Credit Spreads with Dynamic Debt

Abstract

This paper extends the baseline Merton (1974) structural default model, which is intended for static debt spreads, to a setting with dynamic debt, where leverage can be ratcheted up as well as written down through pre-specified exogenous policies. We provide a different and novel solution approach to dynamic debt than in the extant literature. For many dynamic debt covenants, ex-ante credit spread term structures can be derived in closed-form using modified barrier option mathematics, whereby debt spreads can be expressed using combinations of single barrier options (both knock-in and knock-out), double barrier options, double-touch barrier options, in-out barrier options, and one-touch double barrier binary options. We observe that debt principal swap down covenants decrease the magnitude of credit spreads but increase the slope of the credit curve, transforming downward sloping curves into upward sloping ones. On the other hand, ratchet covenants increase the magnitude of ex-ante spreads without dramatically altering the slope of the credit curve. These covenants may be optimized by appropriately setting restructuring boundaries, which entails a trade-off between the reduction in spreads against restructuring costs. Overall, explicitly modeling this latent option to alter debt leads to term structures of credit spreads that are more consistent with observed empirics.