或有資本,信用風險,及最適資本結構

Abstract

經歷嚴重和漫長的金融風暴後，如何管理信用風險並減輕違約造成的損失已成為財 金領域的重要議題。本研究計畫分析 reverse-convertible bonds(暫譯為逆轉換債， 以下以縮寫RCB表示)，該商品在權益或資本的價值掉到特定水平之下時，會被轉換成股 票或是減少到期日償還金額。在Benet et al. (2006) and Hernandez et al. (2010) 的實證研究中，說明該商品可增強發行者的信用。Chidambaran et al. (2001)說明類 似的商品發行不僅減少信用風險，也可以減輕優先債券(senior bond)及次級債券 (junior bond)持有人之間的資產替代問題(asset substitution problem)。 我的研究計畫會建立一個理論模型，利用衍生性金融商品評價理論分析發行RCB 對公 司價值及最適資本結構所造成的影響。我打算將發行RCB 所造成稅盾及破產成本的改 變，帶入Merton (1974) and Black and Cox (1976)所發展的結構式信用風險模型中， 並推導權益價值，債權價值，以及公司價值(firm levered value)的評價公式。然後說 明RCB 具備的轉換成股票或減少償還金額的特性，不僅可減少違約風險，也可增加公司 的價值及最適的槓桿比例(optimal leverage ratio)。此外，我的模型可分析公司同時 發行不同種債券的狀況，並分析不同的債務結構及股債比對公司價值的影響，我的模型 也可分析股東和債券人之間以及優先債券持有人及次級債券持有人之間的資產替代問 題。 和RCB 相比，可轉債有相反的特性，它允許持有人在公司表現良好時轉換成股票。所 以分析發行可轉債對發行者的信用以及公司最適資本結構的影響十分有意義且重要。然 而，可轉債允許持有人在到期日前提前轉換的特性會導致我們無法求出封閉評價公式 解。所以，我會發展數值模型來求股東價值及債權人的價值。這樣可幫助我們分析發行 可轉債對公司最適資本結構以及資產替代問題的影響。

How to manage credit risk and alleviate the lost due to default has become an important issue in financial field after suffering from serious and lengthy financial crisis. This project analyzes a financial product, reverse-convertible bonds (to be referred to as RCB hereafter), that either can be converted into equity or can reduce its repayment when the market value of equity or capital falls below a certain threshold. The empirical studies in Benet et al. (2006) and Hernandez et al. (2010) suggest that this product can enhance the issuer's credibility. Chidambaran et al. (2001) suggest that similar products can not only reduce the credit risk but mitigate the asset substitution problem between junior bond and senior bond holders. My research project will develop a theoretical model to analyze the impact of issuing RCB on the firm levered value and the optimal capital structure based on derivative pricing framework. I plan to incorporate the change of tax benefit and the bankruptcy cost associated with the use of RCB into the structural credit risk model pioneered by Merton (1974) and Black and Cox (1976). I will derive analytical formulas for evaluating the equity value, the debt value, and the firm levered value based on my models. Then I will show that the debt-to-equity conversion or debt reduction features of RCB could not only reduce the default risk, but increase the firm levered value and the optimal leverage ratio. In addition, my models can analyze the case that the firm issues different type of bonds. Thus we can simultaneously analyze the impacts of changing debt structure and leverage ratio on the firm levered value. BTW, my models can also be used to analyze the effect of asset substitution problems between equity and debt holders, and between senior bond and junior bond holders. Comparing to RCB, convertible bonds (CB hereafter) own the opposite provisions by allowing CB holders to convert CB into equities when the firm's performance is good. To analyze the influence of issuing CB on issuer's credibility and on the optimal capital structure is therefore important and interesting. However, the premature conversion provision of CB makes analytical formulae hard to be derived. Thus, I will construct numerical methods to evaluate the values of equity holders, bond holders, and so on. This will help us to study the impact of issuing CB on the analysis of optimal leverage ratio and the asset substitution problem.