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

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

Inheritance diagram for AnalyticContinuousGeometricAveragePriceAsianHestonEngine:

Collaboration diagram for AnalyticContinuousGeometricAveragePriceAsianHestonEngine:

Public Member Functions
	AnalyticContinuousGeometricAveragePriceAsianHestonEngine (ext::shared_ptr< HestonProcess > process, Size summationCutoff=50, Real xiRightLimit=100.0)

void	calculate () const override

std::complex< Real >	Phi (const std::complex< Real > &s, const std::complex< Real > &w, Real T, Real t=0.0, Size cutoff=50) const

Public Member Functions inherited from GenericEngine< ContinuousAveragingAsianOption::arguments, ContinuousAveragingAsianOption::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 >	z1_f (const std::complex< Real > &s, const std::complex< Real > &w, Real T) const

std::complex< Real >	z2_f (const std::complex< Real > &s, const std::complex< Real > &w, Real T) const

std::complex< Real >	z3_f (const std::complex< Real > &s, const std::complex< Real > &w, Real T) const

std::complex< Real >	z4_f (const std::complex< Real > &s, const std::complex< Real > &w) const

std::pair< std::complex< Real >, std::complex< Real > >	F_F_tilde (const std::complex< Real > &z1, const std::complex< Real > &z2, const std::complex< Real > &z3, const std::complex< Real > &z4, Real tau, Size cutoff=50) const

std::complex< Real >	f (const std::complex< Real > &z1, const std::complex< Real > &z2, const std::complex< Real > &z3, const std::complex< Real > &z4, int n, Real tau) const

Private Attributes
Real	v0_

Real	rho_

Real	kappa_

Real	theta_

Real	sigma_

Handle< YieldTermStructure >	dividendYield_

Handle< YieldTermStructure >	riskFreeRate_

Handle< Quote >	s0_

ext::shared_ptr< HestonProcess >	process_

Real	a1_

Real	a2_

Real	a3_ = 0.0

Real	a4_ = 0.0

Real	a5_ = 0.0

std::map< int, std::complex< Real > >	fLookupTable_

Size	summationCutoff_

Real	xiRightLimit_

GaussLegendreIntegration	integrator_

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

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

ContinuousAveragingAsianOption::results	results_

Detailed Description

Pricing engine for European continuous geometric average price Asian.

This class implements a continuous 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 "Pricing of geometric Asian options under Heston's stochastic volatility model", B. Kim & I. S. Wee, Quantative Finance 14:10, 1795-1809 (2014)

Tests:

the correctness of the returned value is tested by reproducing results in Table 1 and Table 4 of the paper

Definition at line 65 of file analytic_cont_geom_av_price_heston.hpp.

Constructor & Destructor Documentation

◆ AnalyticContinuousGeometricAveragePriceAsianHestonEngine()

AnalyticContinuousGeometricAveragePriceAsianHestonEngine	(	ext::shared_ptr< HestonProcess >	process,
		Size	summationCutoff = `50`,
		Real	xiRightLimit = `100.0`
	)

explicit

Definition at line 75 of file analytic_cont_geom_av_price_heston.cpp.

Here is the call graph for this function:

Member Function Documentation

◆ calculate()

void calculate ( ) const

overridevirtual

Implements PricingEngine.

Definition at line 208 of file analytic_cont_geom_av_price_heston.cpp.

Here is the call graph for this function:

◆ Phi()

std::complex< Real > Phi	(	const std::complex< Real > &	s,
		const std::complex< Real > &	w,
		Real	T,
		Real	t = `0.0`,
		Size	cutoff = `50`
	)		const

Definition at line 184 of file analytic_cont_geom_av_price_heston.cpp.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ z1_f()

std::complex< Real > z1_f	(	const std::complex< Real > &	s,
		const std::complex< Real > &	w,
		Real	T
	)		const

private

Definition at line 98 of file analytic_cont_geom_av_price_heston.cpp.

Here is the caller graph for this function:

◆ z2_f()

std::complex< Real > z2_f	(	const std::complex< Real > &	s,
		const std::complex< Real > &	w,
		Real	T
	)		const

private

Definition at line 103 of file analytic_cont_geom_av_price_heston.cpp.

Here is the caller graph for this function:

◆ z3_f()

std::complex< Real > z3_f	(	const std::complex< Real > &	s,
		const std::complex< Real > &	w,
		Real	T
	)		const

private

Definition at line 108 of file analytic_cont_geom_av_price_heston.cpp.

Here is the caller graph for this function:

◆ z4_f()

std::complex< Real > z4_f	(	const std::complex< Real > &	s,
		const std::complex< Real > &	w
	)		const

private

Definition at line 113 of file analytic_cont_geom_av_price_heston.cpp.

Here is the caller graph for this function:

◆ F_F_tilde()

std::pair< std::complex< Real >, std::complex< Real > > F_F_tilde	(	const std::complex< Real > &	z1,
		const std::complex< Real > &	z2,
		const std::complex< Real > &	z3,
		const std::complex< Real > &	z4,
		Real	tau,
		Size	cutoff = `50`
	)		const

private

Definition at line 162 of file analytic_cont_geom_av_price_heston.cpp.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ f()

std::complex< Real > f	(	const std::complex< Real > &	z1,
		const std::complex< Real > &	z2,
		const std::complex< Real > &	z3,
		const std::complex< Real > &	z4,
		int	n,
		Real	tau
	)		const