本文利用邊界元素法(boundary element method)作為數值方法，針對發放股利率(dividend yield)之美式買權(American call option)做評價。
美式選擇權提早履約(early exercise)的問題形成一個自由邊界問題(free boundary problem)，其邊界必須以數值方法解得。透過邊界元素法求得最佳履約價函數後，便可評價出美式買權的價格。
我們先簡介選擇權及其常見的評價方式，然後推導與發放股利率之美式買權相關的數學模型以及邊界元素法在此問題上的解法，最後再計算一實際例子並對所得到的結果作探討。

In this text, the boundary element method is designed to pricing the American call option with dividend yield.
The early exercise problem of the American option is a free boundary problem. The boundary of this problem must be obtained by numerical method. By the boundary element method, we can obtain the optimum exercise function then can evaluate the price of the American call option with dividend yield.

1. Black, F., and M. Scholes, May/June 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy,81,637-659.

2. Boyle, P. P., 1977, “Options：A Monte Carlo Approach ,” Journal of Financial Economics, 4, 323-338.

3. Black, F., July/August 1975, “Fact and Fantasy in the Use of Options,”
Financial AnalystsJournal, 31,36-41,61-72.

4. Brennan, M. J., and E. S. Schwartz, September 1978 ,“Finite Difference
Methods and Jump Processes Arising in the Pricing of Contingent
Claims: A Synthesis, “Journal of Financial and Quantitative Analysis, 13,
462-474.

5. Boyle, P. P., 1986, “Option Valuation Using a Three Jump Process,” Internation Option Journal, 3, 7-12.

6. Barone-Adesi, G. and R. E. Whaley, June1987, “Efficient Analytic Approximation of American Option Values,” Journal of Finance,42
,301-320.

7. Cox, J., S. Ross, and M. Rubinstein, October 1979, “Option Pricing: A Simplified Approach, ” Journal of Financial Economics, 7, 229-264.

8. Chance, D. J., 2004, “Closed – Form American Call Option Pricing： Roll - Geske - Whaley,”.

9. Merton, R. C., Spring 1973, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, 4, 141-183.

10. MacMillan, L. W., 1986, “Analytic Approximation for the American Put Option,” Advances in Futures and Options Research, 1, 119-139.

11. Roll, R., 1977, “An Analytical Formula for Unprotected American Call options on Stocks with Known Dividends,” Journal of Financial Economics, 5, 251-258.

12.Hull, J. C.,2005, “Options, Futures, and Other Derivatives 7th Edition,”

12.蕭義龍,2004,“股價機率模型與實證分析,”國立成功大學應用數學所
碩士論文.
14.嚴至賢,2006,“應用邊界元素法評價發放股利之美式選擇權,”國立成
功大學應用數學所碩士論文。
15.鄭凱仁,2002, “美式買權解析近似解之探討, ”國立中正大學數學研
究所碩士論文。
16.范炳杰,2006, “隨機利率下股利發放之美式買權封閉解, ”私立世新
大學財務金融所碩士論文。
17.黃淑雯,2006, “隨機參數二項式美式選擇權定價, ”國立中興大學應
用數學所碩士論文。
18.陳冠群,2006, “隨機波動模型下美式選擇權之評價, ”私立南台科技
大學財務金融所碩士論文。
19.絲文銘,2006, “選擇權：觀念、理論與實務, ”雙葉書廊有限公司。
20.陳松男,2002, “金融公程學：金融商品創新選擇權理論, ”華泰文化
事業公司。
21.陳威光 ,2001, “選擇權：理論、實務與應用, ”智勝文化事業有限公
司。
22.滑明曙,1999, “股票選擇權：估價方法與交易策略, ”。華泰文化
事業公司。