Random spot recovery rate latent variable portfolio model. More...

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

Inheritance diagram for SpotRecoveryLatentModel< copulaPolicy >:

Collaboration diagram for SpotRecoveryLatentModel< copulaPolicy >:

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

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

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

Real	expCondRecovery (const Date &d, Size iName, const std::vector< Real > &mktFactors) const

Real	expCondRecoveryP (Real uncondDefP, Size iName, const std::vector< Real > &mktFactors) const

Real	expCondRecoveryInvPinvRR (Real invUncondDefP, Real invUncondRR, Size iName, const std::vector< Real > &mktFactors) const

Real	conditionalRecovery (Real latentVarSample, Size iName, const Date &d) const

Real	latentRRVarValue (const std::vector< Real > &allFactors, Size iName) const

Real	conditionalExpLossRR (const Date &d, Size iName, const std::vector< Real > &mktFactors) const

Real	conditionalExpLossRRInv (Real invP, Real invRR, Size iName, const std::vector< Real > &mktFactors) const

Real	expectedLoss (const Date &d, Size iName) 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=copulaType::initTraits())

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

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

	LatentModel (const Handle< Quote > &singleFactorCorrel, Size nVariables, const typename copulaType::initTraits &ini=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
const ext::shared_ptr< LMIntegration > &	integration () const override
	access to integration: More...

Protected Member Functions inherited from LatentModel< copulaPolicy >

Private Types
typedef copulaPolicy::initTraits	initTraits

Private Attributes
const std::vector< Real >	recoveries_

const Real	modelA_

std::vector< Real >	crossIdiosyncFctrs_

Size	numNames_

ext::shared_ptr< Basket >	basket_

ext::shared_ptr< LMIntegration >	integration_

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

Public Types inherited from Observer
typedef set_type::iterator	iterator

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_

Detailed Description

template<class copulaPolicy>
class QuantLib::SpotRecoveryLatentModel< copulaPolicy >

Random spot recovery rate latent variable portfolio model.

: See:

: A Spot Stochastic Recovery Extension of the Gaussian Copula N.Bennani and J.Maetz, MPRA July 2009

: Extension of Spot Recovery model for Gaussian Copula H.Li, October 2009, MPRA

: The model is adpated here for a multifactor set up and a generic copula so it can be used for pricing in single factor mode or for risk metrics in its multifactor version.

Definition at line 42 of file spotlosslatentmodel.hpp.

Member Typedef Documentation

◆ initTraits

typedef copulaPolicy::initTraits initTraits

private

Definition at line 63 of file spotlosslatentmodel.hpp.

Constructor & Destructor Documentation

◆ SpotRecoveryLatentModel()

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

Definition at line 338 of file spotlosslatentmodel.hpp.

Here is the call graph for this function:

Member Function Documentation

◆ integration()

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

overrideprotectedvirtual

access to integration:

Reimplemented from LatentModel< copulaPolicy >.

Definition at line 60 of file spotlosslatentmodel.hpp.

◆ resetBasket()

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

Definition at line 138 of file spotlosslatentmodel.hpp.

◆ conditionalDefaultProbability() [1/2]

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

Definition at line 147 of file spotlosslatentmodel.hpp.

◆ conditionalDefaultProbability() [2/2]

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

Definition at line 161 of file spotlosslatentmodel.hpp.

◆ conditionalDefaultProbabilityInvP()

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

Definition at line 181 of file spotlosslatentmodel.hpp.

◆ expCondRecovery()

Real expCondRecovery	(	const Date &	d,
		Size	iName,
		const std::vector< Real > &	mktFactors
	)		const

Expected conditional spot recovery rate. Conditional on a set of systemic factors and default returns the integrated attainable recovery values.

: Corresponds to a multifactor generalization of the model in eq. 44 on p.15 of Extension of Spot Recovery Model for Gaussian Copula Hui Li. 2009 Only remember that \(\rho_l Z \) there is here (multiple betas): \( \sum_k \beta_{ik}^l Z_k \) and that \( \rho_d \rho_l \) there is here: \( \sum_k \beta_{ik}^d \beta_{ik}^l \)

: (d,l corresponds to first and last set of betas)

Definition at line 201 of file spotlosslatentmodel.hpp.

◆ expCondRecoveryP()

Real expCondRecoveryP	(	Real	uncondDefP,
		Size	iName,
		const std::vector< Real > &	mktFactors
	)		const

Definition at line 219 of file spotlosslatentmodel.hpp.

◆ expCondRecoveryInvPinvRR()

Real expCondRecoveryInvPinvRR	(	Real	invUncondDefP,
		Real	invUncondRR,
		Size	iName,
		const std::vector< Real > &	mktFactors
	)		const

Definition at line 229 of file spotlosslatentmodel.hpp.

◆ conditionalRecovery()

Real conditionalRecovery	(	Real	latentVarSample,
		Size	iName,
		const Date &	d
	)		const

Implements equation 42 on p.14 (second). Remember that for this call to make sense the sample used must be one leading to a default. Theres no check on this. This member typically to be used within a simulation.

Definition at line 256 of file spotlosslatentmodel.hpp.

◆ latentRRVarValue()

Real latentRRVarValue	(	const std::vector< Real > &	allFactors,
		Size	iName
	)		const

Due to the way the latent model is splitted in two parts, we call the base class for the default sample and the LM owned here for the RR model sample. This sample only makes sense if it led to a default.

Parameters

allFactors	All sampled factors, default and RR valiables.
iName	The index of the name for which we want the RR sample

Definition at line 282 of file spotlosslatentmodel.hpp.

◆ conditionalExpLossRR()

Real conditionalExpLossRR	(	const Date &	d,
		Size	iName,
		const std::vector< Real > &	mktFactors
	)		const

Definition at line 291 of file spotlosslatentmodel.hpp.

◆ conditionalExpLossRRInv()

Real conditionalExpLossRRInv	(	Real	invP,
		Real	invRR,
		Size	iName,
		const std::vector< Real > &	mktFactors
	)		const

Definition at line 308 of file spotlosslatentmodel.hpp.

◆ expectedLoss()

Real expectedLoss	(	const Date &	d,
		Size	iName
	)		const

Single name expected loss.

: The main reason of this method is for the testing of this model. The model is coherent in that it preserves the single name expected loss and thus is coherent with the single name CDS market when used in the pricing context. i.e. it should match: \(pdef_i(d) \times RR_i \)

Definition at line 319 of file spotlosslatentmodel.hpp.

Member Data Documentation

◆ recoveries_

const std::vector<Real> recoveries_

private

Definition at line 51 of file spotlosslatentmodel.hpp.

◆ modelA_

const Real modelA_

private

Definition at line 52 of file spotlosslatentmodel.hpp.

◆ crossIdiosyncFctrs_

std::vector<Real> crossIdiosyncFctrs_

private

Definition at line 54 of file spotlosslatentmodel.hpp.

◆ numNames_

Size numNames_

mutableprivate

Definition at line 55 of file spotlosslatentmodel.hpp.

◆ basket_

ext::shared_ptr<Basket> basket_

mutableprivate

Definition at line 56 of file spotlosslatentmodel.hpp.

◆ integration_

ext::shared_ptr<LMIntegration> integration_

private

Definition at line 57 of file spotlosslatentmodel.hpp.

Public Member Functions

Protected Member Functions

Private Types

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ initTraits

Constructor & Destructor Documentation

◆ SpotRecoveryLatentModel()

Member Function Documentation

◆ integration()

◆ resetBasket()

◆ conditionalDefaultProbability() [1/2]

◆ conditionalDefaultProbability() [2/2]

◆ conditionalDefaultProbabilityInvP()

◆ expCondRecovery()

◆ expCondRecoveryP()

◆ expCondRecoveryInvPinvRR()

◆ conditionalRecovery()

◆ latentRRVarValue()

◆ conditionalExpLossRR()

◆ conditionalExpLossRRInv()

◆ expectedLoss()

Member Data Documentation

◆ recoveries_

◆ modelA_

◆ crossIdiosyncFctrs_

◆ numNames_

◆ basket_

◆ integration_