Smoothing transition probability matrices under a risk sensitive approach

Abstract

Rating transition probability matrices are a crucial parameter not only for the credit risk models but also for pricing and investment decisions. Owing to scarce data and temporal observations, however, empirical transition probability matrices do not show intuitive behaviours and a smoothing methodology, which considers the term structure of transition probabilities, is required. This paper investigates and addresses various issues related to rating migration and default probabilities. The study introduces a smoothing methodology on the transition probability matrices using an optimisation algorithm that leads to consistency with empirical observations and desired theoretical properties. The model completes the previous studies in this area and has a flexible target set-up. It is sensitive to the risk measurements and it serves for a reliable and consistent capital management. A loss function which considers the rating migrations costs in reference portfolio is applied and further portfolio credit risk simulations are performed to estimate the impact of the smoothing.