Levy Processes in Credit Risk and Market Models

Abstract

During the last years banks have realized that default risk cannot be neglected. The subjective assessment of credit worthiness has to be replaced with a more objective way of estimating default risk. Mathematical credit risk models in the literature are mainly models based on Brownian motion although it is known that real-life financial data provides a different statistical behavior than that implied by these models. Lévy processes are an appropriate tool to increase accuracy of models in finance. They have been used to model stock prices, and term structures of interest rates, thus allowing more accurate derivative pricing and risk management. In this study we discuss how general Lévy processes can be applied to credit risk and market models. There are also a few jump-diffusion models where the jump-components have sample paths of bounded variation, but some of the very important subclasses are special types of Lévy processes. The emphasis in this study lies on the application of Lévy processes in credit risk models. We will mainly deal with the question of pricing defaultable corporate