Infectious Default Model with Recovery and Continuous Limit
Ayaka Sakata, Masato Hisakado, Shintaro Mori
Abstract
We introduce an infectious default and recovery model for N obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables Si (i=1,...,N). They are expressed by multiplying independent Bernoulli variables Xi,Yij,Y'ij, and default and recovery infections are described by Yij and Y'ij. We obtain the default probability function P(k) for k defaults. Taking its continuous limit, we find two nontrivial probability distributions with the reflection symmetry of Si 1-Si. Their profiles are singular and oscillating and we understand it theoretically. We also compare P(k) with an implied default distribution function inferred from the quotes of iTraxx-CJ. In order to explain the behavior of the implied distribution, the recovery effect may be necessary.
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