Structural default model with mutual obligations

TL;DR

This paper introduces a simple structural default model incorporating mutual obligations among interconnected banks, providing analytical solutions and calibration methods to accurately assess joint and individual bank risks.

Contribution

It presents a new structural default model with closed-form solutions that explicitly accounts for mutual obligations, enhancing risk assessment accuracy.

Findings

Mutual obligations significantly impact survival probabilities.

The model allows for closed-form solutions in the 2D case.

Calibration shows mutual obligations are essential for correct parameter estimation.

Abstract

This paper considers mutual obligations in the interconnected bank system and analyzes their influence on joint and marginal survival probabilities as well as CDS and FTD prices for the individual banks. To make the role of mutual obligations more transparent, a simple structural default model with banks' assets driven by correlated multidimensional Brownian motion with drift is considered. This model enables a closed form representation for many quantities of interest, at least in a 2D case, to be obtained, and moreover, model calibration is provided. Finally, we demonstrate that mutual obligations have to be taken into account in order to get correct values for model parameters.