Lévy Simple Structural Models

Abstract

This paper considers credit portfolio models based on Levy processes in general, and the gamma model in particular. It describes both single-name and multi-name situations using the gamma model, along with calibration fits and a comparison of various simple Levy models. There is also extensive historical data, including the May 2005 Auto crisis, which can be described in terms of the model. Parameter-based risk management using the gamma model is also discussed along with implementation details.

The discrete gamma pool model

“…We show some sample curves for Gamma processes in Figure 1 for γ = 1 and 2 for γ = 100, respectively. It is apparent in Figure 2 that, as Baxter also remarks in (Baxter, 2006;Baxter, 2007), that the distance-to-default process becomes a standard Wiener process as γ → ∞.…”

“…The new model draws on ideas from Baxter's Gamma-Phi model (Baxter, 2006;Baxter, 2007), large homogeneous pool approximations (Vasicek, 1987), as well as the Black-Karasinski model for credit default hazard rates (Black and Karasinski, 1991). As a whole, it combines a series of characteristics that are desirable for the modelling of stochastic spread sensitive credit correlation products.…”

“…The explicit representation of correlation makes it comparatively user friendly when, for instance, applied to optionality products on synthetic collateralised debt obligations and tranches. In addition, the model also allows for a total portfolio default scenario, which has been found to be crucial for fair representation of super-senior risk by other authors, too (Baxter, 2006;Baxter, 2007;Brigo et al, 2007;Hull and White, 2005…”

Lévy information and the aggregation of risk aversion

“…As a consequence, we are able to construct a large and rich family of financial models for asset prices with jump risk in situations where the market exhibits variation among its participants in the excess rate of return required (above the interest rate) as compensation for the assumption of such risk. [45], and Yor [46]. To set the notation, we begin with a few definitions.…”

“…Numerous investigations have been pursued concerning the development of Lévy-based models in finance, and as a consequence the literature is very extensive. We mention, for example, the works of Madan & Senata [34] [45], and Yor [46]. To set the notation, we begin with a few definitions.…”