| 摘要: | 本文針對可轉債評價實務上通常使用的樹模型之文獻進行研究，了解各個可轉債評價樹模型的優點、缺點、建構方式以及使用方式，而後提供一個新的可轉債評價樹模型，其中隨機股價二項樹模型使用Cox-Ross-Rubinstein(1979, CRR)模型建構；隨機無風險利率三項樹模型採用Hull-White(1990, HW)單因子模型建構；含違約風險的利率樹模型則根據Jarrow and Turnbull(1995)提出的方法，在無風險利率樹加上違約機率(????)和恢復率(δ)代表公司債的行為建構而成。不同於Hung and Wang(2002)與Chambers and Lu(2007)中隨機無風險利率二項樹皆使用Black-Derman-Toy(1990, BDT)模型建構，本文採用的Hull-White(1990, HW)單因子模型能夠表現出利率均值回歸的特徵且有負利率的可能性，更適合在實務上應用。本文還考慮股價和無風險利率的相關性，藉由相關係數調整兩者間的聯合機率，並提出一個新的相關係數調整法解決聯合機率可能出現負值的問題並放寬對相關係數的限制範圍。最後，本文提供一個數值例子及兩個實際案例。藉由最後的實際案例搭配市場資料取得與處理以及參數估計的範例，完整演示實務上應用本文評價模型評價可轉換債券的過程及結果，並進行相關係數敏感性及調整法分析。;This article studies the literatures of the tree model for pricing convertible bonds, since convertible bonds are usually priced in practice using tree models. The study includes the advantages, disadvantages, modeling and pricing process of each tree model. Then, this article provides a new tree model for pricing convertible bonds. In this model, the stochastic stock price binomial tree model is modeled using the Cox-Ross-Rubinstein(1979, CRR) model; the stochastic risk-free interest rate trinomial tree model is modeled using the Hull-White single-factor model(1990, HW); and the interest rate tree model with default risk is modeled following the approach in Jarrow and Turnbull(1995), which added default probability(????) and recovery rate(δ) into the risk-free interest rate tree to represent the behavior of corporate bonds. Unlike Hung and Wang(2002) and Chambers and Lu(2007) both modeled the stochastic risk-free interest rate binomial tree using the Black-Derman-Toy(1990, BDT) model, the Hull-White single-factor model(1990, HW) can express the characteristic of mean reversion and negative interest rate, which is more suitable for practical application. This article considers the correlation between the stock price and the risk-free interest rate, and proposes a new adjustment method to solve the problem of the negative joint probability and relax the limit on the correlation coefficient. Finally, this article provides a numerical example and two practical examples. The last practical example in concert with examples of obtaining and processing market data, and estimate parameter to demonstrate the process and results of using this article′s pricing model in practice. Additionally, it analyzes sensitivity and adjustment method of correlation coefficient. |
