AnalyticHestonHullWhiteEngine Class Reference

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

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

Inheritance 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)
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 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< VanillaOption::arguments, VanillaOption::results >
VanillaOption::arguments	arguments_
VanillaOption::results	results_

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

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.

Implements Observer.

calculate()

void calculate ( ) const

overridevirtual

Reimplemented from AnalyticHestonEngine.

addOnTerm()

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

overrideprotectedvirtual

Reimplemented from AnalyticHestonEngine.