Negative correlations in Ising models of credit risk

TL;DR

This paper investigates negative correlations in Ising models applied to credit risk, deriving formulas for node correlations and analyzing their implications through simulations.

Contribution

It introduces explicit formulas for correlations in a subclass of Ising models with negative central-non-central node correlations in credit risk.

Findings

Derived the range of negative correlation values for the model

Established an explicit formula linking node correlations

Conducted simulation studies to validate theoretical results

Abstract

We analyze a subclass of Ising models in the context of credit risk, focusing on Dandelion models when the correlations $\rho$ between the central node and each non-central node are negative. We establish the possible range of values for $\rho$ and derive an explicit formula linking the correlation between any pair of non-central nodes to $\rho$. The paper concludes with a simulation study.