveInterface discountCurveForDiscountRate, double theta, double kappa, double xi, double rho) Create a Heston model (characteristic function)

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.
HestonModelDescriptor	getDescriptor() Return a model descriptor representing this model.
Product<? extends ProductDescriptor>	getProductFromDesciptor(ProductDescriptor productDescriptor) Construct a product from a product descriptor, which may be valued by this mmodel.

Methods inherited from class java.lang.Object

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

Constructor Detail

HestonModel

public HestonModel(HestonModelDescriptor descriptor)

Create a model from a model desciptor.

Parameters:

descriptor - A Heston model descriptor.

HestonModel

public HestonModel(LocalDate referenceDate,
                   double initialValue,
                   DiscountCurveInterface discountCurveForForwardRate,
                   double volatility,
                   DiscountCurveInterface discountCurveForDiscountRate,
                   double theta,
                   double kappa,
                   double xi,
                   double rho)

Create a Heston model (characteristic function)

Parameters:

referenceDate - The date representing the time t = 0. All other double times are following FloatingpointDate.

initialValue - \( S_{0} \) - spot - initial value of S

discountCurveForForwardRate - The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate

volatility - \( \sigma \) the initial volatility level

discountCurveForDiscountRate - The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate

theta - \( \theta \) - the mean reversion level of the stochastic volatility

kappa - \( \kappa \) - the mean reversion speed of the stochastic volatility

xi - \( \xi \) - the volatility of volatility

rho - \( \rho \) - the correlation of the Brownian drivers

HestonModel

public HestonModel(double initialValue,
                   DiscountCurveInterface discountCurveForForwardRate,
                   double volatility,
                   DiscountCurveInterface discountCurveForDiscountRate,
                   double theta,
                   double kappa,
                   double xi,
                   double rho)

Create a Heston model (characteristic function)

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

discountCurveForForwardRate - The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate

volatility - \( \sigma \) the initial volatility level

discountCurveForDiscountRate - The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate

theta - \( \theta \) - the mean reversion level of the stochastic volatility

kappa - \( \kappa \) - the mean reversion speed of the stochastic volatility

xi - \( \xi \) - the volatility of volatility

rho - \( \rho \) - the correlation of the Brownian drivers

HestonModel

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

Create a Heston model (characteristic function)

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

riskFreeRate - \( r^{\text{c}} \) - the risk free rate

volatility - \( \sigma \) the initial volatility level

discountRate - \( r^{\text{d}} \) - the discount rate

theta - \( \theta \) - the mean reversion level of the stochastic volatility

kappa - \( \kappa \) - the mean reversion speed of the stochastic volatility

xi - \( \xi \) - the volatility of volatility

rho - \( \rho \) - the correlation of the Brownian drivers

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).

getDescriptor

public HestonModelDescriptor getDescriptor()

Description copied from interface: Model

Return a model descriptor representing this model.

Specified by:

getDescriptor in interface Model<HestonModelDescriptor>

Returns:

The model descriptor of this model.

getProductFromDesciptor

public Product<? extends ProductDescriptor> getProductFromDesciptor(ProductDescriptor productDescriptor)

Description copied from interface: Model

Construct a product from a product descriptor, which may be valued by this mmodel.

Specified by:

getProductFromDesciptor in interface Model<HestonModelDescriptor>

Parameters:

productDescriptor - Given product descriptor.

Returns:

An instance of a product implementation.