Stochastic Processes in Credit Risk Modelling

Abstract

In credit risk modelling, jump processes are widely used to describe both default and rating migration events. This work is mainly a review of some basic definitions and properties of the jump processes intended for a preliminary step before more ad vanced lectures on credit risk modelling. We focus on the Poisson process and some generalisations, like the compounded and the double stochastic Poisson processes, which are widely used for describing the time-inhomogeneous dynamic either of the default process or of the credit rating transition. As such, much of the material is not new, but focused and organized from a credit risk perspective. Moreover it contains detailed proofs of some fundamental results. Other original contributions come from examples and simulated studies, which help the reader to better understand the features of the described processes.

Keywords: Markov process, Jump process, Poisson process, Cox process, Doubly stochastic Poisson process

JEL Classification: A22, C50, C60