本論文是臺灣期貨交易所委外研究計劃的其中一部分，主要在探討臺灣期貨交易所規劃的股票選擇權契約資本調整制度所潛在的問題。台灣的金融市場目前並沒有標準化的選擇權契約，只有非標準化的認購權證契約，而且認售權證付之闕如。為使台灣金融市場更加成熟，臺灣期貨交易所積極規劃標準規格的選擇權契約。初期先推出以加權指數為標的的選擇權契約，爾後更將發行個股選擇權契約。但個股選擇權契約為維持標準化規格，在標的股票有除權、股票分割與合併等的所謂「資本調整」現象時，無法完全採用認購權證的調整方式。因此，臺灣期貨交易所規劃一套現金撥補制度，以現金撥付的方式補償投資人在標的股票資本調整時維持標準契約規格所導致的損失。本研究即在探討臺灣期貨交易所規劃的現金撥補制度之潛在問題。該現金撥補制度存在以下的假設前提：(1) 選擇權契約是歐式選擇權， (2) 維持投資人以除權參考價計算的投資組合損益不受除權調整影響， (3) 不考慮執行價合併導致投資組合損益結構改變的影響， (4) 計算撥補金的波動性參數以歷史波動性模型估計。
本研究以不同的選擇權評價模型，建立波動性價差交易策略(Volatility Spread Trading)，探討此撥補金制度對不同的價差交易策略所造成的影響。經過本研究取樣二十檔左右的個股實證後發現，撥補金制度假設選擇權契約是歐式選擇權，對投資人的影響程度視選用何種評價模型而定。而因為價差交易投資人收到撥補金時是除權當天開盤時，因此以開盤價計算的投資組合不可能完全不受除權調整的影響。而本研究以指數加權波動性模型(EWMA)與歷史波動性模型相比，即突顯不同波動性模型選用之差異，因此值得期貨交易所對波動性模型之選擇做更深入的探討。最後針對執行價合併導致價差交易策略投資組合損益結構改變的影響，本研究實證後發現此影響可能將會是此撥補金制度最大的潛在問題，值得作更深入的探討。
本研究是利用實際的市場資料所計算的選擇權理論價值作為實證基礎，假如能夠使用其他的研究設計方式或實際的選擇權交易資料，或許更能貼切的描述此撥補金制度潛在問題的嚴重性。臺灣期貨交易所針對以上撥補金制度的潛在問題，應該與社會大眾作充分的溝通，俾使不利的影響降至最低。(為了便於後續研究之便，本研究將選擇權評價模型的估價程式附於附錄以供參考)

This essay investigates the potential problems in capitalization adjustment system of stock option contract designed by Taiwan Futures Exchange. There is no standardized option contract in Taiwan financial market, but only non — standardized contract such as warrant. For the progress of Taiwan market, Taiwan Futures Exchange is planing to establish a standardized option contract expected to be traded recently. Option contract whose target asset is stock index will be promoted at first and individual stock as target asset at a later time. However, in order to maintain standardized contract specification for liquidity consideration, Taiwan Futures Exchange cannot apply the same adjusting method of warrant contract when target stocks have capitalization adjustment such as ex — dividend, stock split, etc. Therefore, Taiwan Futures Exchange designs cash compensation institution to compensate investors’ losses resulted from sustaining standardized contract specification during capitalization adjustment. The cash compensation mechanism has the following premises: (1) Option contract is European. (2) The profit and loss of portfolio calculated by ex — dividend preferred price is zero. (3) Neglecting the influence from strike price combination on investors. (4) Volatility estimator is calculated by historical volatility. In this research, we establish different kinds of volatility spread trading strategies by many distinct option — pricing models and discuss the cash compensation institution’s influence on them. According to the evidence of this survey, we find that if Taiwan Futures Exchange assumes option contract is European, how serious the influential degree will be depends on what kind of pricing model is employed. And because investors receive their cash compensation on ex — dividend day, it is impossible to completely avoid the disturbance of ex — dividend adjustment. In this study, we also signify the difference on experimented result between two volatility estimation models by using EWMA and historical volatility model. It is worthy for Taiwan Futures Exchange to do further research on volatility model selection. Finally, we discover that the most obvious influence on investors of this cash compensation mechanism lies on the omission of result from strike price combination. This shows the opportunity for further studying on this subject. The employed data in this survey come from theoretical value calculated by real market information. If one can design another survey methodology or find real trading data for advanced investigation, it may be capable to entirely describe the significance of this system’s potential damage. To reduce the potential disadvantages of this system, Taiwan Futures Exchange should consult with the possible users, academics and practitioners.

第一章 緒論 …….……………………………………….1
第一節 研究動機與研究目的 ……………………………….1
第二節 研究問題 …………………………………………….3
第三節 研究範圍 …………………………………………….4
第二章 理論基礎與制度探討 ………………………..…7
第一節 各國選擇權合約制度規劃 ………………………….7
第二節 臺灣期貨交易所股票資本調整後
選擇權合約調整制度規劃 ………………………….15
第三節 選擇權評價模型 …………………………………….30
第四節 波動性估計模型 …………………………………….40
第五節 價差交易的種類 …………………………………….42
第三章 研究設計 ………………………………………….….49
第一節 選擇權理論模型之使用 ..…………………………...49
第二節 實證資料來源與處理 ……………………………….51
第三節 研究定位 …………………………………………….55
第四節 虛擬投資組合設計 ………………………………….56
第五節 價差交易策略因執行價合併
損益結構改變之探討 ……………………………….58
第六節 研究設計 …………………………………………….67
第四章 實證分析 ………………………………………..78
第一節 不同研究設計之實證結果 ………………………….78
第二節 各種美式選擇權評價模型
在各研究設計之實證結果 ………………………….84
第五章 結論與建議 ………………………………………..…103
第一節 研究結論 ……………………………………………. 103
第二節 研究建議 …………………………………….…109
第三節 研究限制 ………………………………………….…110
參考文獻 …………………………………………………111
附錄一 現金股利轉換連續股利率之轉換方法 ………113
附錄二 第四章第一節分組實證結果 …………………115
附錄三 美式選擇權評價模型Matlab程式碼 ………..123

1. Adesi, B. Giovanni, and Robert E. Whaley, 1984, Efficient Analytic Approximation of American Option Values, Journal of Finance 42, 301-320.
2. Boyle, P. P., 1977, Options: A Monte Carlo Approach, Journal of Financial Economics 4, 323-338.
3. Boyle, P. P., 1988, A Lattice Framework for Options Pricing with Two State Variable, Journal of Financial and Quantitative Analysis 23, 1-12.
4. Blomeyer, Edward, C., and Herb Johnson, 1988, An Empirical of the Pricing of American Put Options, Journal of Financial and Quantitative Analysis 23, 13-22.
5. Boyle, P. P., J. Evnine, and S. Gibbs, 1989, Numerical Evaluation of Multivariate Contingent Claims, Review of Financial Studies 2, 241-50.
6. Bjerksund, P., and G. Stensland, 1993, American Exchange Options and a Put — Call Transformation: A Note, Journal of Business Finance and Accounting 42, 791-764.
7. Boyle, P. P., and S. H. Lau, 1997, Bumping Up Against the Barrier with the Binomial Method, Journal of Derivatives 1, 6-14.
8. Bollen, Nicolas, 1998, Valuing Options in Regime-Switching Models, Journal of Derivatives 45, 38-49.
9. Broadie, Mark, Jerome Detemple, and Eric Ghysels, 2000, American Options with Stochastic Dividends and Volatility：A Nonparametric Investigation, Journal of Econometrics 94, 53-92.
10. Cox, John C., and Mark Rubinstein., 1979, Option Pricing: A Simplified Approach., Journal of Finance 7, 229-263.
11. Clewlow, Les, and Chris Strickland, 1998, Implementing Derivatives Models, N. J.: John Wiley & Sons.
12. Chance, Don, M., 1999, Research Trends in Derivatives and Risk Management Since Black-Scholes, Journal of Portfolio Management 35, 35-46.
13. Dempster, M. A. H., and J. P. Hutton, 1999, Pricing American Stock Options by Linear Programming, Mathematical Finance 9, 229-255.
14. Dempster, M. A. H., and D. G. Richards, 2000, Pricing American Options Fitting the Smile, Mathematical Finance 10, 157-177.
15. Espen, G. Haug, 1997, The Complete Guide to Option Pricing Formulas, N. J.: McGraw Hill.
16. Fisher, Black, 1976, The Pricing of Commodity Contracts, Journal of Financial Economics 3, 167-179.
17. Geske, Robert, 1979, The Valuation of Compound Options, Journal of Financial Economics 7, 63-85.
18. Hull, John C., 1997, Options, Futures, & Other Derivatives, N. J.: Prentice Hall.
19. Hansen, Asbjorn, T. and Peter Lochte Jorgensen, 2000, Analytical Valuation of American-style Asian Option, Management Science 46, 116-1136.
20. Ju, Nengjiu, and Rui Zhong, 1999, An Approximate Formula for Pricing American Options, Journal of Derivatives 7, 31-40.
21. Lim, Kian Guan, 2000, Pricing American Options with Stochastic Volatility：Evidence from S＆P 500 Futures Options, Journal of Futures Markets 20, 625-659.
22. Roll, Richard, 1977, An Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends, Journal of Financial Economics 5, 251-258.
23. Rendleman, Richard J., Jr., and Brit J. Bartter., 1979, Two — State Option Pricing, Journal of Finance 34, 1093-1110.
24. Stultz, Michael, and Muinul Chowdhury, 1999, A Simple Non-Parametric Approach to Bond Futures Option Pricing, Journal of Fixed Income 50, 67-76.
25. Whaley, Robert E., 1982, Journal of Financial Economics 10, 29-59.
26. 滑明曙，民國88年8月，「選擇權估價理論」，第二版，華泰書局。