OneFactorStudentCopula Class Reference

One-factor Double Student t-Copula. More...

#include <onefactorstudentcopula.hpp>

Inheritance diagram for OneFactorStudentCopula:

Collaboration diagram for OneFactorStudentCopula:

Public Member Functions
	OneFactorStudentCopula (const Handle< Quote > &correlation, int nz, int nm, Real maximum=10, Size integrationSteps=200)
Real	density (Real m) const override
	Density function of M. More...
Real	cumulativeZ (Real z) const override
	Cumulative distribution of Z. More...
Public Member Functions inherited from OneFactorCopula
	OneFactorCopula (Handle< Quote > correlation, Real maximum=5.0, Size integrationSteps=50, Real minimum=-5.0)
virtual Real	density (Real m) const =0
	Density function of M. More...
virtual Real	cumulativeZ (Real z) const =0
	Cumulative distribution of Z. More...
virtual Real	cumulativeY (Real y) const
	Cumulative distribution of Y. More...
virtual Real	inverseCumulativeY (Real p) const
	Inverse cumulative distribution of Y. More...
Real	correlation () const
	Single correlation parameter. More...
Real	conditionalProbability (Real prob, Real m) const
	Conditional probability. More...
std::vector< Real >	conditionalProbability (const std::vector< Real > &prob, Real m) const
	Vector of conditional probabilities. More...
Real	integral (Real p) const
template<class F >
Real	integral (const F &f, std::vector< Real > &probabilities) const
template<class F >
Distribution	integral (const F &f, const std::vector< Real > &nominals, const std::vector< Real > &probabilities) const
int	checkMoments (Real tolerance) const
Public Member Functions inherited from LazyObject
	LazyObject ()
	~LazyObject () override=default
void	update () override
bool	isCalculated () const
void	forwardFirstNotificationOnly ()
void	alwaysForwardNotifications ()
void	recalculate ()
void	freeze ()
void	unfreeze ()
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
void	performCalculations () const override
	Observer interface. More...
Real	cumulativeYintegral (Real y) const

Private Attributes
StudentDistribution	density_
CumulativeStudentDistribution	cumulative_
int	nz_
int	nm_
Real	scaleM_
Real	scaleZ_

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator
Protected Member Functions inherited from OneFactorCopula
Size	steps () const
Real	dm (Size i) const
Real	m (Size i) const
Real	densitydm (Size i) const
Protected Member Functions inherited from LazyObject
virtual void	calculate () const
Protected Attributes inherited from OneFactorCopula
Handle< Quote >	correlation_
Real	max_
Size	steps_
Real	min_
std::vector< Real >	y_
std::vector< Real >	cumulativeY_
Protected Attributes inherited from LazyObject
bool	calculated_ = false
bool	frozen_ = false
bool	alwaysForward_

Detailed Description

One-factor Double Student t-Copula.

The copula model

\[ Y_i = a_i\,M+\sqrt{1-a_i^2}\:Z_i \]

is specified here by setting the probability density functions for \( Z_i \) ( \( D_Z \)) and \( M \) ( \( D_M \)) to Student t-distributions with \( N_z \) and \( N_m \) degrees of freedom, respectively.

The variance of the Student t-distribution with \( \nu \) degrees of freedom is \( \nu / (\nu - 2) \). Since the copula approach requires zero mean and unit variance distributions, variables \( Z \) and \( M \) are scaled by \( \sqrt{(N_z - 2) / N_z} \) and \( \sqrt{(N_m - 2) / N_m}, \) respectively.

Definition at line 53 of file onefactorstudentcopula.hpp.

Constructor & Destructor Documentation

OneFactorStudentCopula()

OneFactorStudentCopula	(	const Handle< Quote > &	correlation,
		int	nz,
		int	nm,
		Real	maximum = 10,
		Size	integrationSteps = 200
	)

Definition at line 25 of file onefactorstudentcopula.cpp.

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Member Function Documentation

density()

Real density ( Real  m ) const

overridevirtual

Density function of M.

Derived classes must override this method and ensure zero mean and unit variance.

Implements OneFactorCopula.

Definition at line 80 of file onefactorstudentcopula.hpp.

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cumulativeZ()

Real cumulativeZ ( Real  z ) const

overridevirtual

Cumulative distribution of Z.

Derived classes must override this method and ensure zero mean and unit variance.

Implements OneFactorCopula.

Definition at line 84 of file onefactorstudentcopula.hpp.

performCalculations()

void performCalculations ( ) const

overrideprivatevirtual

Observer interface.

Implements LazyObject.

Definition at line 43 of file onefactorstudentcopula.cpp.

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cumulativeYintegral()

Real cumulativeYintegral ( Real  y ) const

private

Definition at line 63 of file onefactorstudentcopula.cpp.

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Member Data Documentation

density_

StudentDistribution density_

private

Definition at line 66 of file onefactorstudentcopula.hpp.

cumulative_

CumulativeStudentDistribution cumulative_

private

Definition at line 67 of file onefactorstudentcopula.hpp.

nz_

int nz_

private

Definition at line 68 of file onefactorstudentcopula.hpp.

nm_

int nm_

private

Definition at line 69 of file onefactorstudentcopula.hpp.

scaleM_

Real scaleM_

private

Definition at line 71 of file onefactorstudentcopula.hpp.

scaleZ_

Real scaleZ_

private

Definition at line 72 of file onefactorstudentcopula.hpp.