Double-exponential jump-diffusion processes: a structural model of an endogenous default barrier with a rollover debt structure

Binh Dao and Monique Jeanblanc

Abstract

ABSTRACT

We extend the framework of Leland, who proposed a structural model of rollover debt structure in a Black-Scholes framework.We apply this to the case of a doubleexponential jump-diffusion process, considering a trade-off model with firm risk, risk-free interest rate and payoff rate parameters as well as tax benefits for coupon payments, default costs, violation of the absolute priority rule and tax rebates. We obtain the equity, the debt, the firm and the credit-spread values in closed form. We analyze these values as functions of coupon, leverage and maturity. The yield spreads in our model are significantly different from zero when the maturity tends to zero, correcting the weakness of Leland's model through the use of jump modeling.