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Infectious Default Model with Recovery and Continuous Limit

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  • 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 S_{i} (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery infections are described by Y_{ij} 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 S_{i} \leftrightarrow 1-S_{i}. 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.

Suggested Citation

  • Ayaka Sakata & Masato Hisakado & Shintaro Mori, 2006. "Infectious Default Model with Recovery and Continuous Limit," Papers physics/0610275, arXiv.org, revised Jan 2008.
    • Handle: RePEc:arx:papers:physics/0610275
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