Optimal Capital Structure with Scale Effects under Spectrally Negative Levy Models

TL;DR

This paper extends the optimal capital structure model under spectrally negative Levy processes by incorporating scale effects, providing semi-explicit solutions and analyzing how scale effects influence default strategies and capital structure.

Contribution

It introduces scale-dependent bankruptcy costs and tax benefits into the Levy model, deriving semi-explicit solutions and conditions for optimality.

Findings

Scale effects significantly impact default thresholds.

Optimality conditions depend on monotonicity of tax benefits and loss proportions.

Numerical analysis illustrates the influence of scale effects on capital structure.

Abstract

The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the scale effects by allowing the values of bankruptcy costs and tax benefits to be dependent on the firm's asset value. By using the fluctuation identities for the spectrally negative Levy process, we obtain a candidate bankruptcy level as well as a sufficient condition for optimality. The optimality holds in particular when, monotonically in the asset value, the value of tax benefits is increasing, the loss amount at bankruptcy is increasing, and its proportion relative to the asset value is decreasing. The solution admits a semi-explicit form in terms of the scale function. A series of numerical studies are given to analyze the impacts of scale effects on the default strategy and the optimal capital structure.