Modeling Frailty Correlated Defaults with Multivariate Latent Factors

Firm-level default models are important for bottomup modeling of the default risk of corporate debt portfolios. However, models in the literature typically have several strict assumptions which may yield biased results, notably a linear effect of covariates on the log-hazard scale, no interactions, and the assumption of a single additive latent factor on the log-hazard scale. Using a sample of US corporate firms, we provide evidence that these assumptions are too strict and matter in practice and, most importantly, we provide evidence of a time-varying effect of the relative firm size. We propose a frailty model to account for such effects that can provide forecasts for arbitrary portfolios as well. Our proposed model displays superior out-of-sample ranking of firms by their default risk and forecasts of the industry-wide default rate during the recent global financial crisis.