Risky Debt Dynamic, Jumps and Optimal Financial Policy

Abstract

The model developed is a structural valuation model of risky debt which includes a dynamic of debt. The value of the firm follows a jump diffusion process. The default threshold like the recovery rate are endogenous. Consequently, the optimal default threshold changes as the firm's debt level evolves. The spread curves in terms of maturities have levels and forms that are closer to empirical observations. The problem of the dynamic optimal financial structure is reformulated within this framework. Under certain conditions, it is shown that the leverage ratio of the firm follows a double barrier process, one absorbent, the other reflective. But in a perfect financial market (without financial costs) there is no optimal capital structure when the default is predictive. With jumps we can obtain an optimal financial structure as in Modigliani and Miller works.

Keywords: Credit spreads, Optimal capital structure, Jumps, Risky debt, Structural Models

JEL Classification: G12, G13, G32, G33