Analytic Heston-Hull-White engine based on the H1-HW approximation. More...

#include <analytich1hwengine.hpp>

Inheritance diagram for AnalyticH1HWEngine:

Collaboration diagram for AnalyticH1HWEngine:

Public Member Functions
	AnalyticH1HWEngine (const ext::shared_ptr< HestonModel > &model, const ext::shared_ptr< HullWhite > &hullWhiteModel, Real rhoSr, Size integrationOrder=144)

	AnalyticH1HWEngine (const ext::shared_ptr< HestonModel > &model, const ext::shared_ptr< HullWhite > &hullWhiteModel, Real rhoSr, Real relTolerance, Size maxEvaluations)

Public Member Functions inherited from AnalyticHestonHullWhiteEngine
	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 ()

	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

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

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

Private Attributes
const Real	rhoSr_

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 AnalyticHestonHullWhiteEngine
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_

Detailed Description

Analytic Heston-Hull-White engine based on the H1-HW approximation.

This class is pricing a european option under the following process

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

References:

Lech A. Grzelak, Cornelis W. Oosterlee, On The Heston Model with Stochastic, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1382902

Lech A. Grzelak, Equity and Foreign Exchange Hybrid Models for Pricing Long-Maturity Financial Derivatives, http://repository.tudelft.nl/assets/uuid:a8e1a007-bd89-481a-aee3-0e22f15ade6b/PhDThesis_main.pdf

Tests:: the correctness of the returned value is tested by reproducing results available in web/literature, testing against QuantLib's analytic Heston, the Black-Scholes-Merton Hull-White engine and the finite difference Heston-Hull-White engine

Definition at line 68 of file analytich1hwengine.hpp.

Constructor & Destructor Documentation

◆ AnalyticH1HWEngine() [1/2]

AnalyticH1HWEngine	(	const ext::shared_ptr< HestonModel > &	model,
		const ext::shared_ptr< HullWhite > &	hullWhiteModel,
		Real	rhoSr,
		Size	integrationOrder = `144`
	)

Definition at line 138 of file analytich1hwengine.cpp.

◆ AnalyticH1HWEngine() [2/2]

AnalyticH1HWEngine	(	const ext::shared_ptr< HestonModel > &	model,
		const ext::shared_ptr< HullWhite > &	hullWhiteModel,
		Real	rhoSr,
		Real	relTolerance,
		Size	maxEvaluations
	)

Definition at line 148 of file analytich1hwengine.cpp.

Member Function Documentation

◆ addOnTerm()

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

overrideprotectedvirtual

Reimplemented from AnalyticHestonEngine.

Definition at line 157 of file analytich1hwengine.cpp.

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Member Data Documentation

◆ rhoSr_

const Real rhoSr_

private

Definition at line 84 of file analytich1hwengine.hpp.

Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members