Portfolio credit models

From FinMath

Portfolio credit models describe the frequency of default and/or the time evolution of real or risk neutral default probabilities for a plurality of reference entities. Of interest in the modeling of first-to-default instruments are models incorporating as few as five names. More commonly, portfolio credit models anticipate hundreds if not thousands of assets whose joint default distribution, default intensity evolution, recoveries given default and default swap spread dynamics for various maturities are in play.

Portfolio credit models may be classified as static portfolio credit models or dynamic portfolio credit models depending on the scope of enquiry. The former class is typified by the use of Copula functions describing the joint distribution of credit events assuming marginal survival probabilities backed out from single name credit default swap contracts. The Normal Copula model remains the most commonly used example, despite known problems. Static portfolio credit models are so named because no attempt is made to describe the joint distribution of credit events after "time zero".

The latter class is characterized by explicit or infered dynamic evolution of default intensities (or strongly related traded quantities). Dynamic portfolio credit models ostensibly describe the joint distribution of credit event probabilities at a plurality of time steps. This taxonomy is somewhat unsatisfying because dynamic quantities for any static model can in principle be computed, as with latent variable portfolio credit models. In practice, we may say a model is static if it seeks to model defaults only over a fixed horizon, with no compelling interpolation of extrapolation to other horizons, or if dynamics of the model revealed at successive time steps are suspect, intractable or unspecified.

In an effort to further classify modelling efforts we distinguish between models addressing a single portfolio only (with no obvious generalization treatment cdo squared and so forth) from those designed with calibration to tranches in multiple (especially overlapping) portfolios as a primary objective. Sadly the collection of Multiple portfolio dynamic credit models is rather small, given the difficulty of the enterprise, and as pointed out by Andersen ((pdf)) many Multiple portfolio static credit models are equivalent.

Credit models may naturally incorporate dynamics for equity, interest rate, foreign exchange, commodity and other markets.