dorsal/arxiv
View SchemaInfectious Default Model with Recovery and Continuous Limit
| Authors | Ayaka Sakata, Masato Hisakado, Shintaro Mori |
|---|---|
| Categories | |
| ArXiv ID | physics/0610275 |
| URL | https://arxiv.org/abs/physics/0610275 |
| DOI | 10.1143/JPSJ.76.054801 |
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.
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"abstract": "We introduce an infectious default and recovery model for N obligors.\nObligors are assumed to be exchangeable and their states are described by N\nBernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying\nindependent Bernoulli variables X_{i},Y_{ij},Y\u0027_{ij}, and default and recovery\ninfections are described by Y_{ij} and Y\u0027_{ij}. We obtain the default\nprobability function P(k) for k defaults. Taking its continuous limit, we find\ntwo nontrivial probability distributions with the reflection symmetry of S_{i}\n\\leftrightarrow 1-S_{i}. Their profiles are singular and oscillating and we\nunderstand it theoretically. We also compare P(k) with an implied default\ndistribution function inferred from the quotes of iTraxx-CJ. In order to\nexplain the behavior of the implied distribution, the recovery effect may be\nnecessary.",
"arxiv_id": "physics/0610275",
"authors": [
"Ayaka Sakata",
"Masato Hisakado",
"Shintaro Mori"
],
"categories": [
"physics.data-an",
"q-fin.PR"
],
"doi": "10.1143/JPSJ.76.054801",
"title": "Infectious Default Model with Recovery and Continuous Limit",
"url": "https://arxiv.org/abs/physics/0610275"
},
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