Numerical analysis of an extended structural default model with mutual liabilities and jump risk

TL;DR

This paper develops a finite difference numerical method for a structural default model with mutual liabilities and jump risks, analyzing its stability, and applying it to compute credit derivatives and calibrate to market data.

Contribution

It introduces a finite difference approach for a complex two-dimensional jump-diffusion default model with mutual obligations, including calibration to market data.

Findings

Stable and consistent numerical scheme developed.

Jump risk significantly impacts credit derivative prices.

Model successfully calibrated to market data.

Abstract

We consider a structural default model in an interconnected banking network as in Lipton [International Journal of Theoretical and Applied Finance, 19(6), 2016], with mutual obligations between each pair of banks. We analyse the model numerically for two banks with jumps in their asset value processes. Specifically, we develop a finite difference method for the resulting two-dimensional partial integro-differential equation, and study its stability and consistency. We then compute joint and marginal survival probabilities, as well as prices of credit default swaps (CDS), first-to-default swaps (FTD), credit and debt value adjustments (CVA and DVA). Finally, we calibrate the model to market data and assess the impact of jump risk.