Optimal Capital Structure with Endogenous Default and Volatility Risk

This paper analyzes the capital structure of a firm in an infinite time horizon following [30] under the more general hypothesis that the firm’s assets value process belongs to a fairly large class of stochastic volatility models. By applying singular perturbation theory, we fully describe the (approximate) capital structure of the firm in closed form as a corrected version of [30] and analyze the stochastic volatility effect on all financial variables. We propose a corrected version of the smooth-fit principle under volatility risk useful to determine the optimal stopping problem solution (i.e. endogenous failure level) and a corrected version for the Laplace transform of the stopping failure time. The numerical analysis obtained from exploiting optimal capital structure shows enhanced spreads and lower leverage ratios w.r.t. [30], improving results in a robust model-independent way. JEL Classification Numbers: G12, G13, G33