LossDistHomogeneous Class Reference

Loss Distribution for Homogeneous Pool. More...

#include <lossdistribution.hpp>

Inheritance diagram for LossDistHomogeneous:

Collaboration diagram for LossDistHomogeneous:

Public Member Functions
	LossDistHomogeneous (Size nBuckets, Real maximum)
Distribution	operator() (Real volume, const std::vector< Real > &probabilities) const
Distribution	operator() (const std::vector< Real > &volumes, const std::vector< Real > &probabilities) const override
Size	buckets () const override
Real	maximum () const override
Size	size () const
Real	volume () const
std::vector< Real >	probability () const
std::vector< Real >	excessProbability () const
Public Member Functions inherited from LossDist
	LossDist ()=default
virtual	~LossDist ()=default
virtual Distribution	operator() (const std::vector< Real > &volumes, const std::vector< Real > &probabilities) const =0
virtual Size	buckets () const =0
virtual Real	maximum () const =0

Private Attributes
Size	nBuckets_
Real	maximum_
Size	n_ = 0
Real	volume_ = 0.0
std::vector< Real >	probability_
std::vector< Real >	excessProbability_

Additional Inherited Members
Static Public Member Functions inherited from LossDist
static Real	binomialProbabilityOfNEvents (int n, std::vector< Real > &p)
static Real	binomialProbabilityOfAtLeastNEvents (int n, std::vector< Real > &p)
static std::vector< Real >	probabilityOfNEvents (std::vector< Real > &p)
static Real	probabilityOfNEvents (int n, std::vector< Real > &p)
static Real	probabilityOfAtLeastNEvents (int n, std::vector< Real > &p)

Detailed Description

Loss Distribution for Homogeneous Pool.

Loss Distribution for Homogeneous Pool

Loss distribution for equal volumes but varying probabilities of default.

The method builds the exact loss distribution for a homogeneous pool of underlyings iteratively by computing the convolution of the given loss distribution with the "loss distribution" of an additional credit following

Xiaofong Ma, "Numerical Methods for the Valuation of Synthetic Collateralized Debt Obligations", PhD Thesis, Graduate Department of Computer Science, University of Toronto, 2007
http://www.cs.toronto.edu/pub/reports/na/ma-07-phd.pdf (formula 2.1)

avoiding numerical instability of the algorithm by

John Hull and Alan White, "Valuation of a CDO and nth to default CDS without Monte Carlo simulation", Journal of Derivatives 12, 2, 2004

Definition at line 138 of file lossdistribution.hpp.

Constructor & Destructor Documentation

LossDistHomogeneous()

LossDistHomogeneous	(	Size	nBuckets,
		Real	maximum
	)

Definition at line 140 of file lossdistribution.hpp.

Member Function Documentation

operator()() [1/2]

Distribution operator()	(	Real	volume,
		const std::vector< Real > &	probabilities
	)		const

Definition at line 182 of file lossdistribution.cpp.

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operator()() [2/2]

Distribution operator() ( const std::vector< Real > &  volumes, const std::vector< Real > &  probabilities  ) const

overridevirtual

Implements LossDist.

Definition at line 220 of file lossdistribution.cpp.

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buckets()

Size buckets ( ) const

overridevirtual

Implements LossDist.

Definition at line 144 of file lossdistribution.hpp.

maximum()

Real maximum ( ) const

overridevirtual

Implements LossDist.

Definition at line 145 of file lossdistribution.hpp.

size()

Size size

(

)

const

Definition at line 146 of file lossdistribution.hpp.

volume()

Real volume

(

)

const

Definition at line 147 of file lossdistribution.hpp.

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probability()

std::vector< Real > probability

(

)

const

Definition at line 148 of file lossdistribution.hpp.

excessProbability()

std::vector< Real > excessProbability

(

)

const

Definition at line 149 of file lossdistribution.hpp.

Member Data Documentation

nBuckets_

Size nBuckets_

private

Definition at line 151 of file lossdistribution.hpp.

maximum_

Real maximum_

private

Definition at line 152 of file lossdistribution.hpp.

n_

Size n_ = 0

mutableprivate

Definition at line 153 of file lossdistribution.hpp.

volume_

Real volume_ = 0.0

mutableprivate

Definition at line 154 of file lossdistribution.hpp.

probability_

std::vector<Real> probability_

mutableprivate

Definition at line 155 of file lossdistribution.hpp.

excessProbability_

std::vector<Real> excessProbability_

mutableprivate

Definition at line 156 of file lossdistribution.hpp.