Optimal Capital Structure Model under the CEV Process

Abstract

The well-known Leland (1994) and Leland and Toft (1996) models provide some insights of the capital structure issues. However, in order to obtain analytical solutions of corporate securities, researchers need to impose some unrealistic assumptions to avoid time and path dependency. While evaluating a single corporate debt with finite maturity or complex bankruptcy proceedings, no analytical solution is available and one needs to resort to numerical methods. In this study, we extend the binomial lattice method by Broadie and Kaya (2007) to develop a capital structure model, which incorporates finite maturity as well as the feature of Chapter 11 bankruptcy proceedings. To make the model more realistic, we assume that the underlying asset value follows the constant elasticity of variance (CEV) process. Our numerical results show that when the reorganization period is longer or the elasticity constant β is smaller, the value of corporate risky debt will be lower.