QuantLib: a free/open-source library for quantitative finance
fully annotated source code - version 1.34
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analytic Heston-model engine based on Fourier transform More...
#include <analytichestonengine.hpp>
Classes | |
class | AP_Helper |
class | Integration |
class | OptimalAlpha |
Public Types | |
enum | ComplexLogFormula { Gatheral , BranchCorrection , AndersenPiterbarg , AndersenPiterbargOptCV , AsymptoticChF , AngledContour , AngledContourNoCV , OptimalCV } |
Public Types inherited from Observer | |
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-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 () |
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 |
Private Member Functions | |
Real | priceVanillaPayoff (const ext::shared_ptr< PlainVanillaPayoff > &payoff, Time maturity, Real fwd) const |
Private Attributes | |
Size | evaluations_ |
const ComplexLogFormula | cpxLog_ |
const ext::shared_ptr< Integration > | integration_ |
const Real | andersenPiterbargEpsilon_ |
const Real | alpha_ |
Additional Inherited Members | |
Protected Attributes inherited from GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results > | |
Handle< HestonModel > | model_ |
Protected Attributes inherited from GenericEngine< ArgumentsType, ResultsType > | |
ArgumentsType | arguments_ |
ResultsType | results_ |
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.
L. Andersen and M. Lake, 2018 Robust High-Precision Option Pricing by Fourier Transforms: Contour Deformations and Double-Exponential Quadrature, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3231626
Definition at line 91 of file analytichestonengine.hpp.
enum ComplexLogFormula |
Enumerator | |
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Gatheral | |
BranchCorrection | |
AndersenPiterbarg | |
AndersenPiterbargOptCV | |
AsymptoticChF | |
AngledContour | |
AngledContourNoCV | |
OptimalCV |
Definition at line 100 of file analytichestonengine.hpp.
AnalyticHestonEngine | ( | const ext::shared_ptr< HestonModel > & | model, |
Real | relTolerance, | ||
Size | maxEvaluations | ||
) |
Definition at line 673 of file analytichestonengine.cpp.
AnalyticHestonEngine | ( | const ext::shared_ptr< HestonModel > & | model, |
Size | integrationOrder = 144 |
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) |
Definition at line 659 of file analytichestonengine.cpp.
AnalyticHestonEngine | ( | const ext::shared_ptr< HestonModel > & | model, |
ComplexLogFormula | cpxLog, | ||
const Integration & | itg, | ||
Real | andersenPiterbargEpsilon = 1e-25 , |
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Real | alpha = -0.5 |
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) |
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overridevirtual |
Implements PricingEngine.
Reimplemented in AnalyticHestonHullWhiteEngine.
Definition at line 861 of file analytichestonengine.cpp.
Definition at line 578 of file analytichestonengine.cpp.
Definition at line 621 of file analytichestonengine.cpp.
Size numberOfEvaluations | ( | ) | const |
Definition at line 721 of file analytichestonengine.cpp.
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Real priceVanillaPayoff | ( | const ext::shared_ptr< PlainVanillaPayoff > & | payoff, |
const Date & | maturity | ||
) | const |
Definition at line 725 of file analytichestonengine.cpp.
Real priceVanillaPayoff | ( | const ext::shared_ptr< PlainVanillaPayoff > & | payoff, |
Time | maturity | ||
) | const |
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static |
Definition at line 708 of file analytichestonengine.cpp.
Reimplemented in AnalyticH1HWEngine, AnalyticHestonHullWhiteEngine, BatesEngine, BatesDetJumpEngine, BatesDoubleExpEngine, and BatesDoubleExpDetJumpEngine.
Definition at line 307 of file analytichestonengine.hpp.
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Definition at line 191 of file analytichestonengine.hpp.
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private |
Definition at line 192 of file analytichestonengine.hpp.
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Definition at line 193 of file analytichestonengine.hpp.
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Definition at line 194 of file analytichestonengine.hpp.
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Definition at line 194 of file analytichestonengine.hpp.