TAILIEUCHUNG - Copulas and credit models

By standard indicators of competitiveness, the subprime loan origination market seems quite competitive: no participant has more than 13 percent market share (Bar-Gill 2008). By similar indicators, the credit-card market is even more competitive. For the subprime mortgage market, however, observers have argued that because borrowers find contract terms confusing, they do not do much comparison shopping, so the market is de facto not very competitive. Our analysis will make clear that when ˆ β is known, the features and welfare properties of contracts are the same in a less competitive market. But Section IIIB’s and Section IV’s results on the sorting of consumers according to. | Copulas and credit models Rudiger Frey Swiss Banking Institute University of Zurich freyr@ Alexander J. McNeil Department of Mathematics ETH Zurich mcneil@ Mark A. Nyfeler Investment Office RTC UBS Zurich October 2001 1 Introduction In this article we focus on the latent variable approach to modelling credit portfolio losses. This methodology underlies all models that descend from Merton s firm-value model Merton 1974 . In particular it underlies the most important industry models such as the model proposed by the KMV corporation and CreditMetrics. In these models default of an obligor occurs if a latent variable often interpreted as the value of the obligor s assets falls below some threshold often interpreted as the value of the obligor s liabilities. Dependence between default events is caused by dependence between the latent variables. The correlation matrix of the latent variables is often calibrated by developing factor models that relate changes in asset value to changes in a small number of economic factors. For further reading see papers by Koyluoglu and Hickman 1998 Gordy 2000 and Crouhy Galai and Mark 2000 . A core assumption of the KMV and CreditMetrics models is the multivariate normality of the latent variables. However there is no compelling reason for choosing a multivariate normal Gaussian distribution for asset values. The aim of this article is to show that the aggregate portfolio loss distribution is often very sensitive to the exact nature of the multivariate distribution of the latent variables. This is not simply a question of asset correlation. Even when individual default probabilities of obligors and the matrix of latent variable correlations are held fixed it is still possible to develop alternative models which lead to much heavier-tailed loss distributions. A useful source of alternative models is the family of multivariate normal mixture distributions which includes Student s t distribution