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

Additional Inherited Members

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/stoch…)

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

BatesEngine(3) is an alias of QuantLib_BatesEngine(3).

Fri Sep 23 2016 Version 1.8.1 QuantLib