AnalyticHestonEngine Class Reference

analytic Heston-model engine based on Fourier transform More...

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

Inheritance diagram for AnalyticHestonEngine:

Public Types
enum	ComplexLogFormula {   Gatheral, BranchCorrection, AndersenPiterbarg, AndersenPiterbargOptCV,   AsymptoticChF, OptimalCV }
Public Types inherited from Observer
typedef boost::unordered_set< ext::shared_ptr< Observable > >	set_type
typedef set_type::iterator	iterator

Public Member Functions
	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-8)
std::complex< Real >	chF (const std::complex< Real > &z, Time t) const
std::complex< Real >	lnChF (const std::complex< Real > &z, Time t) const
void	calculate () const
Size	numberOfEvaluations () const
Public Member Functions inherited from GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results >
	GenericModelEngine (const Handle< HestonModel > &model=Handle< HestonModel >())
	GenericModelEngine (const ext::shared_ptr< HestonModel > &model)
Public Member Functions inherited from GenericEngine< VanillaOption::arguments, VanillaOption::results >
PricingEngine::arguments *	getArguments () const
const PricingEngine::results *	getResults () const
void	reset ()
void	update ()
Public Member Functions inherited from PricingEngine
virtual arguments *	getArguments () const =0
virtual const results *	getResults () const =0
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
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 ()

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

Additional Inherited Members
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-model engine based on Fourier transform

Integration detail: Two algebraically equivalent formulations of the complex logarithm of the Heston model exist. Gatherals [2005] (also Duffie, Pan and Singleton [2000], and Schoutens, Simons and Tistaert[2004]) version does not cause discoutinuities whereas the original version (e.g. Heston [1993]) needs some sort of "branch correction" to work properly. Gatheral's version does also work with adaptive integration routines and should be preferred over the original Heston version.

References:

Heston, Steven L., 1993. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. The review of Financial Studies, Volume 6, Issue 2, 327-343.

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)

R. Lord and C. Kahl, Why the rotation count algorithm works, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=921335

H. Albrecher, P. Mayer, W.Schoutens and J. Tistaert, The Little Heston Trap, http://www.schoutens.be/HestonTrap.pdf

J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley Finance

F. Le Floc'h, Fourier Integration and Stochastic Volatility Calibration, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2362968

L. Andersen, and V. Piterbarg, 2010, Interest Rate Modeling, Volume I: Foundations and Vanilla Models, Atlantic Financial Press London.

Tests:

the correctness of the returned value is tested by reproducing results available in web/literature and comparison with Black pricing.

Examples

EquityOption.cpp.