公司債與內含賽局選擇權之評價與分析

Abstract

公司債的設計各式各樣附加選擇權來符合市場的需求，例如贖回選擇權以降低公司的發債成本，或轉換選擇權可讓買債方分享公司成長。因此這些公司債附加選擇權對債券價值影響以及參與者行為進行理論分析相當重要。Acharya and Carpenter (2002)以最大化股東價值的前提下，分析公司債附加贖回和(或)違約條款時，發債者的決策行為以及使用內生給定最佳違約和(或)贖回時間。他們也分析了市場上的因素(如公司資產價值與利率)對公司債價值與內含選擇權價值的影響。洪敏誠(2010)延伸了Acharya and Carpenter (2002)的方法，分析債券投資人如何決策以及最大化公司債附加的賣回和(或)轉換選擇權。基於前兩篇文章，本文分析了具有違約風險的可轉換且可贖回債券，是一種普遍的公司債附加了選擇權給債券發行公司(贖回和違約選擇權)以及債券投資人(轉換選擇權)。我們將債券拆解成host bond(default-free bond)加上賽局選擇權，賽局選擇權由轉換、贖回和違約選擇權。並分析了發債者以及投資者之間的交互影響、債券價值以及內含的賽局選擇權價值。理論分析將用Dai et al. (2013)提出的立體樹狀評價模型的數值方法檢驗。理論分析的結果將來可延伸到具有違約風險的可轉換、可賣回且可贖回債券。

Various options embedded in corporate bonds are designed to meet issuers’ or bond investors’ requirements—like call options for issuers to reduce the cost for raising debt capital— or investors’ ones— like conversion options for investors to share the growth of the issuing firm. Theoretical analyses for the impacts of these options on bond evaluations and participants’ behaviors are thus important. Based on the assumption of maximizing equity values, Acharya and Carpenter (2002) analyze the issuer’s strategies for both embedded call and (or) default options and endogenously determine optimal call and (or) default time. They also analyze the impacts of other market variables like the firm asset value and the interest rate on the values of embedded options and corporate bonds. Hung (2010) extends the methodologies of Acharya and Carpenter (2002) by analyzing how investors exercise their embedded put and (or) convertible options to maximize the values of putable and (or) convertible bonds. Based on two previous works, this thesis analyzes a convertible-callable-defaultable bond— a popular type of corporate bond whose embedded options are either held by issuers (i.e., callable options and defaultable options) or by investors (i.e., conversion options). We decompose the bond into a host bond (or a risk-free bond) plus a game option that is composed of conversion, call, and default options. The interaction between issuers’ and investors’ strategies and the corresponding impacts on the properties and the values of the corporate bond and the embedded game option are analyzed. These theoretical analyses are compared with numerical results generated by the 3D pricing tree model proposed by Dai et al. (2013). The theoretical results can be extended to analyze convertible-callable-putable-defaultable bonds.