# QuantLib_BatesEngine man page

BatesEngine — Bates model engines based on Fourier transform.

## Synopsis

#include <ql/pricingengines/vanilla/batesengine.hpp>

Inherits AnalyticHestonEngine.

Inherited by BatesDetJumpEngine.

### 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

## Detailed Description

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) &=& ppa ( heta - v) dt + sigma sqrt{v} dW_2 \ dW_1 dW_2 &=& rho dt \nd{array} ]

N is a Poisson process with the intensity $lambda$. When a jump occurs the magnitude J has the probability density function $omega(J)$.

1.1 Log-Normal Jump Diffusion: BatesEngine

Logarithm of the jump size J is normally distributed [ omega(J) = ac{1}{sqrt{2pi \delta^2}} \xpleft[-ac{(J-0)^2}{2elta^2}right] ]

1.2 Double-Exponential Jump Diffusion: BatesDoubleExpEngine

The jump size has an asymmetric double exponential distribution [ begin{array}{rcl} omega(J)&=& pac{1}{\ta_u}e^{-ac{1}{\ta_u}J} 1_{J>0} + qac{1}{\ta_d}e^{ac{1}{\ta_d}J} 1_{J<0} \ p + q &=& 1 \nd{array} ]

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) &=& ppa ( heta - v) dt + sigma sqrt{v} dW_2 \ dlambda(t) &=& ppa_lambda( heta_lambda-lambda) dt \ dW_1 dW_2 &=& rho dt \nd{array} ]

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)

Tests

the correctness of the returned value is tested by reproducing results available in web/literature, testing against QuantLib's jump diffusion engine and comparison with Black pricing.

Examples: EquityOption.cpp.

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

The man page BatesEngine(3) is an alias of QuantLib_BatesEngine(3).

Wed Feb 7 2018 Version 1.10.1 QuantLib