#include <gaussianlhplossmodel.hpp>

Inheritance diagram for GaussianLHPLossModel:

Collaboration diagram for GaussianLHPLossModel:

Public Types
typedef GaussianCopulaPolicy	copulaType

Public Types inherited from LatentModel< GaussianCopulaPolicy >
typedef GaussianCopulaPolicy	copulaType

Public Types inherited from Observer
typedef set_type::iterator	iterator

Public Member Functions
	GaussianLHPLossModel (const Handle< Quote > &correlQuote, const std::vector< Handle< RecoveryRateQuote > > &quotes)

	GaussianLHPLossModel (Real correlation, const std::vector< Real > &recoveries)

	GaussianLHPLossModel (const Handle< Quote > &correlQuote, const std::vector< Real > &recoveries)

void	update () override

Real	expectedTrancheLoss (const Date &d) const override

Real	probOverLoss (const Date &d, Real remainingLossFraction) const override

Real	expectedShortfall (const Date &d, Probability perctl) const override
	Returns the ESF as an absolute amount (rather than a fraction) More...

Real	percentile (const Date &d, Real perctl) const override
	Value at Risk given a default loss percentile. More...

Probability	averageProb (const Date &d) const

Real	averageRecovery (const Date &d) const

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 LatentModel< GaussianCopulaPolicy >
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 ()

Protected Member Functions
Real	percentilePortfolioLossFraction (const Date &d, Real perctl) const

Real	expectedRecovery (const Date &d, Size iName, const DefaultProbKey &ik) const override

Protected Member Functions inherited from DefaultLossModel
	DefaultLossModel ()=default

virtual std::vector< Real >	splitVaRLevel (const Date &d, Real loss) const
	Associated VaR fraction to each counterparty. More...

virtual std::vector< Real >	splitESFLevel (const Date &d, Real loss) const
	Associated ESF fraction to each counterparty. More...

virtual std::map< Real, Probability >	lossDistribution (const Date &) const
	Full loss distribution. More...

virtual Real	densityTrancheLoss (const Date &d, Real lossFraction) const
	Probability density of a given loss fraction of the basket notional. More...

virtual std::vector< Probability >	probsBeingNthEvent (Size n, const Date &d) const

virtual Real	defaultCorrelation (const Date &d, Size iName, Size jName) const
	Pearsons' default probability correlation. More...

virtual Probability	probAtLeastNEvents (Size n, const Date &d) const

Protected Member Functions inherited from LatentModel< GaussianCopulaPolicy >
virtual const ext::shared_ptr< LMIntegration > &	integration () const

Private Member Functions
void	resetModel () override
	Concrete models do now any updates/inits they need on basket reset. More...

Real	expectedTrancheLossImpl (Real remainingNot, Real prob, Real averageRR, Real attachLimit, Real detachLimit) const

Private Attributes
Real	sqrt1minuscorrel_

Handle< Quote >	correl_

std::vector< Handle< RecoveryRateQuote > >	rrQuotes_

Real	beta_

BivariateCumulativeNormalDistribution	biphi_

Static Private Attributes
static CumulativeNormalDistribution const	phi_

Additional Inherited Members
Protected Attributes inherited from DefaultLossModel
RelinkableHandle< Basket >	basket_

Protected Attributes inherited from LatentModel< GaussianCopulaPolicy >
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

Portfolio loss model with analytical expected tranche loss for a large homogeneous pool with Gaussian one-factor copula. See for example "The Normal Inverse Gaussian Distribution for Synthetic CDO pricing.", Anna Kalemanova, Bernd Schmid, Ralf Werner, Journal of Derivatives, Vol. 14, No. 3, (Spring 2007), pp. 80-93. http://www.defaultrisk.com/pp_crdrv_91.htm

It can be used to price a credit derivative or to provide risk metrics of a portfolio.

Definition at line 61 of file gaussianlhplossmodel.hpp.

Member Typedef Documentation

◆ copulaType

typedef GaussianCopulaPolicy copulaType

Definition at line 64 of file gaussianlhplossmodel.hpp.

Constructor & Destructor Documentation

◆ GaussianLHPLossModel() [1/3]

GaussianLHPLossModel	(	const Handle< Quote > &	correlQuote,
		const std::vector< Handle< RecoveryRateQuote > > &	quotes
	)

Definition at line 33 of file gaussianlhplossmodel.cpp.

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◆ GaussianLHPLossModel() [2/3]

GaussianLHPLossModel	(	Real	correlation,
		const std::vector< Real > &	recoveries
	)

Definition at line 51 of file gaussianlhplossmodel.cpp.

◆ GaussianLHPLossModel() [3/3]

GaussianLHPLossModel	(	const Handle< Quote > &	correlQuote,
		const std::vector< Real > &	recoveries
	)

Definition at line 67 of file gaussianlhplossmodel.cpp.

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Member Function Documentation

◆ update()

void update ( )

overridevirtual

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 78 of file gaussianlhplossmodel.hpp.

◆ resetModel()

void resetModel ( )

overrideprivatevirtual

Concrete models do now any updates/inits they need on basket reset.

Implements DefaultLossModel.

Definition at line 88 of file gaussianlhplossmodel.hpp.

◆ expectedTrancheLossImpl()

Real expectedTrancheLossImpl	(	Real	remainingNot,
		Real	prob,
		Real	averageRR,
		Real	attachLimit,
		Real	detachLimit
	)		const

private

Parameters

attachLimit as a fraction of the underlying live portfolio notional

Definition at line 85 of file gaussianlhplossmodel.cpp.

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◆ expectedTrancheLoss()

Real expectedTrancheLoss ( const Date & d ) const

overridevirtual

Reimplemented from DefaultLossModel.

Definition at line 98 of file gaussianlhplossmodel.hpp.

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◆ probOverLoss()

Real probOverLoss	(	const Date &	d,
		Real	remainingLossFraction
	)		const

overridevirtual

The passed remainingLossFraction is in live tranche units, not portfolio as a fraction of the remaining(live) tranche (i.e. a_remaining=0% and det_remaining=100%)

Reimplemented from DefaultLossModel.

Definition at line 118 of file gaussianlhplossmodel.cpp.

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◆ expectedShortfall()

Real expectedShortfall	(	const Date &	d,
		Probability	perctl
	)		const

overridevirtual

Returns the ESF as an absolute amount (rather than a fraction)

Reimplemented from DefaultLossModel.

Definition at line 156 of file gaussianlhplossmodel.cpp.

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◆ percentilePortfolioLossFraction()

Real percentilePortfolioLossFraction	(	const Date &	d,
		Real	perctl
	)		const

protected

Definition at line 187 of file gaussianlhplossmodel.cpp.

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◆ expectedRecovery()

Real expectedRecovery	(	const Date &	,
		Size	iName,
		const DefaultProbKey &
	)		const

overrideprotectedvirtual

Expected RR for name conditinal to default by that date.

Reimplemented from DefaultLossModel.

Definition at line 136 of file gaussianlhplossmodel.hpp.

◆ percentile()

Real percentile	(	const Date &	d,
		Real	percentile
	)		const

overridevirtual

Value at Risk given a default loss percentile.

Reimplemented from DefaultLossModel.

Definition at line 142 of file gaussianlhplossmodel.hpp.

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◆ averageProb()

Probability averageProb ( const Date & d ) const

Definition at line 153 of file gaussianlhplossmodel.hpp.

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◆ averageRecovery()

Real averageRecovery ( const Date & d ) const

Definition at line 171 of file gaussianlhplossmodel.hpp.

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Member Data Documentation

◆ sqrt1minuscorrel_

Real sqrt1minuscorrel_

mutableprivate

Definition at line 193 of file gaussianlhplossmodel.hpp.

◆ correl_

Handle<Quote> correl_

private

Definition at line 195 of file gaussianlhplossmodel.hpp.

◆ rrQuotes_

std::vector<Handle<RecoveryRateQuote> > rrQuotes_

private

Definition at line 196 of file gaussianlhplossmodel.hpp.

◆ beta_

Real beta_

private

Definition at line 208 of file gaussianlhplossmodel.hpp.

◆ biphi_

BivariateCumulativeNormalDistribution biphi_

private

Definition at line 209 of file gaussianlhplossmodel.hpp.

◆ phi_

CumulativeNormalDistribution const phi_

staticprivate

Initial value:

=

CumulativeNormalDistribution()

Definition at line 210 of file gaussianlhplossmodel.hpp.

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ copulaType

Constructor & Destructor Documentation

◆ GaussianLHPLossModel() [1/3]

◆ GaussianLHPLossModel() [2/3]

◆ GaussianLHPLossModel() [3/3]

Member Function Documentation

◆ update()

◆ resetModel()

◆ expectedTrancheLossImpl()

◆ expectedTrancheLoss()

◆ probOverLoss()

◆ expectedShortfall()

◆ percentilePortfolioLossFraction()

◆ expectedRecovery()

◆ percentile()

◆ averageProb()

◆ averageRecovery()

Member Data Documentation

◆ sqrt1minuscorrel_

◆ correl_

◆ rrQuotes_

◆ beta_

◆ biphi_

◆ phi_