OPTIMAL CAPITAL STRUCTURE WITH SCALE EFFECTS UNDER SPECTRALLY NEGATIVE LÉVY MODELS

The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland & Toft (1996), and was later extended to the spectrally negative Lévy model by Hilberink Rogers (2002) and Kyprianou Surya (2007). This paper incorporates 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 Lévy 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 bankruptcy strategy and the optimal capital structure.