Efficient solution of structural default models with correlated jumps and mutual obligations

TL;DR

This paper extends the structural default model to multiple banks with mutual liabilities driven by correlated Levy processes, introducing a novel stable computational method for multi-dimensional problems, and analyzes the impact of mutual liabilities on survival probabilities.

Contribution

It develops a new computational approach for multi-dimensional Levy-driven default models with mutual obligations, generalizing previous one-dimensional methods.

Findings

The method is unconditionally stable and second-order accurate.

It efficiently computes marginal and joint survival probabilities.

Numerical examples illustrate the impact of mutual liabilities.

Abstract

The structural default model of Lipton and Sepp, 2009 is generalized for a set of banks with mutual interbank liabilities whose assets are driven by correlated Levy processes with idiosyncratic and common components. The multi-dimensional problem is made tractable via a novel computational method, which generalizes the one-dimensional fractional partial differential equation method of Itkin, 2014 to the two- and three-dimensional cases. This method is unconditionally stable and of the second order of approximation in space and time; in addition, for many popular Levy models it has linear complexity in each dimension. Marginal and joint survival probabilities for two and three banks with mutual liabilities are computed. The effects of mutual liabilities are discussed, and numerical examples are given to illustrate these effects.