Infectious Default Model with Recovery and Continuous Limits

by Ayaka Sakata of the University of Tokyo,
Masato Hisakado of Standard & Poor's, and
Shintaro Mori of Kitasato University

January 20, 2008

Abstract: 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.

Keywords: default correlation, correlated binomial, default distribution, continuous limit.

Published in: Journal of the Physical Society of Japan, Vol. 76, No. 5, (May 2007), pp. 054801-054807.

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