BinomialLossModel< LLM > Class Template Reference

#include <binomiallossmodel.hpp>

Inheritance diagram for BinomialLossModel< LLM >:

Collaboration diagram for BinomialLossModel< LLM >:

Public Types
typedef LLM::copulaType	copulaType

Public Member Functions
	BinomialLossModel (ext::shared_ptr< LLM > copula)
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
std::vector< Real >	expectedDistribution (const Date &date) const
std::vector< Real >	lossPoints (const Date &) const
	attainable loss points this model provides More...
std::map< Real, Probability >	lossDistribution (const Date &d) const override
	Returns the cumulative full loss distribution. More...
Real	percentile (const Date &d, Real percentile) const override
	Loss level for this percentile. More...
Real	expectedShortfall (const Date &d, Real percentile) const override
	Expected shortfall given a default loss percentile. More...
Real	expectedTrancheLoss (const Date &d) const override
Real	averageLoss (const Date &, const std::vector< Real > &reminingNots, const std::vector< Real > &) const
	Average loss per credit. More...
Real	condTrancheLoss (const Date &, const std::vector< Real > &lossVals, const std::vector< Real > &bsktNots, const std::vector< Probability > &uncondDefProbs, const std::vector< Real > &) const
std::vector< Real >	expConditionalLgd (const Date &d, const std::vector< Real > &mktFactors) const
std::vector< Real >	lossProbability (const Date &date, const std::vector< Real > &bsktNots, const std::vector< Real > &uncondDefProbInv, const std::vector< Real > &mktFactor) const
	Loss probability density conditional on the market factor value. More...
Protected Member Functions inherited from DefaultLossModel
	DefaultLossModel ()=default
virtual Probability	probOverLoss (const Date &d, Real lossFraction) const
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 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
virtual Real	expectedRecovery (const Date &, Size iName, const DefaultProbKey &) const

Protected Attributes
const ext::shared_ptr< LLM >	copula_
Real	attachAmount_
Real	detachAmount_
Protected Attributes inherited from DefaultLossModel
RelinkableHandle< Basket >	basket_

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

Detailed Description

template<class LLM>
class QuantLib::BinomialLossModel< LLM >

Binomial Defaultable Basket Loss Model

Models the portfolio loss distribution by approximatting it to an adjusted binomial. Fits the two moments of the loss distribution through an adapted binomial approximation. This simple model allows for portfolio inhomogeneity with no excesive cost over the LHP.

See:

Approximating Independent Loss Distributions with an Adjusted Binomial Distribution , Dominic O'Kane, 2007 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE

Modelling single name and multi-name credit derivatives Chapter 18.5.2, Dominic O'Kane, Wiley Finance, 2008

The version presented here is adaptated to the multifactorial case by computing a conditional binomial approximation; notice that the Binomial is stable. This way the model can be used also in risk management models rather than only in pricing. The copula is also left undefined/arbitrary.

LLM: Loss Latent Model template parameter able to model default and loss.

The model is allowed and arbitrary copula, although initially designed for a Gaussian setup. If these exotic versions were not allowed the template parameter can then be dropped but the use of random recoveries should be added in some other way.

Definition at line 61 of file binomiallossmodel.hpp.

Member Typedef Documentation

copulaType

typedef LLM::copulaType copulaType

Definition at line 63 of file binomiallossmodel.hpp.

Constructor & Destructor Documentation

BinomialLossModel()

BinomialLossModel ( ext::shared_ptr< LLM >  copula )

explicit

Definition at line 64 of file binomiallossmodel.hpp.

Member Function Documentation

resetModel()

void resetModel ( )

overrideprivatevirtual

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

Implements DefaultLossModel.

Definition at line 67 of file binomiallossmodel.hpp.

expectedDistribution()

std::vector< Real > expectedDistribution ( const Date &  date ) const

protected

Returns the probability of the default loss values given by the method lossPoints.

Definition at line 80 of file binomiallossmodel.hpp.

Here is the call graph for this function:

lossPoints()

std::vector< Real > lossPoints ( const Date &  d ) const

protected

attainable loss points this model provides

Definition at line 272 of file binomiallossmodel.hpp.

lossDistribution()

std::map< Real, Probability > lossDistribution ( const Date &  d ) const

overrideprotectedvirtual

Returns the cumulative full loss distribution.

Reimplemented from DefaultLossModel.

Definition at line 329 of file binomiallossmodel.hpp.

percentile()

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

overrideprotectedvirtual

Loss level for this percentile.

Reimplemented from DefaultLossModel.

Definition at line 346 of file binomiallossmodel.hpp.

expectedShortfall()

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

overrideprotectedvirtual

Expected shortfall given a default loss percentile.

Reimplemented from DefaultLossModel.

Definition at line 373 of file binomiallossmodel.hpp.

Here is the call graph for this function:

expectedTrancheLoss()

Real expectedTrancheLoss ( const Date &  d ) const

overrideprotectedvirtual

Reimplemented from DefaultLossModel.

Definition at line 312 of file binomiallossmodel.hpp.

averageLoss()

Real averageLoss ( const Date &  d, const std::vector< Real > &  reminingNots, const std::vector< Real > &  mktFctrs  ) const

protected

Average loss per credit.

Definition at line 247 of file binomiallossmodel.hpp.

condTrancheLoss()

Real condTrancheLoss ( const Date &  d, const std::vector< Real > &  lossVals, const std::vector< Real > &  bsktNots, const std::vector< Probability > &  uncondDefProbs, const std::vector< Real > &  mkf  ) const

protected

Definition at line 292 of file binomiallossmodel.hpp.

expConditionalLgd()

std::vector< Real > expConditionalLgd ( const Date &  d, const std::vector< Real > &  mktFactors  ) const

protected

Definition at line 112 of file binomiallossmodel.hpp.

lossProbability()

std::vector< Real > lossProbability ( const Date &  date, const std::vector< Real > &  bsktNots, const std::vector< Real > &  uncondDefProbInv, const std::vector< Real > &  mktFactor  ) const

protected

Loss probability density conditional on the market factor value.

Definition at line 147 of file binomiallossmodel.hpp.

Here is the caller graph for this function:

Member Data Documentation

copula_

const ext::shared_ptr<LLM> copula_

protected

Definition at line 133 of file binomiallossmodel.hpp.

attachAmount_

Real attachAmount_

mutableprotected

Definition at line 137 of file binomiallossmodel.hpp.

detachAmount_

Real detachAmount_

protected

Definition at line 137 of file binomiallossmodel.hpp.