Modeling Frailty Correlated Defaults With Multivariate Latent Factors

Firm-level default models are important for bottom-up 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