Default prediction with the Merton-type structural model based on the NIG Lévy process

摘要

Merton’s model (Merton, 1974) has long been a standard for estimating company’s probability of default (PD) for listed companies. The major advantage of Merton’s model is the use of current market prices to determine the probability of default. The logic behind the model is simple; the market prices best reflect all the relevant information (being forward looking estimates of company’s prospect) and should be (and are) superior to the balance sheet disclosures, which at best are ex post realisations of company’s performance. It is thus a pity that the benefits (strengths) of Merton’s model are hindered by a significant shortcoming of the model namely the assumption of normally distributed returns.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.