BatesEngine Class Reference

Bates model engines based on Fourier transform. More...

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

Inheritance diagram for BatesEngine:

Public Member Functions
	BatesEngine (const ext::shared_ptr< BatesModel > &model, Size integrationOrder=144)
	BatesEngine (const ext::shared_ptr< BatesModel > &model, Real relTolerance, Size maxEvaluations)
Public Member Functions inherited from AnalyticHestonEngine
	AnalyticHestonEngine (const ext::shared_ptr< HestonModel > &model, Real relTolerance, Size maxEvaluations)
	AnalyticHestonEngine (const ext::shared_ptr< HestonModel > &model, Size integrationOrder=144)
	AnalyticHestonEngine (const ext::shared_ptr< HestonModel > &model, ComplexLogFormula cpxLog, const Integration &itg, Real andersenPiterbargEpsilon=1e-25, Real alpha=-0.5)
void	calculate () const override
std::complex< Real >	chF (const std::complex< Real > &z, Time t) const
std::complex< Real >	lnChF (const std::complex< Real > &z, Time t) const
Size	numberOfEvaluations () const
Real	priceVanillaPayoff (const ext::shared_ptr< PlainVanillaPayoff > &payoff, const Date &maturity) const
Real	priceVanillaPayoff (const ext::shared_ptr< PlainVanillaPayoff > &payoff, Time maturity) const
Public Member Functions inherited from GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results >
	GenericModelEngine (Handle< HestonModel > model=Handle< HestonModel >())
Public Member Functions inherited from GenericEngine< VanillaOption::arguments, VanillaOption::results >
PricingEngine::arguments *	getArguments () const override
const PricingEngine::results *	getResults () const override
void	reset () override
void	update () override
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
	Observable (Observable &&)=delete
Observable &	operator= (Observable &&)=delete
void	notifyObservers ()
Public Member Functions inherited from Observer
	Observer (const Observer &)
Observer &	operator= (const Observer &)
std::pair< iterator, bool >	registerWith (const ext::shared_ptr< Observable > &)
void	registerWithObservables (const ext::shared_ptr< Observer > &)
Size	unregisterWith (const ext::shared_ptr< Observable > &)
void	unregisterWithAll ()
virtual void	deepUpdate ()

Protected Member Functions
std::complex< Real >	addOnTerm (Real phi, Time t, Size j) const override

Additional Inherited Members
Public Types inherited from AnalyticHestonEngine
enum	ComplexLogFormula {   Gatheral , BranchCorrection , AndersenPiterbarg , AndersenPiterbargOptCV ,   AsymptoticChF , AngledContour , AngledContourNoCV , OptimalCV }
Public Types inherited from Observer
typedef set_type::iterator	iterator
Static Public Member Functions inherited from AnalyticHestonEngine
static void	doCalculation (Real riskFreeDiscount, Real dividendDiscount, Real spotPrice, Real strikePrice, Real term, Real kappa, Real theta, Real sigma, Real v0, Real rho, const TypePayoff &type, const Integration &integration, ComplexLogFormula cpxLog, const AnalyticHestonEngine *enginePtr, Real &value, Size &evaluations)
static ComplexLogFormula	optimalControlVariate (Time t, Real v0, Real kappa, Real theta, Real sigma, Real rho)
Protected Attributes inherited from GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results >
Handle< HestonModel >	model_
Protected Attributes inherited from GenericEngine< VanillaOption::arguments, VanillaOption::results >
VanillaOption::arguments	arguments_
VanillaOption::results	results_

Detailed Description

Bates model engines based on Fourier transform.

this classes price european options under the following processes

1. Jump-Diffusion with Stochastic Volatility

   \[\begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]

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

\[\omega(J) = \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \]

1.2 Double-Exponential Jump Diffusion: BatesDoubleExpEngine

The jump size has an asymmetric double exponential distribution

\[\begin{array}{rcl} \omega(J)&=& p\frac{1}{\eta_u}e^{-\frac{1}{\eta_u}J} 1_{J>0} + q\frac{1}{\eta_d}e^{\frac{1}{\eta_d}J} 1_{J<0} \\ p + q &=& 1 \end{array} \]

1. Stochastic Volatility with Jump Diffusion and Deterministic Jump Intensity

   \[\begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ d\lambda(t) &=& \kappa_\lambda(\theta_\lambda-\lambda) dt \\ dW_1 dW_2 &=& \rho dt \end{array} \]

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.

Member Function Documentation

addOnTerm()

std::complex< Real > addOnTerm ( Real phi, Time t, Size j ) const

overrideprotectedvirtual

Reimplemented from AnalyticHestonEngine.