Modeling the Dependence between PD and LGD

Abstract

In the current Basel framework, the A-IRB formula, used by banks or other financial institutions to compute their Regulatory Capital to hedge Credit Risk, completely neglects any possible dependence between Probability of Default and Loss Given Default. This happens since it uses a stressed version of the first parameter only, which is computed according to a mathematical model (ASRF), while for the latter is simply requested a parameter which can\properly describe a downturn period. Therefore the main goal of this thesis is to investigate a possible correlation between these two parameters and, eventually, propose a new formula to compute the Regulatory Capital which could incorporate this potential relationship. Hence, in order to achieve this goal, we first estimate both parameters, developing a well known statistical tool (Survival Analysis) and confirming (or even improving) the results of some previous studies which claim that this approach is actually suitable for the modelling of both quantities, clearly with a different meaning of the results which have to be properly interpreted. In a second phase we study the common behavior of these two risk parameters and present a completely new application in Credit Risk of a Bivariate Non Central Beta distribution, starting from empirical evidences of positive correlation. This approach is not only absolutely new in this field, but it also suggests a new methodology to stress both the parameters and to compute the Unexpected Losses. Consequently, it allows to obtain a new model for the Regulatory Capital of a bank and any other financial institutions, which actually takes into account any possible dependence between Probability of Default and Loss Given Default. The empirical analysis to test the proposed model is performed on public data coming from the US mortgage market, published by Freddie Mac. We obviously acknowledge that our solution is only a small step towards a long and hard path, therefore we encourage and recommend further research in this direction, since we believe that this could really lead to a more conscientious modelling of the Regulatory Capital for Credit Risk and, hence, to safer markets.