Britten-Jones and Neuberger(2000)在擴散假設下，推導出無模型設定隱含波動
度(model free implied volatility)，Jiang and Tian(2005)將無模型設定的隱含波動度
擴展至資產價格服從跳躍-擴散過程(diffusions and jumps process)之假設，本文依
據Jiang and Tian(2005)，算出買權和賣權的無模型設定隱含波動度，並和Black and 
Scholes隱含波動度、落階一期已實現波動度、選擇權未平倉量、選擇權日交易
量等變數作迴歸分析，檢視無模型設定隱含波動度是否為眾多變數中對實際波動
度包含最多的資訊，且為預測實際波動度的最佳指標。此外再依照以Joseph 
K.W.Fung(2007)信號模型，檢驗無模型設定隱含波動度是否能在市場發生異常波
動前，為一良好之警示信號。
實證結果如下：
1.  在單變量迴歸中，買權無模型設定隱含波動度確實為所有變數中，對實際波動度的解釋能力最高，包含最多的資訊；在包含迴歸中，比起其它波動度預測指標，買權無模型設定隱含波動度較可以統合其它變數之資訊，大致能包含Black and Scholes隱含波動度、選擇權未平倉量、選擇權日交易量變數的資訊。
2.   將樣本外預測之結果應用於Joseph K.W.Fung(2007)信號模型，發現在2007年10月18日市場真實波動度為31.97%，信號在同年9月時已經超過1，因為本文僅檢視2007年台股受房貸衝擊之影響，鑑於樣本數略嫌不足之餘，因此實證結果僅能指出買權無模型設定隱含波動度於JosephK.W.Fung
(2007)信號模型下，可能為一良好之及早警示信號。

Britten-Jones and Neuberger(2000) derived the model-free implied volatility
under the assumption that the price of underlying asset follows diffusion process. Jiang and Tian(2005) further extend the model-free implied volatility to asset price process with jumps. This thesis examines the forecasting ability and information content of the model-free implied volatility of call, model-free implied volatility of put, Black and Scholes implied volatility, the lagged realized volatility, option interest of TXO and volume of TXO. According to the signal model of Joseph K.W. Fung(2007),this thesis also examines whether the model-free implied volatility could have been an useful warning signal prior to periods of the abnormal volatility.
The empirical results show as follows：
1. Based on an univariate regression, the Adj for the model-free implied volatility of call is higher than other potential indicators of realized volatility. The model-free implied volatility of call contains more information than other potential indicators. The encompassing regression results show that the model-free implied volatility of call subsumes all information contained in the most potential indicators of future realized volatility.
2. Because it seems that numbers of the samples are not enough. Under the signal
  model of Joseph K.W.Fung(2007),the model-free implied volatility of call may be
  an useful warning signal prior to periods of the abnormal volatility.

目錄
第一章   緒論	1
第一節 研究背景	1
第二節 研究動機	3
第三節 研究目的	4

第二章   文獻探討	7
第一節 各種波動度模型估計之相關研究	7
第二節	各種波動度對實際波動度預測能力之比較	11
第三節 未平倉量、成交量和實際波動度之關係	14

第三章   研究方法	20
第一節 實證研究資料	20
第二節 買權無模型設定的隱含波動度	22
第三節	賣權無模型設定隱含波動度	27
第四節 Black and Scholes 隱含波動度	28
第五節	實際波動度	29
第六節 歷史波動度	31
第七節 選擇權未平倉量和選擇權日交易量	32
第八節 迴歸分析與信號模型	37

第四章 實證分析	42
第一節 迴歸分析結果	42
第二節 樣本外預測結果	57

第五章 結論與建議	59

參考文獻	61







表目錄
表3-1  各個變數之簡單統計量...............................................................................32
表3-2  30天期波動度、選擇權未平倉量、選擇權日交易量之相關性矩陣.….34
表4-1  30天期波動度、選擇權未平倉量、選擇權日交易量之單變量迴歸…..46
表4-2  30天期 和其它變數之包含迴歸.........................................................47
表4-3  30天期 和其它變數之包含迴歸.........................................................48
表4-4  30天期 、 和其它變數之包含迴歸..............................................49
表4-5  30天期波動度之包含迴歸…......................................................................50
表4-6  30天期波動度取對數和其它變數取對數之單變量迴歸..........................51
表4-7  30天期ln 和其它變數取對數之包含迴歸.........................................52
表4-8  30天期ln 和其它變數取對數之包含迴歸.........................................53
表4-9  30天期ln 、ln 和其它變數取對數之包含迴歸...........................54
表4-10  30天期波動度取對數之包含迴歸............................................................55
表4-11  30天期 之自我迴歸結果…...............................................................56
表4-12  信號和異常波動度表…………………….................................................57










圖目錄
圖3-1  各波動度預測模型與實際波動度之走勢圖…............................................35
圖3-2  選擇權未平倉量與實際波動度之走勢圖…................................................36
圖3-3  選擇權日交易量與實際波動度之走勢圖…................................................36

中文文獻
1. 呂美儀 (2007)，「臺指選擇權隱含波動度預測能力之實證分析」，淡江大學財務金融學系碩士班碩士論文。
2. 李進生、袁淑芳 (2005)，「台指選擇權與現貨市場之正向價格回饋行為研究：隱含波動值指標和未平倉口數之應用」，經營管理論叢，第一屆管理與決策2005年學術研討會特刊，頁191~206。
3. 李校德 (2004)，「未平倉量與價格波動性之關聯性」，淡江大學財務金融學系
碩士班碩士論文。
4. 周文初 (2003)，「台灣股價指數報酬與指數選擇權交易量相關性之研究」，淡江大學財務金融學系碩士在職專班碩士論文。
5. 倪衍森、吳曼華、鄭亦妏 (2005)，「在Black-Scholes 評價模型下台指選擇權最適波動性估計方法之研究」，管理科學研究，第2卷第1期，頁93~109。
6. 許美滿 (2007)，「衍生性市場創新、交易機制與隱含波動」，淡江大學財務金融學系博士班博士論文。
7. 黃雯卿 (2007)，「無模型設定隱含波動度之實證研究-以台灣股價指數選擇權為例」，東華大學國際經濟研究所碩士論文。
8. 謝文良、李進生、袁淑芳、林惠雪 (2007)，「台灣股價指數現貨、期貨與選擇權市場之價格發現研究—put-call parity之應用」，中華管理評論國際學報，第十卷第二期，頁1~24。
9. 鍾惠民、吳壽山、周賓凰、范懷文合著 (2002)，「財金計量」，台北，雙葉書廊。

英文文獻
1. Ait-Sahalia, Y., and A. W. Lo (1998), “Nonparametric Estimation of State-price Densities Implied in Financial Asset Prices,” Journal of Finance, pp.499-547.
2. Andersen, T. G., and T. Bollerslev (1998), “Answering the Critics:Yes, ARCH Models Do Provide Good Volatility Forecasts,” International Economic Review, pp. 885-905.
3. Andrea, B., and J. C. Jackwerth (1998), “Explaining Option Prices:Deterministic vs.Stochastic Models, Working paper, London Business School.
4. Arjun C., and Kamath R., and Chakorpipat R., and Sanjay Ramchander (1995), “Lead-lag Associations between Option Trading and Cash Market Volatility,” Applied Financial Economics, pp.373-381.
5. Bakshi, G., and C. Cao, and Zhiwu C. (1997), “Empirical Performance of
  Alternative Option Price Models,” Journal of Finance, Vol. 52, pp.2003-2049.
6. Barndorff-Nielsen, O. E., and N. Shephard (2003), “Realized power Variation and Stochastic Volatility Models,” Bernouilli, pp.243-265.
7. Bates, D. (1991), “The Crash of ’87: Was it Expected？The Evidence from Options
  Markets,” Journal of Finance, pp.1009-1044.
8. Bernard, D., Fleming J., and R. E. Whaley (1998), “Implied Volatility Functions:
  Empirical Tests, Journal of Finance, pp.2059-2106.
9. Black, F., and M., Scholes (1973), “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, pp.637-659.
10. Blair, B.J., S. Poon, and S. J., Taylor (2000), “Forecasting S&P100 Volatility: the Incremental Information Content of Implied Volatilities and High-frequency Index Returns,” Journal of Econometrics, pp.5-26.
11. Bolerslev, Tim, and Michael, Gibson, and Hao Zhou (2006), “Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-Implied and Realized Volatilities”.
12. Britten-Jones, M., and A. Neuberger (2000), “Option Prices, Implied Price Processes, Stochastic Volatility,” Journal of Finance, pp.839-866.
13. Brooks, C. (1998), “Predicing Stock Index Volatility：Can Market Volume Help？,” Journal of Forecasting, Vol. 17, pp.59-80.
14. Bruno D. (1994), “Pricing with a smile,” Risk, pp.18-20.
15. Canina, L., and S. Figlewski (1993), “The Information Content of Implied Volatility,” The review of financial studies, Vol. 6, pp.591-681.
16. Christensen, B.J., and N.R., Prabhala (1998), “The Relation between Implied and
   Realized Volatility,” Journal of Financial Economics, pp.125-150.
17. David I.H., J.L., Stephen, and N., Paul (1998), “Test for Forecast Encompassing,”
   Journal of Business & Economic Statistics, Vol. 16.
18. Day, T.E., and M.L., Craig (1992), “Stock Market Volatility and the Information
   Content of stock Index Options,” Journal of Econometrics, pp.267-287.
19. Derman, Emanuel, and Kani, Iraj, and Zou, Joseph Z. (1996), “The Local
   Volatility Surface: Unlocking the Information in Index Option Prices,” Financial
   Analytis of Journal, pp.25-36.
20. Dimson E., P. Marsh, and M. Staunton (2007), “Volatility and Portfolio protection
   over 107 years,” Beta Workshop in Historical Economics Financial History,
   pp.1-36.
21. Dumas, B., J. Fleming, and R. Whaley (1998), “Implied Volatility Functions: Empirical Tests,” Journal of Finance, pp.2059-2106.
22. Ederington, L., and W. Guan (2002), “Why Are Those Options Smiling？,” Journal of Derivatives, pp.9-34.
23. Ederington, L. H., and W. Guan (2002), “Measuring Implied Volatility is an Average Better？Which Average？,” Journal of Futures Market, Vol. 22, pp.811-837.
24. Fleming, J. (1998), “The Quality of Market Volatility Forecasts Implied by S&P
100 Index Option Prices,” Journal of Empirical Finance, pp.317-345.
25. Hagelin, N. (2000), “Index Option Market Activity and Cash Market Volatility under Different Market Conditions：An Empirical Study from Swedn,” pp597-613.
26. Harvey, C. R., and R. E. Whaley (1992b), “ Dividends and S&P100 Index Option Valuation,” Journal of Futures Markets, pp.123-137.
27. Jackwerth, J. C., and M. Rubinstein (1996), “Recovering Probability Distribution from Option Price,” Journal of Finance, Vol. 51, pp.1611-1631.
28. Jiang, G. J., and Y.S. Tian (2005), “The Model-Free Implied Volatility and Its Information Content,” The Review of Financial Studies, Vol. 18, pp.1305-1342.
29. Jorion, P. (1995), “Predicting Volatility in the Foreign Exchange Market ,” Journal of Financial, Vol. 50, pp. 507-528.
30. Joseph K. W. Fung (2007), “The Information Content of Option Implied Volatility Surrounding the 1997 Hong Kong Stock Market Crash,” The Journal of Futures Markets, Vol. 27, pp.555-574.
31. Karpoff (1986), “A Theory of Trading Volume,” Journal of Finance, pp.1069-1087
32. Kim, M., and G. R. Kim, and M. Kim (2004), “Stock market Volatility and Trading Activities in the KOSPI 200 Derivatives Markets,” Applied Economics Letters, pp.49-53.
33. Lakonishok, J., and I. Lee, and N. D. Pearson, and A. M. Pteshman (2006), “Option Market Activity,” The Review of Financial Studies, Vol.20, pp.813-857.
34. Lamoureux, C.G., and W. D. Lastrapes (1993), “Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatility,” The Review of Financial Studies, pp.293-326.
35. Latane, H. A., and R. J. Rendleman (1976), “Standard Deviations of Stock Price Ratios Implied in Options Prices,” The Journal of Finance, Vol. 31, pp.369-381.
36. Mayhew S., and C. Stivers (2003), “Stock Return Dynamics, Option Volume, and the Information Content of Implied Volatility,’’ The Journal of Futures Markets, Vol. 23, No. 7, pp.615-646.
37. Patell, J., and M. Wolfson (1979), “Anticipated Information Release Reflected in Call Option Prices,” Journal of Accounting and Economics, pp. 117-140.
38. Poon, S. H., and C. W. J. Granger (2003), “Forecasting Volatility in Financial Markets: A Review”, Journal of Economic Literature, pp.478-539.
39. Poteshman A. M. (2006), “Unusual Option Market Activity and the Terrorist
Attacks of September 11, 2001,” Journal of Business, Vol. 79, pp.1703-1725.
40. Rubinstein, M. (1994), “Implied Binomial Trees,” Journal of Finance, pp.771-818.
41. Schachter B. (1988), “Open Interest in Stock Options around Quarterly Earnings Announcements,” Journal of Accounting Research, Vol. 26, pp.353-372.
42. Schwert, G.W. (1990), “Stock Volatility and the Crash of ’87,” The Review of Financial Studies, Vol. 3, pp. 77-102.
43. Stoll, H. R., and R. E. Whaley (1990), “The Dynamics of Stock Index and Stock Index Futures Returns,” Journal of Financial and Quantitative Analysis, pp.441-468.