A Dynamic Model of Optimal Capital Structure and Debt Maturity with Stochastic Interest Rates

We thank an anonymous referee, an Associate Editor, Gurdip Bakshi, and Jay Huang for their valuable comments and suggestions. We also thank Henry Cao, Hua He, Hayne Leland, Mark Rubinstein, and Matt Spiegel for their advice on an earlier version where a static model was developed. Abstract This paper develops a model in which an optimal capital structure and an optimal debt maturity are jointly determined in a stochastic interest rate environment. Valuation formulas are derived in closed form and numerical solutions are used to obtain comparative statics. The model yields leverage ratios and debt maturities that are consistent in spirit with empirical observations. It is demonstrated that a dynamic model is crucial to obtain reasonable leverage ratios and that a stochastic interest rate is important to study optimal debt maturity structure. It is also demonstrated that a model of optimal capital structure with a constant interest rate cannot price risky bonds and determine optimal capital and debt structures simultaneously in a satisfactory manner.