QuantLib_HestonProcess man page

HestonProcess — Square-root stochastic-volatility Heston process.

Synopsis

#include <ql/processes/hestonprocess.hpp>

Inherits StochasticProcess.

Inherited by BatesProcess.

Public Types

enum Discretization { PartialTruncation, FullTruncation, Reflection, NonCentralChiSquareVariance, QuadraticExponential, QuadraticExponentialMartingale, BroadieKayaExactSchemeLobatto, BroadieKayaExactSchemeLaguerre, BroadieKayaExactSchemeTrapezoidal }

Public Member Functions

HestonProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > &dividendYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Discretization d=QuadraticExponentialMartingale)

Size size () const
returns the number of dimensions of the stochastic process
Size factors () const
returns the number of independent factors of the process
Disposable< Array > initialValues () const
returns the initial values of the state variables
Disposable< Array > drift (Time t, const Array &x) const
returns the drift part of the equation, i.e., $ mu(t, mathrm{x}_t) $
Disposable< Matrix > diffusion (Time t, const Array &x) const
returns the diffusion part of the equation, i.e. $ sigma(t, mathrm{x}_t) $
Disposable< Array > apply (const Array &x0, const Array &dx) const

Disposable< Array > evolve (Time t0, const Array &x0, Time dt, const Array &dw) const

Real v0 () const

Real rho () const

Real kappa () const

Real theta () const

Real sigma () const

const Handle< Quote > & s0 () const

const Handle< YieldTermStructure > & dividendYield () const

const Handle< YieldTermStructure > & riskFreeRate () const

Time time (const Date &) const

Real pdf (Real x, Real v, Time t, Real eps=1e-3) const

Additional Inherited Members

Detailed Description

Square-root stochastic-volatility Heston process.

This class describes the square root stochastic volatility process governed by [ begin{array}{rcl} dS(t, S) &=& mu S dt + sqrt{v} S dW_1 \ dv(t, S) &=& ppa ( heta - v) dt + sigma sqrt{v} dW_2 \ dW_1 dW_2 &=& rho dt \nd{array} ]

Examples: EquityOption.cpp.

Member Function Documentation

Disposable<Array> apply (const Array & x0, const Array & dx) const [virtual]

applies a change to the asset value. By default, it returns $ mathrm{x} + Delta mathrm{x} $.

Reimplemented from StochasticProcess.

Disposable<Array> evolve (Time t0, const Array & x0, Time dt, const Array & dw) const [virtual]

returns the asset value after a time interval $ Delta t $ according to the given discretization. By default, it returns [ E(mathrm{x}_0,t_0,Delta t) + S(mathrm{x}_0,t_0,Delta t) cdot Delta mathrm{w} ] where $ E $ is the expectation and $ S $ the standard deviation.

Reimplemented from StochasticProcess.

Time time (const Date &) const [virtual]

returns the time value corresponding to the given date in the reference system of the stochastic process.

Note:

As a number of processes might not need this functionality, a default implementation is given which raises an exception.

Reimplemented from StochasticProcess.

Author

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Referenced By

HestonProcess(3) and pdf(3) are aliases of QuantLib_HestonProcess(3).

Fri Sep 23 2016 Version 1.8.1 QuantLib