BatesEngine (3) - Linux Manuals

NAME

QuantLib::BatesEngine - Bates model engines based on Fourier transform.

SYNOPSIS

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

Inherits QuantLib::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

[ ^J - 1) S dN \ dv(t, S) &=& ppa ( heta - v) dt + igma qrt{v} dW_2 \ dW_1 dW_2 &=& ho dt \nd{array} ].PP N is a Poisson process with the intensity \$

\$. When a jump occurs the magnitude J has the probability distribution function \$ al Jump Diffusion: BatesEngine

Logarithm of the jump size J is normally distributed [ p Diffusion: BatesDoubleExpEngine

The jump size has an asymmetric double exponential distribution [ terministic Jump Intensity

[ ^J - 1) S dN \ dv(t, S) &=& ppa ( heta - v) dt + igma qrt{v} dW_2 \ d

(t) &=& ppa_
( heta_
-
) dt \ dW_1 dW_2 &=& ho dt \nd{array} ].PP 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 volatilit: 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.

Author

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