臺灣博碩士論文加值系統

摘要
可轉換公司債近年來已經成為國內企業融通資金的重要工具，在計算上雖然有很多文獻提供方法，其中大多以利用Nelson and Ramaswamy(1990)的變數變換法為主，但此法在每個節點都須做變數變換與計算機率的動作，所以處理上比較費時。而本文是利用簡單的二元樹演算法為基礎，建構出隨機利率下的股價選擇權評價模型，也就是由利率與股價組成二因子四元樹(金字塔型 )模型。在模型展開過程中，利用強制重合和固定機率的方法，快速建構出整個樹形圖，再應用於計算歐式和美式選擇權以及可轉換公司債的評價。
本文發現在適當參數設定下，利用利率樹所計算之債券價格與二因子四元樹所計算出的歐式買權價格，當切割期數增加時會漸漸收斂至公式解。所以本文之演算方法有其適用性存在，因此進一步利用相同方法去應用於美式股價選擇權之計算上，求出近似解。最後發現本文所建構之樹形圖演算法，不失為一個簡單且可免除繁複計算之評價可轉換公司債的方法之一。

Abstract
In the recent years, Convertible bond (CB) is a very important finance method to enterprises in domestic. Most of papers use Nelson and Ramaswamy’s(1990) transform process to not only must make the transformation but also calculate the probability in every node. So it takes time to process all procedures. Our paper uses the basic of simple binomial tree, and further constructed stock options pricing model with stochastic interest rate. In the other words, we constructed the quaternary tree with two-factor (pyramidal form) which was composed by interest rate and stock’s price. In the process of establishing pricing model, we use coercive recombine, fix the probability, establish all lattice configuration fleetly and apply to pricing European-style options, American-style options, and CB.

We find bond’s prices and European-style call option’s prices which use our lattice algorithm when ∆t becomes very small that the prices converged to formula’s solutions. So, our algorithm has existence of applicability. We also try to use the same method to pricing American-style stock options and solve the approach solutions. By this way, we find our lattice algorithm is a simple and uncomplicated calculated method to pricing CB.

目次
第一章緒論 1
第一節研究背景與動機 1
第二節研究目的 2
第三節論文架構 3
第二章文獻回顧 4
第一節隨機利率模型 4
第二節歐式選擇權評價模型 6
第三節樹形圖結構之演進與應用 10
第三章研究方法 15
第一節建構利率二元樹 15
第二節相關四元樹評價模型介紹 19
第三節建構利率與股價四元樹 23
第四章實證分析 31
第一節債券價格之實證 31
第二節歐式選擇權之實證 32
第三節美式選擇權之計算 35
第五章結論與建議 37
第一節結論 37
第二節建議 37
參考文獻 39
附錄 41

參考文獻
中文部分
期刊論文
林綾怡(2001)，“可轉換公司債價格行為探討”，大華債券期刊，民90.12，頁37-49。
高銘淞(2000)，“利率均數復歸之特性探討與模型建構”，國立臺灣大學國際企業學研究所，碩士論文。
張大成;薛兆雯(2002)，“可轉換公司債之評價—六元樹分析方法”，貨幣觀測與
信用評等，民91.07 ，頁114-121。
程國榮(2000)，“以Hull and White利率模型評價可轉換公司債”，國立高雄第一科技大學金融營運研究所，碩士論文。
薛慶溫(2001)， “可轉換公司債之定價分析”，國立成功大學數學研究所，碩士論文。

網路資源
公開資訊觀測站http://newmops.tse.com.tw/。
台灣期貨交易所http://www.taifex.com.tw/chinese/home.htm。
證券櫃檯買賣中心http://www.otc.org.tw/ch/index.php。

其他
文曄科技股份有限公司發行國內第四次無擔保轉換公司債簡式公開說明書。

英文部分
Books
Hull, J. (2006), “Options, Futures, and Other Derivatives”, six edition (Pearson
Education, Ltd.).
Tuckman, B. (2002), “Fixed Income Securities: Tools for Today''s Markets”, second edition (John Wiley and Sons, Inc.).

Journal Articles
Amin, K. and R. Jarrow (1992), “Pricing Option on Risky Assets in a Stochastic Interest Rate Economy”, Mahematical Finance, Vol. 2, pp. 217-237.
Black, F. and M. Scholes (1973), “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, Vol. 81, pp. 637-654.
Boyle, P. (1986), “Options Valuation Using a Three-Jump Process”, International
Option Journal, Vol. 3, pp. 7-12.
Cox, J., J. Ingersoll, and S. Ross (1985), “A Theory of the Term Structure of Interest Rates”, Econometrica, Vol. 53, pp. 385-408.
Cox, J., S. Ross, and M. Rubinstein (1979), “Option Pricing: A Simplified Approach”,
The Journal of Financial Economics, Vol. 7, pp. 229-263.
Chen, R.R. and T. Yang (2006), “A Sample Algorithm for Pricing Contingent Claims with Stochastic Interest Rates”, Working Paper.
Heath, D., R. Jarrow, and A. Morton (1992), “Bond Pricing and Term Structure of Interest Rate: A New Methodology”, Econometrica, Vol. 60, pp. 77-105.
Hilliard, J., A. Schwartz, and A. Tucker (1996), “Bivariate Binomial Options Pricing with Generalized Interest Rate Processes”, The Journal of Financial Research, Vol.19, pp. 585-602.
Jamshidian, F. (1989), “An Exact Bond Option Pricing Formula”, Journal of Finance, Vol. 44,pp. 205-209.
Kishimoto, N. (1989), “Pricing contingent claims under interest rate and asset price risk”,The Journal of Financial, Vol. 28, pp. 571-590.
Morton, R. (1973), “Theory of Rational Option Pricing”, Bell Journal of Economics, Vol. 4, pp. 141-183.
Nelson, D. and K. Ramaswamy (1990), “Simple Binomial Processes as Diffusion Approximations in Financial Models”, The Review of Financial Studies, Vol. 3, pp. 393-430.
Ritchken, P. and R. Trevor (1999), “Pricing Options under Generalized GARCH and Stochastic Volatility Processes”, The Journal of Finance, Vol. 54, pp. 377-402.
Rabinovitch, R. (1989), “Pricing Stock and Bond Options when the Default-Free Rate is Stochastic”, The Journal of Financial and Quantitative Analysis, Vol. 24, pp. 447-457.
Wei, J. (1993), “Valuing American Equity Options with a Stochastic Interest Rate：A Note”, The Journal of Financial Engineering, Vol. 2, pp. 195-206.
Vasicek, O. (1977), “An Equilibrium Characterization of the Term Structure”, Journal of Financial Economics, Vol. 5, pp. 177-188.