A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk

Abstract

We model 1981-2002 annual default frequencies for a panel of US firms in different rating and age classes from the Standard and Poor's database. The data is decomposed into a systematic and firm-specific risk component, where the systematic component reflects the general economic conditions and default climate. We have to cope with (i) the shared exposure of each age cohort and rating class to the same systematic risk factor;(ii) strongly non-Gaussian features of the individual time series; (iii) possible dynamics of an unobserved common risk factor; (iv) changing default probabilities over the age of the rating, and (v) missing observations. We propose a non-Gaussian multivariate state space model that deals with all of these issues simultaneously. The model is estimated using importance sampling techniques that have been modified to a multivariate setting. We show in a simulation study that such a multivariate approach improves the performance of the importance sampler.

Estimating systematic continuous‐time trends in recidivism using a non‐Gaussian panel data model

“…We stress that this is not a restriction imposed by the methodology. However, this restriction allows us to compare our results with the simple discrete-time specification used by Koopman and Lucas (2007). The comparison of the two trend models illustrates the flexibility of non-Gaussian state-space modelling with respect to dynamic specification.…”

“…., A. Our model uses the non-Gaussian panel time-series specification developed by Koopman and Lucas (2007). The basic structure of this model is derived from a common framework in credit risk modelling.…”

“…Given that we have aggregated monthly data for approximately 13 years, we can also consider an exact discrete-time specification, where f t follows a simple random walk with t measured in months. This is one of the models considered by Koopman and Lucas (2007):…”

“…This is a challenging task and innovative within a criminological context. We adopt the non-Gaussian panel data model with latent dynamic factors of Koopman and Lucas (2007). They used the model for credit risk analysis to identify common and idiosyncratic risk factors for defaults of firms.…”

“…As our panel consists of many points in time, we can allow for different time-series specifications of the trend. We compare the continuous-time model with the discrete-time model of Koopman and Lucas (2007).…”