By Christian Bluhm
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Paperback: 384 pages
writer: For Dummies; three version (October five, 2009)
Product Dimensions: nine. three x 7. four x zero. eight inches
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Additional info for An Introduction to Credit Risk Modeling
The rigidity of loss statistics is “perfect” in this situation. Realistic scenarios live somewhere between the two discussed extreme cases Corr[Li , Lj ] = 0 and Corr[Li , Lj ] = 1. }, pi = P[Li ≥ 1] , (2. 11) where pi again denotes the default probability of obligor i. Note that (2. 11) allows for multiple defaults of a single obligor. The likelihood of the event that obligor i defaults more than once is given by P[Li ≥ 2] = 1 − e−λi (1 + λi ) , which is typically a small number. 5 basispoints.
2) conditional on Λ = λ the portfolio loss is again a Poisson distribution with intensity mλ, the probability of exactly k defaults equals ∞ P[L = k | Λ = λ] dF (λ) P[L = k] = (2. 18) 0 ∞ = e−mλ 0 mk λ k dF (λ) . k! Again, note that due to the unbounded support of the Poisson distribution the absolute loss L can exceed the number of “physically” possible defaults. As already mentioned at the beginning of this section, the probability of a multiple-defaults event is small for typical parametrizations.
Nevertheless there are some families of distributions that are established as best practice choices for particular cases. 5 are a very natural choice for analytical approximations, because they are limit distributions of a well understood model. ©2003 CRC Press LLC In practice, analytical approximation techniques can be applied quite successfully to so-called homogeneous portfolios. ) industries and countries, and so on. There are many portfolios satisfying such constraints. For example, many retail banking portfolios and also many portfolios of smaller banks can be evaluated by analytical approximations with sufficient precision.