Analytic Heston engine incl. stochastic interest rates. More...

#include <analytichestonhullwhiteengine.hpp>

Inheritance diagram for AnalyticHestonHullWhiteEngine:

Collaboration diagram for AnalyticHestonHullWhiteEngine:

Public Member Functions
	AnalyticHestonHullWhiteEngine (const ext::shared_ptr< HestonModel > &hestonModel, ext::shared_ptr< HullWhite > hullWhiteModel, Size integrationOrder=144)

	AnalyticHestonHullWhiteEngine (const ext::shared_ptr< HestonModel > &model, ext::shared_ptr< HullWhite > hullWhiteModel, Real relTolerance, Size maxEvaluations)

void	update () override

void	calculate () const override

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 ()=default

	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

Protected Attributes
const ext::shared_ptr< HullWhite >	hullWhiteModel_

Protected Attributes inherited from GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results >
Handle< HestonModel >	model_

Protected Attributes inherited from GenericEngine< ArgumentsType, ResultsType >
ArgumentsType	arguments_

ResultsType	results_

Private Member Functions
void	setParameters ()

Private Attributes
Real	m_

Real	a_

Real	sigma_

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)

Detailed Description

Analytic Heston engine incl. stochastic interest rates.

This class is pricing a european option under the following process

\[ \begin{array}{rcl} dS(t, S) &=& (r-d) S dt +\sqrt{v} S dW_1 \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dr(t) &=& (\theta(t) - a r) dt + \eta dW_3 \\ dW_1 dW_2 &=& \rho dt \\ dW_1 dW_3 &=& 0 \\ dW_2 dW_3 &=& 0 \\ \end{array} \]

References:

Karel in't Hout, Joris Bierkens, Antoine von der Ploeg, Joe in't Panhuis, A Semi closed-from analytic pricing formula for call options in a hybrid Heston-Hull-White Model.

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 analytic Heston and Black-Scholes-Merton Hull-White engine

Definition at line 65 of file analytichestonhullwhiteengine.hpp.

Constructor & Destructor Documentation

◆ AnalyticHestonHullWhiteEngine() [1/2]

AnalyticHestonHullWhiteEngine	(	const ext::shared_ptr< HestonModel > &	hestonModel,
		ext::shared_ptr< HullWhite >	hullWhiteModel,
		Size	integrationOrder = `144`
	)

Definition at line 26 of file analytichestonhullwhiteengine.cpp.

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◆ AnalyticHestonHullWhiteEngine() [2/2]

AnalyticHestonHullWhiteEngine	(	const ext::shared_ptr< HestonModel > &	model,
		ext::shared_ptr< HullWhite >	hullWhiteModel,
		Real	relTolerance,
		Size	maxEvaluations
	)

Definition at line 38 of file analytichestonhullwhiteengine.cpp.

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Member Function Documentation

◆ update()

void update ( )

overridevirtual

This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.

Reimplemented from GenericEngine< ArgumentsType, ResultsType >.

Definition at line 52 of file analytichestonhullwhiteengine.cpp.

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