- QuantLib
- BatesProcess
 
Square-root stochastic-volatility Bates process. More...
#include <ql/processes/batesprocess.hpp>

| Public Member Functions | |
| BatesProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > ÷ndYield, 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< Array > | drift (Time t, const Array &x) const | 
| returns the drift part of the equation, i.e.,   | |
| Disposable< Array > | evolve (Time t0, const Array &x0, Time dt, const Array &dw) const | 
| Real | lambda () const | 
| Real | nu () const | 
| Real | delta () const | 
Square-root stochastic-volatility Bates process.
This class describes the square root stochastic volatility process incl jumps governed by
![\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \\ \omega(J) &=& \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \end{array} \]](form_327.png) 
returns the asset value after a time interval  according to the given discretization. By default, it returns
 according to the given discretization. By default, it returns 
![\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]](form_357.png) 
 where  is the expectation and
 is the expectation and  the standard deviation.
 the standard deviation. 
Reimplemented from HestonProcess.