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 }
 

Public Member Functions

 AnalyticHestonEngine (const boost::shared_ptr< HestonModel > &model, Real relTolerance, Size maxEvaluations)
 
 AnalyticHestonEngine (const boost::shared_ptr< HestonModel > &model, Size integrationOrder=144)
 
 AnalyticHestonEngine (const boost::shared_ptr< HestonModel > &model, ComplexLogFormula cpxLog, const Integration &itg)
 
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 boost::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 Observer
 Observer (const Observer &)
 
Observeroperator= (const Observer &)
 
std::pair< std::set
< boost::shared_ptr
< Observable > >::iterator,
bool > 
registerWith (const boost::shared_ptr< Observable > &)
 
Size unregisterWith (const boost::shared_ptr< Observable > &)
 
void unregisterWithAll ()
 

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, const ComplexLogFormula cpxLog, const AnalyticHestonEngine *const enginePtr, Real &value, Size &evaluations)
 

Protected Member Functions

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

Additional Inherited Members

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

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