Evaluation of tranche in securitization and long-range Ising model

✍ Scribed by K. Kitsukawa; S. Mori; M. Hisakado

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 331 KB
• Volume: 368
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2005.12.057

✦ Synopsis

This econophysics work studies the long-range Ising model of a finite system with N spins and the exchange interaction J=N and the external field H as a model for homogeneous credit portfolio of assets with default probability P d and default correlation r d . Based on the discussion on the ðJ; HÞ phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for P d ; r d and the normalization factor Z in terms of the model parameters N and J; H. The effect of the default correlation r d on the probabilities PðN d ; r d Þ for N d defaults and on the cumulative distribution function Dði; r d Þ 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 r d and that of the senior tranche increases linearly, which are important in their pricing and ratings.