Multi-Dimensional self-exciting NBD process and Default portfolios

TL;DR

This paper introduces a multidimensional self-exciting negative binomial distribution process to model interactions among 13 sectors in default portfolios, enabling network-based impact analysis and shock propagation insights.

Contribution

It extends the SE-NBD process to multiple dimensions, allowing for sector interaction estimation and impact classification, which was not previously available.

Findings

Identified real-estate and FI sectors as upstream shock sources.

Demonstrated shock amplification through sector network interactions.

Compared MD-SE-NBD with MD-Hawkes, highlighting differences in variance modeling.

Abstract

In this study, we apply a multidimensional self-exciting negative binomial distribution (SE-NBD) process to default portfolios with 13 sectors. The SE-NBD process is a Poisson process with a gamma-distributed intensity function. We extend the SE-NBD process to a multidimensional process. Using the multidimensional SE-NBD process (MD-SE-NBD), we can estimate interactions between these 13 sectors as a network. By applying impact analysis, we can classify upstream and downstream sectors. The upstream sectors are real-estate and financial institution (FI) sectors. From these upstream sectors, shock spreads to the downstream sectors. This is an amplifier of the shock. This is consistent with the analysis of bubble bursts. We compare these results to the multidimensional Hawkes process (MD-Hawkes) that has a zero-variance intensity function.