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

#include <ql/experimental/credit/onefactorstudentcopula.hpp>

Inheritance diagram for OneFactorStudentGaussianCopula:

Collaboration diagram for OneFactorStudentGaussianCopula:

Public Member Functions
	OneFactorStudentGaussianCopula (const Handle< Quote > &correlation, 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_

CumulativeNormalDistribution	cumulative_

int	nm_

Real	scaleM_

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 Student t - Gaussian 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 \( Z_i \) ( \( D_Z \)) to a Gaussian and for \( M \) ( \( D_M \)) to a Student t-distribution with \( N_m \) degrees of freedom.

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, \( M \) is scaled by \( \sqrt{(N_m - 2) / N_m}. \)

Definition at line 161 of file onefactorstudentcopula.hpp.