Structural default model with mutual obligations

In this paper we consider mutual obligations in an interconnected bank system and analyze their impact on the joint and marginal survival probabilities for individual banks. We also calculate prices of the corresponding credit default swaps and first-to-default swaps. To make the role of mutual obligations more transparent, we develop a simple structural default model with banks’ assets driven by correlated multidimensional Brownian motion with drift. We calculate closed form expressions for many quantities of interest and use them for the efficient model calibration. We demonstrate that mutual obligations have noticeable impact on the system behavior.