AnalyticH1HWEngine Class Reference

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

#include <ql/pricingengines/vanilla/analytich1hwengine.hpp>

Inheritance 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)
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
Protected Member Functions inherited from AnalyticHestonHullWhiteEngine
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 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< VanillaOption::arguments, VanillaOption::results >
VanillaOption::arguments	arguments_
VanillaOption::results	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

Member Function Documentation

addOnTerm()

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

overrideprotectedvirtual

Reimplemented from AnalyticHestonEngine.