- QuantLib
- BatesEngine
 
Bates model engines based on Fourier transform. More...
#include <ql/pricingengines/vanilla/batesengine.hpp>

| Public Member Functions | |
| BatesEngine (const boost::shared_ptr< BatesModel > &model, Size integrationOrder=144) | |
| BatesEngine (const boost::shared_ptr< BatesModel > &model, Real relTolerance, Size maxEvaluations) | |
| Protected Member Functions | |
| std::complex< Real > | addOnTerm (Real phi, Time t, Size j) const | 
Bates model engines based on Fourier transform.
this classes price european options under the following processes
1. Jump-Diffusion with Stochastic Volatility
![\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]](form_322.png) 
N is a Poisson process with the intensity  . When a jump occurs the magnitude J has the probability density function
. When a jump occurs the magnitude J has the probability density function  .
.
1.1 Log-Normal Jump Diffusion: BatesEngine
Logarithm of the jump size J is normally distributed
![\[ \omega(J) = \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \]](form_324.png) 
1.2 Double-Exponential Jump Diffusion: BatesDoubleExpEngine
The jump size has an asymmetric double exponential distribution
![\[ \begin{array}{rcl} \omega(J)&=& p\frac{1}{\eta_u}e^{-\frac{1}{\eta_u}J} 1_{J>0} + q\frac{1}{\eta_d}e^{\frac{1}{\eta_d}J} 1_{J<0} \\ p + q &=& 1 \end{array} \]](form_325.png) 
2. Stochastic Volatility with Jump Diffusion and Deterministic Jump Intensity
![\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ d\lambda(t) &=& \kappa_\lambda(\theta_\lambda-\lambda) dt \\ dW_1 dW_2 &=& \rho dt \end{array} \]](form_326.png) 
2.1 Log-Normal Jump Diffusion with Deterministic Jump Intensity BatesDetJumpEngine
2.2 Double-Exponential Jump Diffusion with Deterministic Jump Intensity BatesDoubleExpDetJumpEngine
References:
D. Bates, Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options, Review of Financial Sudies 9, 69-107.
A. Sepp, Pricing European-Style Options under Jump Diffusion Processes with Stochastic Volatility: Applications of Fourier Transform (<http://math.ut.ee/~spartak/papers/stochjumpvols.pdf>)