HestonProcess Class Reference
[Stochastic processes]

Square-root stochastic-volatility Heston process. More...

#include <ql/processes/hestonprocess.hpp>

Inheritance diagram for HestonProcess:

List of all members.

Public Types

enum  Discretization {
  PartialTruncation, FullTruncation, Reflection, NonCentralChiSquareVariance,
  QuadraticExponential, QuadraticExponentialMartingale
}

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
Disposable< ArrayinitialValues () const
 returns the initial values of the state variables
Disposable< Arraydrift (Time t, const Array &x) const
 returns the drift part of the equation, i.e., $ \mu(t, \mathrm{x}_t) $
Disposable< Matrixdiffusion (Time t, const Array &x) const
 returns the diffusion part of the equation, i.e. $ \sigma(t, \mathrm{x}_t) $
Disposable< Arrayapply (const Array &x0, const Array &dx) const
Disposable< Arrayevolve (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


Detailed Description

Square-root stochastic-volatility Heston process.

This class describes the square root stochastic volatility process governed by

\[ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]


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.

Reimplemented in BatesProcess.

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.