常數彈性變異數過程下的最佳資本結構模型

Abstract

在資本結構模型中，最具代表性的Leland (1994) 以及Leland and Toft (1996)模型提供了一些關於資本結構問題的深入分析。然而，為了求公司證券的解析解，學者必須加入一些不符合實際的假設，以排除公司證券價值與時間的相關性。評價單一具到期日公司債或者是包含複雜破產法規之公司債時，並無法導出封閉解，必須使用數值方法處理。本文延伸Broadie and Kaya (2007)的研究，使用二元樹模型，評價具到期日與第十一章破產法規架構下之公司債。為了使模型更有彈性，並更貼近實際，我們允許標的資產價格波動度變動，亦即發展一個常數彈性變異數(CEV)過程下，考量破產程序的資本結構模型。本研究數值分析結果指出，當重整的期限越長，或是CEV過程彈性係數 越小時，公司債價值越低。

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 is smaller, the value of corporate risky debt will be lower.