Aggregating sectors in the infectious defaults model
How to model the dependence between defaults in a portfolio subject to credit risk is a question of great importance. The infectious default model of Davis and Lo offers a way to model the dependence. Every company defaulting in this model may 'infect' another company causing it to default. An unsolved question, however, is how to aggregate independent sectors, since a naive straightforward computation quickly gets cumbersome, even when homogeneous assumptions are made. Here, two algorithms are derived that overcome the computational problem and further make it possible to use different exposures and probabilities of default for each sector. For an 'outbreak' of defaults to occur in a sector, at least one company has to default by itself. This fact is used in the derivations of the two algorithms. The first algorithm is derived from the probability generating function of the total credit loss in each sector and the fact that the outbreaks are independent Bernoulli random variables. The second algorithm is an approximation and is based on a Poisson number of outbreaks in each sector. This algorithm is less cumbersome and more numerically stable, but still seems to work well in a realistic setting.
Year of publication: |
2004
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Authors: | Hammarlid, Ola |
Published in: |
Quantitative Finance. - Taylor & Francis Journals, ISSN 1469-7688. - Vol. 4.2004, 1, p. 64-69
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Publisher: |
Taylor & Francis Journals |
Saved in:
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