常數彈性變異數過程下考量破產程序的資本結構模型與實證分析

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，然而此二模型的最適槓桿與利差並非十分符 合歷史平均。因此，近期的研究模型，加入了較符合實際狀況的特性，以改善模型預測 的槓桿與利差，例如，Hilberink and Rogers (2002) 以及Chen and Kou (2009) 加入了資 產跳躍的過程。然而，在選擇權訂價模型中廣泛使用的隨機波動度，卻幾乎未應用於資 本結構模型。 除此之外，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 除公司證券與時間的相關性。儘管與實際不符，大多數的資本結構模型假設無限期的債 券，或是假設債券到期時可續發同面額債券，此假設在公司陷入財務困境時將更不合 理。相反的，具到期日的債券，在考量破產程序具寬限期下，通常並無解析解。為克服 此困難，Broadie and Kaya (2007)首先將選擇權訂價文獻中廣泛使用的二元樹方法引進 結構風險模型的訂價。 因此，本研究將延續Broadie and Kaya (2007)的研究，發展一個常數彈性變異數過 程下，考量破產程序的資本結構模型。常數彈性變異數模型的複雜度可允許波動度變 動，同時在二元樹應用上，僅需使用二維的格子樹。儘管常數彈性變異數模型不如隨機 波動度模型具有彈性，但應用在考量破產程序的模型中，隨機波動度模型所需的高維度 二元樹執行的成本將非常高。 本研究首先將進行文獻探討，接下來我們將發展一個常數彈性變異數過程下，考量 破產程序的資本結構模型。詳細分析數值方法的收斂，以及資產過程對公司債以及公司 破產決策所造成的影響。最後，於實證分析中，我們將常數彈性變異數過程下，巴黎選 擇權架構中所包含的六個模型，進行違約預測能力分析。

While the well-known Leland (1994) and Leland and Toft (1996) models provide some insights of the capital structure issues, their predicted optimal leverage and yield spreads seem not to be consistent with historical average. Consequently, the more recent studies introduce additional realistic features in order to meliorate the model-predicted leverage and yield spreads. For example, Hilberink and Rogers (2002) and Chen and Kou (2009) add jumps into the asset value process. However, stochastic volatility feature, another important and commonly adopted assumption in option pricing, is still rare in structural modeling literature. In addition, in order to obtain analytical solutions of corporate securities, researchers need to impose some unrealistic assumptions to avoid time and path dependence. Most capital structure models assume infinite maturity bond or continuously rollover bonds although these bonds are rarely used in practice, especially when firms are in financial distress. By contrast, for finite maturity bonds, it is difficult to obtain analytical solutions in models of bankruptcy proceedings that include grace periods since it introduces path dependency. To overcome the difficulties, Broadie and Kaya (2007) are the first to introduce binomial lattice approach, widely adopted in option pricing literature, into structural credit risk modeling. Therefore, in this study, we will extend the work by Broadie and Kaya (2007) to develop a capital structure model incorporating the feature of Chapter 11 bankruptcy proceedings under the CEV (Constant Elasticity of Variance) process. The CEV model is complex enough to allow for changing volatility and simple enough to apply binomial method in a two-dimensional lattice. Although the CEV model is not as general and flexible as the stochastic volatility models, when applied to structural models, especially in the case of Chapter 11 modeling with path-dependency, high-dimensional lattice models are very expensive to implement. This paper will first review and theoretically examine existing capital structure models of various bankruptcy proceedings. Next, we will develop a capital structure model with the feature of Chapter 11 bankruptcy proceedings under the CEV process. We will explicitly analyze the convergence of the numerical method, and the effects of firm value process for corporate debt values as well as the implication in bankruptcy decisions. Finally, to gain empirical support, we will compare the performance of default prediction power of six models nested within the CEV Parisian option framework.