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

#include <batesengine.hpp>

Inheritance diagram for BatesEngine:

Collaboration 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 >())

	GenericModelEngine (const ext::shared_ptr< HestonModel > &model)

Public Member Functions inherited from GenericEngine< ArgumentsType, ResultsType >
PricingEngine::arguments *	getArguments () const override

const PricingEngine::results *	getResults () const override

void	reset () override

void	update () override

Public Member Functions inherited from PricingEngine
	~PricingEngine () override=default

virtual arguments *	getArguments () const =0

virtual const results *	getResults () const =0

virtual void	reset ()=0

virtual void	calculate () const =0

Public Member Functions inherited from Observable
	Observable ()

	Observable (const Observable &)

Observable &	operator= (const Observable &)

	Observable (Observable &&)=delete

Observable &	operator= (Observable &&)=delete

virtual	~Observable ()=default

void	notifyObservers ()

Public Member Functions inherited from Observer
	Observer ()=default

	Observer (const Observer &)

Observer &	operator= (const Observer &)

virtual	~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	update ()=0

virtual void	deepUpdate ()

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

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

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< ArgumentsType, ResultsType >
ArgumentsType	arguments_

ResultsType	results_

Detailed Description

Bates model engines based on Fourier transform.

this classes price european options under the following processes

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

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

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.

Definition at line 106 of file batesengine.hpp.

Constructor & Destructor Documentation

◆ BatesEngine() [1/2]

BatesEngine	(	const ext::shared_ptr< BatesModel > &	model,
		Size	integrationOrder = `144`
	)

explicit

Definition at line 26 of file batesengine.cpp.

◆ BatesEngine() [2/2]

BatesEngine	(	const ext::shared_ptr< BatesModel > &	model,
		Real	relTolerance,
		Size	maxEvaluations
	)

Definition at line 32 of file batesengine.cpp.

Member Function Documentation

◆ addOnTerm()

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

overrideprotectedvirtual

Reimplemented from AnalyticHestonEngine.

Reimplemented in BatesDetJumpEngine.

Definition at line 39 of file batesengine.cpp.

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Public Member Functions

Protected Member Functions