Bankruptcy, Counterparty Risk, and Contagion

This paper provides a unifying framework for the modeling of various types of credit risks such as contagion effects. We argue that Markov chains can efficiently be used to tackle these problems. However, our approach is not limited to pricing problems with contagion. Other applications include the modeling of a more sophisticated default process of a firm. On the theoretical side, we derive pricing formulas for three building blocks that are generalizations of contingent claims studied in Lando (1998). These claims can be thought of as atoms forming the basis for all credit risky payments. Furthermore, we demonstrate that, in general, all contingent claims exposed to credit risk satisfy a system of partial differential equations. This is the key result to calculate prices of credit risky claims explicitly and efficiently.