As numerous authors point out (Barndorff-Nielsen, 1997 [5,6]; Prause, 1999; Eberlein, 2001; Brambilla et al. 2015), stock returns are not normally distributed which significantly limits the use of model in practice. Moreover the estimates of PDs can be biased downwards exposing the banks to the possibility of undercapitalisation and systematic shocks.
It is the purpose of this paper to remedy this situation. Firstly we extend the Merton model by allowing for normal inverse Gaussian (NIG) distributed returns. As several authors point out using the examples of options (Schoutens, 2009), NIG in most cases provides a robust statistical platform for estimating stock returns. We further extend our approach by constructing a robust EM algorithm for estimating PDs within the Merton NIG framework.
We also test the reliability of the NIG improved Merton model against classical Merton’s model for estimating PDs. Applying our results to Ljubljana stock exchange we find that the PD estimates using classical Merton’s model are biased, whereas the estimates from NIG Merton’s model are robust.