AnalyticH1HWEngine Class Reference
Pricing engines » Vanilla option engines

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

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

Inheritance diagram for AnalyticH1HWEngine:
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## Public Member Functions

| AnalyticH1HWEngine (const ext::shared_ptr< HestonModel > &model, const ext::shared_ptr< HullWhite > &hullWhiteModel, Real rhoXV, 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, const ext::shared_ptr< HullWhite > &hullWhiteModel, Size integrationOrder=144)
| AnalyticHestonHullWhiteEngine (const ext::shared_ptr< HestonModel > &model, const ext::shared_ptr< HullWhite > &hullWhiteModel, Real relTolerance, Size maxEvaluations)
void | update ()
void | calculate () const
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-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
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 ()

## Protected Member Functions

std::complex< Real > | addOnTerm (Real phi, Time t, Size j) const
Protected Member Functions inherited from AnalyticHestonHullWhiteEngine
std::complex< Real > | addOnTerm (Real phi, Time t, Size j) const

## Additional Inherited Members

Public Types inherited from AnalyticHestonEngine
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
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