在浮動利率下，以賽局理論評價可轉換公司債

Abstract

本文以Hull-White的利率樹為基礎，建立了一個會模擬浮動利率而和投資資產變動的立體樹狀模型，來評價可轉換公司債，且在評價模型中考量到公司的股利支出(Dividend Payout)、稅盾(Tax Benefits)及破產成本(Bankruptcy Cost)的影響，以賽局理論(Game Theory)去分析可轉換公司債在1.發行公司在最小化可轉換公司債價值(Minimize CB Value)和最大化股東權益(Maximize Equity)兩種不同的贖回策略下2.可轉換公司債持有人在最小化可轉換公司債價值及最大化股東權益，兩種不同的轉換策略下3.可轉換公司債持有人在獨佔持有(monopoly)、塊狀履約(block)以及完全競爭(perfect competitive)這三種不同的持有情況下4.普通債和可轉換公司債在不同償債優先順序下。找到各種情況下的轉換比率及贖回的最適決策，達到納許均衡(Nash equilibrium)，並藉由倒推法可以求出可轉換公司債的初始價值。此外，本文透過動態規劃法(Dynamic Programing)對可轉換公司債的生存年限進行估計，發現當公司以最大化股東權益作為贖回決策依據時，可轉換公司債的平均生存年限較原先最小化可轉換公司債價值之贖回判斷為長，所以對市場上觀察到的可轉換公司債的贖回延遲提出了另一種解釋。並且配合文獻，探討利率波動度與債券價格之間的變動關係，以及債券存續期間和conversion fraction之間的關係，證實了本文的評價模型與實證結果相符合。最後以NVIDIA在2000年所發行之可轉債進行評價及分析。

This thesis builds a three-dimensional tree that simulates the evolution of the issuing firm value and the stochastic short rate based on the Hull-White short rate tree model to price convertible bonds (CBs). My pricing model considers the influence of the dividend payout, tax benefit and the bankruptcy cost. The game theory is applied to model the sequential conversion behavior under two call policies, minimization of CB value and the maximization of the equity value, and three different conversion scenarios: monopoly case (CBs are owned by one holder), block case (sequential conversion is not allowed), and the competitive case (CBs are owned by many holders and each holder is a price taker). The Nash equilibrium for each node of our tree can be numerically searched to determine the call policy of issuer and the conversion policy of CB holder(s) at that node. I also consider how seniority of CBs influences the prices and the durations of CBs and other outstanding bonds. This thesis also uses the dynamic programming method to estimate the expected maturity of a CB under different scenario. Numerical results suggest that the expected maturity under the maximization of equity policy is larger than the expected maturity under the minimization of CB value policy. This could explain why empirical studies find the ``call delay’’ phenomenon since their researches are based on the latter policy. Besides, the numerical results generated by my model are consistent to the phenomenon found in many empirical studies. For example, I analyze the relationship between the interest rate volatility and the bond price, the relationship between bond duration and the conversion fraction. Finally, I use my model to price the CB issued by NVIDIA in 2000 to confirm the reliability of my model.