Mathematical models in credit risk

Abstract

Exposure and uncertainty are two main components of any type of risk and particularly of credit risk. The future evolution of economic systems, in condition of uncertainty and vulnerability to financial default, should be described using appropriate tools. Therefore, a variety of stochastic processes, more and more sophisticated, are used in credit risk modeling. This paper contains an overview and an interpretation of the evolution of credit risk modeling in connection with stochastic processes, from early approaches to the latest developments based on affine and Lévy processes.