Infectious Default Model with Recovery and Continuous Limits(Cross-disciplinary physics and related areas of science and technology)

概要

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We introduce an infectious default and recovery model for N obligors. The obligors are assumed to be exchangeable and their states are described by N Bernoulli-type random variables S_i (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_i, Y_<ij>, and Y'_<ij>, and the default and recovery infections are described by Y_<ij> and Y'_<ij>. We obtain the default probability function P(k) for k defaults. By considering a continuous limit, we find two nontrivial probability distributions with a reflection symmetry of S_i⟷1-S_i. Their profiles are singular and oscillating and we theoretically investigate it. We also compare P(k) with an implied default distribution function inferred from the quotes of iTraxx-CJ, which is a portfolio credit derivative of Japanese 50 companies. In order to explain the behavior of the implied distribution, the recovery effect may be necessary.
社団法人日本物理学会の論文
2007-05-15