Bankruptcy, Counterparty Risk, and Contagion

This paper provides a unifying framework for the modeling ofvarious types of credit risks such as contagion effects. Weargue that Markov chains can efficiently be used to tackle theseproblems. However, our approach is not limited to pricing problemswith contagion. On the theoretical side, we derive pricing formulasfor three building blocks that are generalizations of contingentclaims studied in Lando (1998). These claims can be thoughtof as atoms forming the basis for all credit risk payments.Furthermore, we demonstrate that, in general, all contingentclaims exposed to credit risk satisfy a system of partial differentialequations. This is the key result to calculate prices of creditrisk claims explicitly and efficiently.