A Probabilistic Approach for Valuing Exchange Option with Default Risk

We study a probabilistic approach for valuing an exchange option with default risk. The structural model of Klein [6] is used for mod- eling default risk. Under the structural model, we derive the closed-form pricing formula of the exchange option with default risk. Specifically, we provide the pricing formula of the option with the bivariate normal cumu- lative function via a change of measure technique and a multidimensional Girsanov’s theorem.