BatesProcess Class Reference

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

#include <ql/processes/batesprocess.hpp>

Inheritance diagram for BatesProcess:

List of all members.

Public Member Functions

 BatesProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > &dividendYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Real lambda, Real nu, Real delta, HestonProcess::Discretization d=HestonProcess::FullTruncation)
Size factors () const
 returns the number of independent factors of the process
Disposable< Arraydrift (Time t, const Array &x) const
 returns the drift part of the equation, i.e., $ \mu(t, \mathrm{x}_t) $
Disposable< Arrayevolve (Time t0, const Array &x0, Time dt, const Array &dw) const
Real lambda () const
Real nu () const
Real delta () const

Detailed Description

Square-root stochastic-volatility Bates process.

This class describes the square root stochastic volatility process incl jumps governed by

\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \\ \omega(J) &=& \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \end{array} \]

Examples:
EquityOption.cpp.

Member Function Documentation

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 HestonProcess.