Pricing engine for European discrete geometric average price Asian. More...

#include <ql/experimental/asian/analytic_discr_geom_av_price_heston.hpp>

Inheritance diagram for AnalyticDiscreteGeometricAveragePriceAsianHestonEngine:

Collaboration diagram for AnalyticDiscreteGeometricAveragePriceAsianHestonEngine:

Public Member Functions
	AnalyticDiscreteGeometricAveragePriceAsianHestonEngine (ext::shared_ptr< HestonProcess > process, Real xiRightLimit=100.0)

void	calculate () const override

std::complex< Real >	Phi (std::complex< Real > s, std::complex< Real > w, Time t, Time T, Size kStar, const std::vector< Time > &t_n, const std::vector< Time > &tauK) const

Public Member Functions inherited from GenericEngine< DiscreteAveragingAsianOption::arguments, DiscreteAveragingAsianOption::results >
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 ()

Private Member Functions
std::complex< Real >	F (const std::complex< Real > &z1, const std::complex< Real > &z2, Time tau) const

std::complex< Real >	F_tilde (const std::complex< Real > &z1, const std::complex< Real > &z2, Time tau) const

std::complex< Real >	z (const std::complex< Real > &s, const std::complex< Real > &w, Size k, Size n) const

std::complex< Real >	omega (const std::complex< Real > &s, const std::complex< Real > &w, Size k, Size kStar, Size n) const

std::complex< Real >	a (const std::complex< Real > &s, const std::complex< Real > &w, Time t, Time T, Size kStar, const std::vector< Time > &t_n) const

std::complex< Real >	omega_tilde (const std::complex< Real > &s, const std::complex< Real > &w, Size k, Size kStar, Size n, const std::vector< Time > &tauK) const

Private Attributes
Real	v0_

Real	rho_

Real	kappa_

Real	theta_

Real	sigma_

Real	logS0_

Handle< YieldTermStructure >	dividendYield_

Handle< YieldTermStructure >	riskFreeRate_

Handle< Quote >	s0_

ext::shared_ptr< HestonProcess >	process_

std::map< Size, std::complex< Real > >	omegaTildeLookupTable_

Real	xiRightLimit_

GaussLegendreIntegration	integrator_

Real	tr_t_

Real	Tr_T_

std::vector< Real >	tkr_tk_

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator

Protected Attributes inherited from GenericEngine< DiscreteAveragingAsianOption::arguments, DiscreteAveragingAsianOption::results >
DiscreteAveragingAsianOption::arguments	arguments_

DiscreteAveragingAsianOption::results	results_

Detailed Description

Pricing engine for European discrete geometric average price Asian.

This class implements a discrete geometric average price Asian option with European exercise under the Heston stochastic vol model where spot and variance follow the processes

\[ \begin{array}{rcl} dS(t, S) &=& (r-d) S dt +\sqrt{v} S dW_1 \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \\ \end{array} \]

References:

Implements the analytical solution for continuous geometric Asian options developed in "A Recursive Method for Discretely Monitored Geometric Asian Option Prices", B. Kim, J. Kim, J. Kim & I. S. Wee, Bull. Korean Math. Soc. 53, 733-749 (2016)

Tests:

the correctness of the returned value is tested by reproducing results in Tables 1, 2 and 3 of the paper

Definition at line 64 of file analytic_discr_geom_av_price_heston.hpp.

Constructor & Destructor Documentation

◆ AnalyticDiscreteGeometricAveragePriceAsianHestonEngine()

AnalyticDiscreteGeometricAveragePriceAsianHestonEngine	(	ext::shared_ptr< HestonProcess >	process,
		Real	xiRightLimit = `100.0`
	)

explicit

Definition at line 59 of file analytic_discr_geom_av_price_heston.cpp.

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Member Function Documentation

◆ calculate()

void calculate ( ) const

overridevirtual

Implements PricingEngine.

Definition at line 202 of file analytic_discr_geom_av_price_heston.cpp.

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◆ Phi()

std::complex< Real > Phi	(	std::complex< Real >	s,
		std::complex< Real >	w,
		Time	t,
		Time	T,
		Size	kStar,
		const std::vector< Time > &	t_n,
		const std::vector< Time > &	tauK
	)		const

Definition at line 174 of file analytic_discr_geom_av_price_heston.cpp.

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