Negative correlations in Ising models of credit risk

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.