Default event Latent Model. More...

#include <defaultprobabilitylatentmodel.hpp>

Inheritance diagram for DefaultLatentModel< copulaPolicy >:

Collaboration diagram for DefaultLatentModel< copulaPolicy >:

Public Member Functions
	DefaultLatentModel (const std::vector< std::vector< Real > > &factorWeights, LatentModelIntegrationType::LatentModelIntegrationType integralType, const initTraits &ini=initTraits())

	DefaultLatentModel (const Handle< Quote > &mktCorrel, Size nVariables, LatentModelIntegrationType::LatentModelIntegrationType integralType, const initTraits &ini=initTraits())

void	resetBasket (const ext::shared_ptr< Basket > &basket) const

Probability	conditionalDefaultProbability (Probability prob, Size iName, const std::vector< Real > &mktFactors) const

Probability	conditionalDefaultProbabilityInvP (Real invCumYProb, Size iName, const std::vector< Real > &m) const

Probability	probOfDefault (Size iName, const Date &d) const

Real	defaultCorrelation (const Date &d, Size iNamei, Size iNamej) const

Probability	probAtLeastNEvents (Size n, const Date &date) const

Public Member Functions inherited from LatentModel< copulaPolicy >
void	update () override

Size	size () const

Size	numFactors () const
	Number of systemic factors. More...

Size	numTotalFactors () const
	Number of total free random factors; systemic and idiosyncratic. More...

	LatentModel (const std::vector< std::vector< Real > > &factorsWeights, const typename copulaType::initTraits &ini=typename copulaType::initTraits())

	LatentModel (const std::vector< Real > &factorsWeight, const typename copulaType::initTraits &ini=typename copulaType::initTraits())

	LatentModel (Real correlSqr, Size nVariables, const typename copulaType::initTraits &ini=typename copulaType::initTraits())

	LatentModel (const Handle< Quote > &singleFactorCorrel, Size nVariables, const typename copulaType::initTraits &ini=typename copulaType::initTraits())

const std::vector< std::vector< Real > > &	factorWeights () const
	Provides values of the factors \( a_{i,k} \). More...

const std::vector< Real > &	idiosyncFctrs () const
	Provides values of the normalized idiosyncratic factors \( Z_i \). More...

Real	latentVariableCorrel (Size iVar1, Size iVar2) const
	Latent variable correlations: More...

Probability	cumulativeY (Real val, Size iVariable) const

Probability	cumulativeZ (Real z) const
	Cumulative distribution of Z, the idiosyncratic/error factors. More...

Probability	density (const std::vector< Real > &m) const
	Density function of M, the market/systemic factors. More...

Real	inverseCumulativeDensity (Probability p, Size iFactor) const
	Inverse cumulative distribution of the systemic factor iFactor. More...

Real	inverseCumulativeY (Probability p, Size iVariable) const

Real	inverseCumulativeZ (Probability p) const

std::vector< Real >	allFactorCumulInverter (const std::vector< Real > &probs) const

Real	latentVarValue (const std::vector< Real > &allFactors, Size iVar) const

const copulaType &	copula () const

Real	integratedExpectedValue (const ext::function< Real(const std::vector< Real > &v1)> &f) const

std::vector< Real >	integratedExpectedValueV (const ext::function< std::vector< Real >(const std::vector< Real > &v1)> &f) const

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 ()

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 ()

Protected Member Functions
void	update () override

Probability	conditionalDefaultProbability (const Date &date, Size iName, const std::vector< Real > &mktFactors) const

Probability	condProbProduct (Real invCumYProb1, Real invCumYProb2, Size iName1, Size iName2, const std::vector< Real > &mktFactors) const

Real	conditionalProbAtLeastNEvents (Size n, const Date &date, const std::vector< Real > &mktFactors) const
	Conditional probability of n default events or more. More...

const ext::shared_ptr< LMIntegration > &	integration () const override
	access to integration: More...

Protected Member Functions inherited from LatentModel< copulaPolicy >

Protected Attributes
ext::shared_ptr< Basket >	basket_

ext::shared_ptr< LMIntegration >	integration_

Protected Attributes inherited from LatentModel< copulaPolicy >
std::vector< std::vector< Real > >	factorWeights_

Handle< Quote >	cachedMktFactor_

std::vector< Real >	idiosyncFctrs_

Size	nFactors_
	Number of systemic factors. More...

Size	nVariables_
	Number of latent model variables, idiosyncratic terms or model dim. More...

copulaType	copula_

Private Types
typedef copulaPolicy::initTraits	initTraits

Additional Inherited Members
Public Types inherited from LatentModel< copulaPolicy >
typedef copulaPolicy	copulaType

Public Types inherited from Observer
typedef set_type::iterator	iterator

Detailed Description

template<class copulaPolicy>
class QuantLib::DefaultLatentModel< copulaPolicy >

Default event Latent Model.

This is a model for joint default events based on a generic Latent Model. It models solely the default events in a portfolio, not making any reference to severities, exposures, etc... An implicit correspondence is stablished between the variables modelled and the names in the basket given by the basket and model variable access indices. The class is parametric on the Latent Model copula.

Definition at line 44 of file defaultprobabilitylatentmodel.hpp.

Member Typedef Documentation

◆ initTraits

typedef copulaPolicy::initTraits initTraits

private

Definition at line 60 of file defaultprobabilitylatentmodel.hpp.

Constructor & Destructor Documentation

◆ DefaultLatentModel() [1/2]

DefaultLatentModel	(	const std::vector< std::vector< Real > > &	factorWeights,
		LatentModelIntegrationType::LatentModelIntegrationType	integralType,
		const initTraits &	ini = `initTraits()`
	)

Parameters

factorWeights	Latent model independent factors weights for each variable.
integralType	Integration type.
ini	Copula initialization if any.

Warning:: Baskets with realized defaults not tested/WIP.

Definition at line 70 of file defaultprobabilitylatentmodel.hpp.

◆ DefaultLatentModel() [2/2]

DefaultLatentModel	(	const Handle< Quote > &	mktCorrel,
		Size	nVariables,
		LatentModelIntegrationType::LatentModelIntegrationType	integralType,
		const initTraits &	ini = `initTraits()`
	)

Definition at line 79 of file defaultprobabilitylatentmodel.hpp.

Member Function Documentation

◆ resetBasket()

void resetBasket ( const ext::shared_ptr< Basket > & basket ) const

Definition at line 97 of file defaultprobabilitylatentmodel.hpp.

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◆ conditionalDefaultProbability() [1/2]

Probability conditionalDefaultProbability	(	Probability	prob,
		Size	iName,
		const std::vector< Real > &	mktFactors
	)		const

Returns the probability of default of a given name conditional on the realization of a given set of values of the model independent factors. The date at which the probability is given is implicit in the probability since theres not other time dependence in this model.

Parameters

prob	Unconditional probability of default.
iName	desired name.
mktFactors	Value of LM independent factors.

Warning:: Most often it is preferred to use the method below avoiding the cumulative inversion.

Definition at line 114 of file defaultprobabilitylatentmodel.hpp.

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◆ update()

void update ( )

overrideprotectedvirtual

This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.

Implements Observer.

Definition at line 131 of file defaultprobabilitylatentmodel.hpp.

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◆ conditionalDefaultProbabilityInvP()

Probability conditionalDefaultProbabilityInvP	(	Real	invCumYProb,
		Size	iName,
		const std::vector< Real > &	m
	)		const

Returns the probability of default of a given name conditional on the realization of a given set of values of the model independent factors. The date at which the probability is given is implicit in the probability since theres not other time dependent in this model. Same intention as above but provides a performance opportunity, if the integration is along the market factors (as usually is) avoids computing the inverse of the probability on each call.

Parameters

invCumYProb	Inverse cumul of the unconditional probability of default, has to follow the same copula law for results to be coherent
iName	desired name.
m	Value of LM independent factors.

Definition at line 151 of file defaultprobabilitylatentmodel.hpp.

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◆ conditionalDefaultProbability() [2/2]

Probability conditionalDefaultProbability	(	const Date &	date,
		Size	iName,
		const std::vector< Real > &	mktFactors
	)		const

protected

Returns the probability of default of a given name conditional on the realization of a given set of values of the model independent factors.

Parameters

date	The date for the probability of default.
iName	desired name.
mktFactors	Value of LM independent factors.

Same intention as the above methods. Usage of this one is typically more expensive because most often the date we call this method with repeats itself and with this one the probability can not be cached outside the call.

Definition at line 179 of file defaultprobabilitylatentmodel.hpp.

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◆ condProbProduct()

Probability condProbProduct	(	Real	invCumYProb1,
		Real	invCumYProb2,
		Size	iName1,
		Size	iName2,
		const std::vector< Real > &	mktFactors
	)		const

protected

Conditional default probability product, intermediate step in the correlation calculation.

Definition at line 191 of file defaultprobabilitylatentmodel.hpp.

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◆ conditionalProbAtLeastNEvents()

Real conditionalProbAtLeastNEvents	(	Size	n,
		const Date &	date,
		const std::vector< Real > &	mktFactors
	)		const

protected

Conditional probability of n default events or more.

Definition at line 279 of file defaultprobabilitylatentmodel.hpp.

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◆ integration()

const ext::shared_ptr< LMIntegration > & integration ( ) const

overrideprotectedvirtual

access to integration:

Reimplemented from LatentModel< copulaPolicy >.

Definition at line 205 of file defaultprobabilitylatentmodel.hpp.

◆ probOfDefault()

Probability probOfDefault	(	Size	iName,
		const Date &	d
	)		const

Computes the unconditional probability of default of a given name. Trivial method for testing

Definition at line 211 of file defaultprobabilitylatentmodel.hpp.

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◆ defaultCorrelation()

Real defaultCorrelation	(	const Date &	d,
		Size	iNamei,
		Size	iNamej
	)		const

Pearsons' default probability correlation. Users should consider specialization on the copula type for specific distributions since that might simplify the integrations, most importantly if this is to be used in calibration of observations for factor coefficients as it is expensive to integrate directly.

Definition at line 249 of file defaultprobabilitylatentmodel.hpp.

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