利用三因子樹狀模型評價可轉換公司債

A Modified Tree Model for Pricing Convertible Bonds with Equity, Interest Rate, and Default Risk

曾右仲(You-Zhong Zeng)

指導教授 ： 呂育道

國立臺灣大學/管理學院/財務金融學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.10149

摘要

可轉換公司債是常見的金融商品之一，此商品允許投資人在特定期間內，將公司債轉以合約約定比率轉換成公司股票，目前市面上可見的還有包含買權或賣權等其他條件的可轉換公司債，樹狀結構相較於蒙地卡羅模擬法在評價此類條件有其優勢。本文目的是延續Chambers and Lu (2007)的樹狀模型，討論此模型在切割期數變大時，會遭遇機率不滿足限制的問題，並提供修正方法。

關鍵字

可轉換公司債 ； 樹狀結構 ； Chambers and Lu

並列摘要

Convertible bonds are some of the most popular financial products. They allow investors to exchange the company’s bonds for the company’s stocks within certain periods of time in the future. Some convertible bonds embed other options such as call option and put option. The tree method has advantages in pricing convertible bonds with embedded options over the Monte Carlo method. This thesis extends the tree method of Chambers and Lu (2007) and discusses the problem of the probability out of the valid range. It then provides a method to address this problem.

並列關鍵字

convertible bonds ； tree method ； Chambers and Lu

參考文獻

[1] Boyle, P.P., K.S. Tan and W. Tian. (2001): “Calibrating the Black-Dermon-Toy model: some theoretical results,” Applied Mathematical Finance, 8 (2001) 27–48.

[2] Chambers, D.R. and Q. Lu. (2007): “A Tree Model for Pricing Convertible Bonds with Equity, Interest Rate, and Default Risk,” The Journal of Derivatives, 4 (Summer 2007), 25–46.

[3] Cox, J.C., S.A. Ross and M. Rubinstein. (1979): “Option pricing: A Simplified Approach,” Journal of Financial Economics, 7 (Semptember 1979), 229–263.

[6] Hung, M. and J. Wang. (2002): “Pricing Convertible Bonds Subject to Default Risk,” The Journal of Derivatives, 10 (Winter 2002), 75–87.

[7] Jarrow, R.A. and S.M. Turnball (1995): “Pricing Derivatives on Financial Securities Subject to Credit Risk,” Journal of Finance, Vol.50 (March 1995), 53–85.