SpotRecoveryLatentModel< copulaPolicy > Class Template Reference

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

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

Inheritance 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.
Size	numTotalFactors () const
	Number of total free random factors; systemic and idiosyncratic.
	LatentModel (const std::vector< std::vector< Real > > &factorsWeights, const typename copulaType::initTraits &ini=typename copulaType::initTraits())
const std::vector< std::vector< Real > > &	factorWeights () const
	Provides values of the factors \( a_{i,k} \).
const std::vector< Real > &	idiosyncFctrs () const
	Provides values of the normalized idiosyncratic factors \( Z_i \).
Real	latentVariableCorrel (Size iVar1, Size iVar2) const
	Latent variable correlations:
Probability	cumulativeY (Real val, Size iVariable) const
Probability	cumulativeZ (Real z) const
	Cumulative distribution of Z, the idiosyncratic/error factors.
Probability	density (const std::vector< Real > &m) const
	Density function of M, the market/systemic factors.
Real	inverseCumulativeDensity (Probability p, Size iFactor) const
	Inverse cumulative distribution of the systemic factor iFactor.
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 std::function< Real(const std::vector< Real > &v1)> &f) const
std::vector< Real >	integratedExpectedValueV (const std::function< std::vector< Real >(const std::vector< Real > &v1)> &f) const
Public Member Functions inherited from Observer
	Observer (const Observer &)
Observer &	operator= (const 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	deepUpdate ()
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
	Observable (Observable &&)=delete
Observable &	operator= (Observable &&)=delete
void	notifyObservers ()

Protected Member Functions
const ext::shared_ptr< LMIntegration > &	integration () const override
	access to integration:

Additional Inherited Members
typedef copulaPolicy	copulaType
Public Types inherited from Observer
typedef set_type::iterator	iterator
std::vector< std::vector< Real > >	factorWeights_
Handle< Quote >	cachedMktFactor_
std::vector< Real >	idiosyncFctrs_
Size	nFactors_
	Number of systemic factors.
Size	nVariables_
	Number of latent model variables, idiosyncratic terms or model dim.
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.

Member Function Documentation

integration()

template<class copulaPolicy>

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

overrideprotectedvirtual

access to integration:

Reimplemented from LatentModel< copulaPolicy >.

expCondRecovery()

template<class CP>

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)

conditionalRecovery()

template<class CP>

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.

latentRRVarValue()

template<class CP>

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

expectedLoss()

template<class CP>

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: \(pdef_i(d) \times RR_i \)