臺灣博碩士論文加值系統

雖然已有許多文獻提出不同的方法來評價美式選擇權，但由於計算上的困難目前關於美式選擇權的定價大部分都是逼近解，或是採用數值方法來求解。對一般投資人來說不易了解，即使了解其理論背景也常因計算繁瑣問題而讓人望之卻步。
本研究希望建立一套股票選擇權分析系統，使一般投資大眾可以容易計算美式選擇權提早執行的界限。此系統將常見的評價模型模組化，讓投資者可以輕易使用分析系統作決策而不需要具備艱深的理論基礎。本論文建立的評價分析系統分為兩大部分，一是評價分析系統，另一是資產價格模擬系統。評價分析系統提供使用者在不同模型下進行選擇權的評價分析；而資產價格模擬系統則是一套由電腦虛擬產生資產價格的系統。

In the literature, many methods are proposed to value American options. However, due to computational difficulty, there are only approximate solution or numerical method to evaluate American options. It is not easy for general investors either to understand nor to apply.
In this thesis, we build up an option pricing and virtual asset model system, which provides a friendly environment for general public to calculate early exercise boundary of an American option. This system modularize the well-handled pricing models to provide the investors an easy way to value American options without learning difficult financial theories. The system consists two parts: the first one is an option pricing system, the other one is an asset model simulation system. The option pricing system provides various option pricing methods to the users; the virtual asset model system generates virtual asset prices for different underlying models.

第一章 導論 5
第二章 選擇權介紹 7
2.1 股票選擇權 7
2.2 美式選擇權提早履約的條件 8
2.3 提早履約的界限 9
第三章 各種評價模型 13
3.1 Black-Scholes選擇權評價模型 14
3.2 二項式樹狀評價模型 16
3.3 有限差分法 18
3.4 二次逼近法 20
第四章 選擇權評價分析系統 22
4.1 選擇權評價分析 22
4.2 標的資產價格模型 25
第五章 資料分析 36
5.1 資料取得 36
5.2 選擇權鏈資料 36
5.3 實證結果 38
第六章 結論 40
參考文獻 40
附錄ㄧ、30支股票選擇權代號列表 42
附錄二、30支股票選擇權模擬結果 43
附錄三、模擬股價過程 70
附錄四、系統架構 71

[1] Barone-Adesi, G., and R. Whaley. (1987),Efficient Analytical Approximation of American Option Values. Journal of Finance, 42,pp. 301-320.
[2] Black, F., and M. Scholes. (1973),The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, pp. 637-659.
[3] Brennan, M., and E. Schwartz. (1977),The Valuation of American Put Options. Journal of Finance, 32, pp. 449-462.
[4] Basso, A., Nardon, M. and Pianca, P. (2002),Optimal exercise of American options. Quaderni del Dipartimento di Matematica Applicata, n. 105, Universit`a “Ca’ Foscari” di Venezia.
[5] Bollerslev, T. (1986), Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, Vol. 31, pp.307-327.
[6] Cox, J. C., S. A. Ross, and M. Rubinstein. (1979),Option Pricing: A simplified Approach. Journal of Financial Economics, 7, pp.229-264.
[7] Geske, R., and H. E. Johnson. (1984),The American Put Valued Analytically. Journal of Finance, 39, pp. 1511-1524.
[8] Johnson, H. (1983),An Analytical Approximation for the American Put Price. Journal of Financial and Quantitative Analysis, 18, pp.141-148.
[9] Hull, John C.(2000), Options, Futures, and Other Derivatives, 4th edition. Prentice Hall, United States of America.
[10] Ju., N., and Zhong, R. (1998), An Approximate Formula for Pricing American Options. Review of Financial Studies, 11, 3 pp.627-646.
[11] MacMillan, L. W. (1986),An Analytical Approximation for the American Put Prices. Advances in Futures and Options Research, 1, pp.119-139.
[12] Merton, R. C. (1973),Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, 4, pp. 141-183.
[13] Neftci, Salih N. (2000),An Introduction to the Mathematics of Financial Derivative, second edition, p.499, Elsevier Science, United States of America.
[14] Tsay, Ruey S. (2002), Analysis of Financial Time Series, pp.93-100, 244-251. Wiley Inter-Science, United States of America.
[15] 陳戚光, (2001), 選擇權：理論˙實務與應用, pp.319-320, 台灣.