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Quantitative Finance · Glossary

What is Default correlation?

Definition 15.1 Rates, Credit, XVA and Risk · Chapter 15 — Portfolio Credit

The default correlation of two names over a horizon is the correlation of their default indicators 1τi≤T\mathbf 1_{\tau_i\le T} and 1τj≤T\mathbf 1_{\tau_j\le T}:

ρijD=P(τi≤T,τj≤T)−pipjpi(1−pi)pj(1−pj).\rho^{D}_{ij} = \frac{\P(\tau_i\le T,\tau_j\le T)-p_ip_j}{\sqrt{p_i(1-p_i)p_j(1-p_j)}}.
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