dorsal/arxiv
View SchemaEvaluation of Tranche in Securitization and Long-range Ising Model
| Authors | K. Kitsukawa, S. Mori, M. Hisakado |
|---|---|
| Categories | |
| ArXiv ID | physics/0603040 |
| URL | https://arxiv.org/abs/physics/0603040 |
| DOI | 10.1016/j.physa.2005.12.057 |
| Journal | Physica A368(2006),191-206 |
Abstract
This econophysics work studies the long-range Ising model of a finite system with $N$ spins and the exchange interaction $\frac{J}{N}$ and the external field $H$ as a modely for homogeneous credit portfolio of assets with default probability $P_{d}$ and default correlation $\rho_{d}$. Based on the discussion on the $(J,H)$ phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for $P_{d},\rho_{d}$ and the normalization factor $Z$ in terms of the model parameters $N$ and $J,H$. The effect of the default correlation $\rho_{d}$ on the probabilities $P(N_{d},\rho_{d})$ for $N_{d}$ defaults and on the cumulative distribution function $D(i,\rho_{d})$ are discussed. The latter means the average loss rate of the``tranche'' (layered structure) of the securities (e.g. CDO), which are synthesized from a pool of many assets. We show that the expected loss rate of the subordinated tranche decreases with $\rho_{d}$ and that of the senior tranche increases linearly, which are important in their pricing and ratings.
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"abstract": "This econophysics work studies the long-range Ising model of a finite system\nwith $N$ spins and the exchange interaction $\\frac{J}{N}$ and the external\nfield $H$ as a modely for homogeneous credit portfolio of assets with default\nprobability $P_{d}$ and default correlation $\\rho_{d}$. Based on the discussion\non the $(J,H)$ phase diagram, we develop a perturbative calculation method for\nthe model and obtain explicit expressions for $P_{d},\\rho_{d}$ and the\nnormalization factor $Z$ in terms of the model parameters $N$ and $J,H$. The\neffect of the default correlation $\\rho_{d}$ on the probabilities\n$P(N_{d},\\rho_{d})$ for $N_{d}$ defaults and on the cumulative distribution\nfunction $D(i,\\rho_{d})$ are discussed. The latter means the average loss rate\nof the``tranche\u0027\u0027 (layered structure) of the securities (e.g. CDO), which are\nsynthesized from a pool of many assets. We show that the expected loss rate of\nthe subordinated tranche decreases with $\\rho_{d}$ and that of the senior\ntranche increases linearly, which are important in their pricing and ratings.",
"arxiv_id": "physics/0603040",
"authors": [
"K. Kitsukawa",
"S. Mori",
"M. Hisakado"
],
"categories": [
"physics.soc-ph",
"q-fin.ST"
],
"doi": "10.1016/j.physa.2005.12.057",
"journal_ref": "Physica A368(2006),191-206",
"title": "Evaluation of Tranche in Securitization and Long-range Ising Model",
"url": "https://arxiv.org/abs/physics/0603040"
},
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