A New Framework for Dynamic Credit Portfolio Loss Modelling

Abstract

We present the SPA framework, a novel approach to the modeling of the dynamics of portfolio default losses. In this framework, models are specified by a two-layer process. The first layer models the dynamics of portfolio loss distributions in the absence of information about default times. This background process can be explicitly calibrated to the full grid of marginal loss distributions as implied by initial CDO tranche values indexed on maturity, as well as to the prices of suitable options. We give sufficient conditions for consistent dynamics. The second layer models the loss process itself as a Markov process conditioned on the path taken by the background process. The choice of loss process is non-unique. We present a number of choices, and discuss their advantages and disadvantages. Several concrete model examples are given, and valuation in the new framework is described in detail. Among the specific securities for which algorithms are presented are CDO tranche options and leveraged super-senior tranches.

Two-Dimensional Markovian Model for Dynamics of Aggregate Credit Loss

“…The local intensity model has recently been considered by van der Voort (2005) who applied it to the pricing of forward starting CDOs. This model also appears in the works of Sidenius et al (2005) and Schönbucher (2005) who use it as a part of their constructions of the dynamic framework. We regard the local intensity model as a very useful tool for the calibration of models with richer dynamics, but which, by itself, is generally insufficient as a dynamic model (see, e.g., the numerical results for tranche options in Section 4.2).…”

“…The general framework of aggregate-lossbased approaches to basket credit derivatives was put forward by Giesecke and Goldberg (2005), Schönbucher (2005), and Sidenius et al (2005). Examples of specific models can be found in the works by Bennani (2005) Both Schönbucher (2005) and Sidenius et al (2005) aimed to build a credit portfolio counterpart of the Heath-Jarrow-Morton (HJM) framework of the interest rate modeling. In the HJM framework, the problem of fitting the initial term structure of interest rates is non-existent because the discount curve serves as an initial condition and not as a calibration constraint.…”

“…In the calibration of credit portfolio models, the role of the discount curve is played by the surface of the loss distribution, π(L, t) = P[L t ≤ L]. In the spirit of the HJM framework, Schönbucher (2005) and Sidenius et al (2005) eliminated the problem of the calibration to the distribution of loss by making it an initial condition. This, however, was achieved at a price of losing the ability to simulate the loss process without introducing a large number of additional stochastic degrees of freedom, which led to severe computational problems and accentuated the need for a more specific approach.…”

Dynamics of multivariate default system in random environment

“…In the former approach, one starts with a model for the marginal distribution of each default time and then the correlation between them is made precise (see Frey and McNeil [18] for a survey). While in the top-down models which are particularly developed for the portfolio credit derivatives (see for example Arnsdorff and Halperin [2], Bielecki, Crépey and Jeanblanc [5], Cont and Minca [10], Dassios and Zhao [11], Ehlers and Schönbucher [14], Filipović, Overbeck and Schmidt [17], Giesecke, Goldberg and Ding [20], Sidenius, Piterbarg and Andersen [32] among others), we study directly the cumulative loss process and its intensity dynamics.…”

Analytic Dynamic Factor Copula Model

“…For example, Bennani (2005), Schönbucher (2005) and Sidenius et al (2008) proposed similar frameworks to model the dynamics of the aggregate portfolio losses by modeling the forward loss rates. With these pool loss dynamics, the pricing of credit derivatives becomes straightforward.…”