Structural credit risk models with Lévy processes: the VG and NIG cases

We propose alternative structural credit risk models for determining probabilities of default (PDs) based on two well-known Lévy processes - the Variance Gamma (VG) process and the Normal Inverse Gaussian (NIG) process, respectively. In particular, using Lévy processes, we propose a methodology to overcome the distributional drawbacks of the classical Merton model. Therefore, we discuss an empirical comparison of estimated PDs obtained from the VG and the NIG models on a dataset of 24 companies with strong capitalization in the US market. The empirical evidence suggests that both the models are able to capture the situation of instability that affects each company in considered period and, in fact, are very sensitive to the periods of the financial crisis.