Modeling dependencies between rating categories and their effects on prediction in a credit risk portfolio

The internal-ratings based Basel II approach increases the need for the development of more realistic default probability models. In this paper we follow the approach taken in McNeil and Wendin (2006) by constructing generalized linear mixed models for estimating default probabilities from annual data on companies with different credit ratings. The models considered, in contrast to McNeil and Wendin (2006), allow parsimonious parametric models to capture simultaneously dependencies of the default probabilities on time and credit ratings. Macro-economic variables can also be included. Estimation of all model parameters are facilitated with a Bayesian approach using Markov Chain Monte Carlo methods. Special emphasis is given to the investigation of predictive capabilities of the models considered. In particular predictable model specifications are used. The empirical study using default data from Standard and Poor gives evidence that the correlation between credit ratings further apart decreases and is higher than the one induced by the autoregressive time dynamics

Stochastic volatility models for ordinal valued time series with application to finance

In this paper we introduce two stochastic volatility models where the response variable takes on only finite many ordered values. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation we develop an e±cient Grouped Move Multigrid Monte Carlo (GM-MGMC) sampler. We apply both models to price changes of the IBM stock in January, 2001 at the NYSE. Dependencies of the price change process on covariates are quantified and compared with theoretical considerations on such processes. We also investigate whether this data set requires modeling with a heavy-tailed Student-t distribution

Introducing and evaluating a Gibbs sampler for spatial Poisson regression models

In this paper we present a Gibbs sampler for a Poisson model including spatial effects. Frühwirth-Schnatter und Wagner (2004b) show that by data augmentation via the introduction of two sequences of latent variables a Poisson regression model can be transformed into a normal linear model. We show how this methodology can be extended to spatial Poisson regression models and give details of the resulting Gibbs sampler. In particular, the influence of model parameterisation and different update strategies on the mixing of the MCMC chains are discussed. The developed Gibbs samplers are analysed in two simulation studies and appliedto model the expected number of claims for policyholders of a German car insurance data set. In general, both large and small simulated spatial effects are estimated accurately by the Gibbs samplers and reasonable low autocorrelations are obtained when the data variability is rather large. However, for data with very low heterogeneity, the autocorrelations resulting from the Gibbs samplers are very high, withdrawing the computational advantage over a Metropolis Hastings independence sampler which exhibits very low autocorrelations in all settings

Spatial modelling of claim frequency and claim size in insurance

In this paper models for claim frequency and claim size in non-life insurance are considered. Both covariates and spatial random e ects are included allowing the modelling of a spatial dependency pattern. We assume a Poisson model for the number of claims, while claim size is modelled using a Gamma distribution. However, in contrast to the usual compound Poisson model going back to Lundberg (1903), we allow for dependencies between claim size and claim frequency. Both models for the individual and average claim sizes of a policyholder are considered. A fully Bayesian approach is followed, parameters are estimated using Markov Chain Monte Carlo (MCMC). The issue of model comparison is thoroughly addressed. Besides the deviance information criterion suggested by Spiegelhalter et al. (2002), the predictive model choice criterion (Gelfand and Ghosh (1998)) and proper scoring rules (Gneiting and Raftery (2005)) based on the posterior predictive distribution are investigated. We give an application to a comprehensive data set from a German car insurance company. The inclusion of spatial e ects significantly improves the models for both claim frequency and claim size and also leads to more accurate predictions of the total claim sizes. Further we quantify the significant number of claims e ects on claim size