選擇權訂價模型中，波動性的估計是重要探討之議題，學者專家們相繼提出各種波動性之估計模型，欲尋找出何種波動性模型所得之選擇權理論價格與實際市場價格差距最小，本文中以台灣加權股價指數及台灣股價指數選擇權為研究標的，利用變幅估計式（Range Based Estimators）估計其波動性，結合採用不對稱GJR-GARCH模型及MA、AR、EWMA、RW及ARMA等時間序列模型等作為預測模型，並以平均絕對誤差（mean absolute errors， MAE）、均方誤差（mean squared errors，MSE）、平均混合誤差（mean mixed error，MME）等傳統損失函數及優勢預測能力檢定（Superior Predictive Ability Test，SPA）模型，來衡量不同方法模型中何種模型預測績效較能貼近實際市場波動性，希望能藉此找出一適合的模型，可較準確地預測出台灣股價指數波動度，藉以降低台指選擇權之交易風險。結果顯示結合變幅估計式之預測模型對於台灣加權股價指數有較佳的預測效果，而對台灣股價指數選擇權，則以GJR-GARCH模型預測效果較佳。

On the field of the option pricing model, the prediction of volatility is one of the important topics among others. For the purpose of searching for a model reflecting the narrowest gap between the theoretical prices of option and the actual market price, the scholars and experts have proposed a variety of models for volatility prediction.  This article takes TAIEX and TAIEX Option as the research object, using Range-Based Estimators to estimate the volatility, along with asymmetric GJR-GARCH model and the MA, AR, EWMA, RW and ARMA time series model as the models for the prediction of TAIEX and TAIEX Option.  Furthermore, some traditional loss function such as mean absolute errors, MAE, mean squared errors, MSE, and mean mixed errors, MME as well as the Superior Predictive Ability Test, SPA are applied in this article to determine which model with the foregoing methods has better accuracy in predicting the volatility of the actual market.  In addition, the goal of this article is in a hope to search out a proper model which can predict the volatility of TAIEX more accurately, and to reduce the transaction risk of TAIEX Option by way of such model.  In conclusion, the result indicates that the combination of Range-Based Estimators of the predicting model presents a better effect on prediction for TAIEX, while GJR-GARCH is better for TAIEX Option.

目錄
頁次
第一章	緒論……………………………………1
第一節	研究背景與動機………………………1
第二節	研究目的………………………………3
第三節	研究架構………………………………4
第四節	研究流程圖……………………………5
第二章	文獻回顧………………………………6
第一節	波動性估計模型相關文獻……………6
第二節	台指選擇權市場實證之相關文獻……8
第三章	研究方法………………………………12
第一節	單根檢定………………………………12
第二節	ARCH效果檢定…………………………15
第三節	條件變異數不對稱檢定………………17
第四節	波動率的估計方法……………………19
第五節	樣本外預測……………………………23
第六節	評量預測模型績效方法………………24
第四章	實證結果分析…………………………28
第一節	研究對象、研究期間與資料處理……29 
第二節	基本統計量分析………………………30
第三節	單根檢定………………………………31
第四節	ARCH效果檢定…………………………33
第五節	條件變異數不對稱檢定………………34
第六節	各模型之估計結果績效檢定…………35
第五章	結論……………………………………46
附表…………………………………………………47
參考文獻……………………………………………57

表目錄
頁次
【表4-1-1】台灣加權股價指數選擇權之樣本個數………………29
【表4-2-1】台灣加權股價指數日報酬率之基本統計量…………30
【表4-3-1】台灣加權股價指數原始序列之單根檢定（水準項）32
【表4-3-1】台灣加權股價指數原始序列之單根檢定（差分項）32
【表4-4-1】台灣加權股價指數ARCH效果檢定……………………33
【表4-5-1】台灣加權股價指數條件變異數不對稱效果檢定……34
【表4-6-1】損失函數為MAE之SPA檢定結果(前10名)……………36
【表4-6-2】損失函數為MSE之SPA檢定結果(前10名)……………37
【表4-6-3】損失函數為MME(O)之SPA檢定結果(前10名)…………38
【表4-6-4】損失函數為MME(U)之SPA檢定結果(前10名)…………39
【表4-6-5】價外買權預測績效SPA檢定結果(前10名)……………40
【表4-6-6】價平買權預測績效SPA檢定結果(前10名)……………41
【表4-6-7】價內買權預測績效SPA檢定結果(前10名)……………42
【表4-6-8】價外賣權預測績效SPA檢定結果(前10名)……………43
【表4-6-9】價平賣權預測績效SPA檢定結果(前10名)……………44
【表4-6-10】價內賣權預測績效SPA檢定結果(前10名) …………45

一、國外文獻
Akgiray, V. (1989), Conditional heteroscedasticity in the series of stock return evidence and forecasts, Journal of Business, Vol. 62, p.55-80.
Anders W. (2006), Garch forecasting performance under different distribution assumptions, Journal of Forecasting, 25, 561-578.
Basel M. A. A. and Valentina C., (2005), Predicting the volatility of the S&P-500 stock index via GARCH model：The role of asymmetries, International Journal of Forecasting, 21, 167-183.
Beckers, S. (1981), Standard deviation implied in option prices as predictors of future stock price variability, Journal of Banking and Finance, Vol. 5, p.363-382.
Black, F. and M. S. (1973), The pricing of options and corporate liabilities, Journal of Political Economy, Vol. 81, p.637-659.
Bollerslev, T. (1986), Generalized autoregressive conditional heteroscedasticity, Journal of Econometrica, Vol. 31, p.307-327.
Lin C. T., Hung J. C. and Wang Y. H. (2005), Forecasting the one-period-ahead volatility of the internatilal stock indices：GARCH Model vs. GM(1,1)-GARCH Model, Journal of Grey System, Vol. 8, No. 1, 1-12.
Chu, S. H. and S. Freund, (1996), Volatility estimation for stock index options：A GARCH Approach, The Quarterly Review of Economics and Finance, Vol. 36, p.431-450
David G. M. and Alan E.H. Speight, (2007), Weekly volatility forecasts with applications to risk management, The Journal of Risk Finance Vol. 8, No. 3, p.214-229.
Engle, R. F. (1982), Autoregressive conditional heteroscedasticity with estimates of of the variance of untied kingdom inflation, Econometrica, July, p.987-1007.
Fleming, J. (1998), The quality of market volatility forecasts implied by S&P 100 index option prices, Journal of Empirical Finance, Vol. 5, p.317-345.
Garman, M. B. & Klass, M. J. (1980), On the estimation of security price volatilities from historical data, Journal of Business, 53, 67-78.
Gloria G. R., Lee, T. H. And Santosh M. (2004), Forecasting volatility：A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood, International Journal of Forecasting 20, 629-645.
Jacob, J. and Vipul, (2008), Estimation and forecasting of stock volatility with range-based estimators, The Journal of Futures Markets, Vol. 28, No. 6, 561-581.
Hansen, B. E. (1994), “Autoregressive conditional density estimation”, International Economic Review, 35, 705-730.
Hung, J. C., Chi, C. F., “Evaluating and Improving GARCH-based Volatility Forecasts with Extreme-Value Volatility Estimators, H. and R. J. Rendleman, (1976), Standard Deviation of stock price ratios implied by option premia, Journal of Finance, Vol. 31, p.369-382.
Parkinson, M. (1980), The extreme value method for estimating the variance of the rate of return, Journal of Business, 53, 61-65.
Rogers, L.C.G. & Satchell, S.E. (1991), Estimating variance from high, low and closing prices, Annals of Applied Probability, 1, 504-512.
Siem J. K., Borus, J. and Eugenie, H. (2005), Forecasting daily variability of the S&P 100 stock index using historical, realized and implied volatility measurements, Journal of Empirical Finance, 12, 445-475.
Twm E. and David G. M. (2007), Volatility forecasts：The role of asymmetric and long-memory dynamics and regional evidence, Applied Financial Economics, 17, 1421-1430.
Vipul and Joshy J. (2007), Forecasting performance of extreme-value volatility estimators, The Journal of Futures Market, Vol. 27, No. 11, 1085-1105.

二、國內文獻
李命志、洪瑞成、劉洪鈞（2007），「厚尾GARCH模型之波動性預測能力比較」，輔仁管理評論，第14卷第2期，頁47-72。
涂惠娟、蔡垂君（2006），「台指選擇權風險值之研究」，交大商管學報，第11卷，第2期，頁57-69。
林佩容（1999），「Black-Scholesd模型在不同波動性衡量下之表現-股價指數選擇權」，碩士論文，國立東華大學企業管理研究所。
陳正暉（2004），「波動度資訊內涵暨預測模型之探究-以台灣股票市場為例」，碩士論文，銘傳大學財務金融研究所。
陳昶均（2004），「不同波動性估計模型下台指選擇權評價績效之比較」，碩士論文，東吳大學商學院企業管理研究所。
莊益源（2003），「波動率模型預測能力的比較-以台指選擇權為例」，台灣金融財務季刊，第4輯第2期，頁41-63。
莊益源、邱臙珍、李登賀（2008），「納入開收盤、最高低價的風險值模型」，經濟研究（Taipei Economic Inquiry），44：2，頁139-176。
葉銀華、蔡麗如（2000），「不對稱GARCH族模型預測能力之比較研究」，輔仁管理評論，第7卷第1期，頁183-196。
謝文良、李進生、袁淑芳（2006），「台股市場波動性指標之建構、資訊內涵與交易策略」，管理與系統，第13卷第4期，頁471-497。