Correlated Default Modeling with a Forest of Binomial Trees

Abstract

This paper exploits the endogenous default function framework of Das and Sundaram (2007) to develop an approach for modeling correlated default on binomial trees usually used for pricing equity options. We show how joint default contracts may be valued on these trees. The model accommodates different correlation assumptions and practical implementation considerations. Credit portfolio characteristics are examined within the model and found to be consistent with stylized empirics. Risk premia for default are computable and shown to be relatively higher for poor quality firms. Equity volatility is shown to impact correlated credit loss distributions substantially. Two kinds of default dependence are explored, one coming from default intensity correlations, and the other from further conditional dependence in defaults after accounting for intensity correlations (residual copula correlation). Both are found to impact credit loss distributions, though the absence of either makes these distributions less sensitive to correlation assumptions; on balance intensity correlations are more critical.