本研究以 2003 年 1 月 1 日至 2015 年 9 月 30 日的美國、歐洲、日本、韓國波動率指數為樣本，運用共整合檢定法，探討各國波動率指數是否存在長期均衡關係；透過多變量GARCH模型，分析各國股票市場間之投資人恐慌情緒是否會有傳遞擴散的效果。
本研究結果發現，各國波動率指數存在領先落後關係，美國波動率指數相對其他各國波動率指數具有領先關係，亦存在長期均衡關係，且VIX與各國波動率指數之間相關性，皆存在顯著正相關。當美國市場投資人情緒發生恐慌時，亦會影響歐洲、日本、韓國三國股票市場；而歐洲投資人的恐慌情緒亦會影響日本、韓國股票市場，顯見跨國投資人恐慌情緒會有傳遞擴散現象。

This thesis utilized the co-integration test to investigate whether long-run equilibrium relationships between volatility index in U.S and the volatility indexes in other countries (such as Europe, Japan, and South Korea, ) from Jan 1, 2003 to Sep 30, 2015. We also used the multivariate GARCH model to analyze the short term volatility effects and to examine whether the contagion effect of investor fear sentiment among those countries.
In term of lead-lag relationship, the results of this thesis showed VIX had leading the volatility indexes of other countries. The long-run equilibrium relationships between volatility index in U.S and the volatility indexes in other countries existed. Moreover, there is a significant correlation coefficient between VIX and the volatility indexes in those countries. Investor fear sentiment in US affected the investors in Europe, Japan, and South Korea. Investor fear sentiment in Europe also affected the investors in Japan, and South Korea. Contagion effect of for Multinational investors fear sentiment existed.

第一章 緒論……………………………………………………………………….…1
第一節 研究背景與動機……………………………………………………1
第二節 研究目的…………………………………………………………..…4
第三節 研究架構…………………………………………………………..…5
第四節 研究流程圖……………………………………………………….…6
第二章 文獻回顧…………………………………………………………….…7
第一節 各國波動率指數編製方式…………..…………...7
第二節 投資人情緒相關文獻…………………………………………14
第三節 波動率指數之相關文獻……………………………………18
第三章 研究方法…………………………………………………….…………24
第一節 單根檢定…………………………………………………….…………24
第二節 共整合檢定……………………………………………….…………27
第三節 多變量GARCH模型…………………………………………..30
第四章 實證結果分析………………………………………………………37
第一節 資料來源與處理…………………………………………………37
第二節 基本統計量分析…………………………………………………38
第三節 單根檢定分析……………………………………….……………44
第四節 共整合檢定分析…………………………..…………..…46
第五節 多變量GARCH模型分析……………………………..…47
第五章 結論…………………………………………………………………………50
參 考 文 獻…………………………………………………………………………52
表目錄
頁次
【表 4-1】基本敘述統計………………...…….……………………….....…………39
【表 4-2】美國波動率指數單根檢定…………………………….………....………44
【表 4-3】歐洲波動率指數單根檢定……………………………………….………45
【表 4-4】日本波動率指數單根檢定………………………………….…....………45
【表 4-5】韓國波動率指數單根檢定……………………………….……....………45
【表 4-6】共整合向量個數檢定……………..………………………….......………46
【表 4-7】各國波動率指數多變量GARCH(1,1)模型之估計………….....…..……47

圖目錄
頁次
【圖 1-1】研究流程圖…………………………………….……………………..…...6
【圖 4-1】VIX收盤價走勢…………………………………....…….………………42
【圖 4-2】VSTOXX收盤價走勢………………………….……….……..…………42
【圖 4-3】NKVI收盤價走勢…………………………….…….……………………43
【圖 4-4】VKOSPI收盤價走勢……………………….………….…………………43

一、國內文獻
1.包心婷（2010），波動度指數蔓延效果之研究-以次級房貸事件為例，私立淡江大學財務金融學系碩士在職專班碩士論文。
2.李彥賢、邱志昌、李政毅（2012），美國波動度指數與期貨長短期波動不對稱之研究，商管科技季刊，第13卷第3期，頁321-337。
3.李建興、黃玉珂、林依潔 (2015)，VIX 指數作為擇時指標之探討—以台灣與中國股票市場為例，兩岸金融季刊，第3卷第2期，頁1-25。 
4.徐清俊、顏雯津（2008），情緒指標與股價報酬關係之研究，明新學報，第34卷第1期，頁89-106。
5.張森林、葉宗穎 （2011），投資人情緒對市場狀態與股票價格的預測能力，證券市場發展季刊，第23卷第2期，頁1-28。
6.葉智丞、李春安（2012），投資人情緒、從眾與非從眾行為關聯性之研究，證券市場發展季刊，第24卷第3期，頁141-182。
7.鄭高輯、林泉源（2010），投資人情緒對投機型股票報酬之影響，商略學報，第2卷第1期，頁21-35。
8.駱武昌、吳明珊、吳斯偉（2011），台灣、歐洲與美國股市間波動外溢效果，會計與財金研究，第4卷第2期，頁29-50。

二、國外文獻
1.Akaike, H., 1973. Information theory and an extension of the maximum likelihood principle. In Proceedings of the Second International Symposium on Information Theory, Petrov, B. N., Caski, F. Eds., Akademiai Kiado, Budapest, 267-281.
2.Baker, M., Stein, J. C., 2004. Market liquidity as a sentiment indicator. Journal of Financial Markets 7, 271-299. 
3.Baker, M., Wurgler, J., 2006. Investor sentiment and the cross-section of stock returns. Journal of Finance 61, 1645-1680. 
4.Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307-327.
5.Bollerslev, T., Engle, R. F., Wooldridge, J. M., 1988. A capital asset pricing model with time-varying covariances. Journal of Political Economy 96, 116-131.
6.Brown, G. W., Cliff, M. T., 2004. Investor sentiment and the near-term stock market. Journal of Empirical Finance 11, 1-27.
7.Copeland, M. M., Copeland, T. E., 1999. Market timing: style and size rotation using the VIX. Financial Analyst’s Journal 55, 73-81.
8.Connors, L., 2002. Timing your S&P trades with VIX. Futures, June, 31, 46-47.
9.Da, Z., Engelberg, J., Gao, P., 2015. The sum of all fears investor sentiment and asset prices. Review of Financial Studies 28, 1-32.
10.Dickey, D. A., Fuller, W. A., 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427-431.
11.Dickey, D. A., Fuller, W. A., 1981. Likelihood ratio statistics for autoregressive
time series with a unit root. Econometrica 49, 1057-1072.
12.Engle, R. F., 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987-1007.
13.Engle, R. F., Granger, C. W. J., 1987. Co-integration and error correction: representation, estimation, and testing. Econometrica 55, 251-276.
14.Engle, R. F., Kroner, K. F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122-150.
15.Fama, E. F., 1970. Efficient capital markets：a review of theory and empirical work. Journal of Finance 25, 383-417.
16.Fleming, J., Ostdiek, B., Whaley, R. E., 1995. Predicting stock market volatility: a new measure. Journal of Futures Markets 15, 265-302. 
17.French, K. R., Schwert, G. W., Stambaugh, R. F., 1987. Expected stock returns and volatility. Journal of Financial Economics 19, 3-29. 
18.Frijns, B., Tallau C., Tourani-Rad, A., 2010. The information content of implied volatility: evidence from Australia. Journal of Futures Markets 30, 134-155. 
19. Giot, P., 2005. Relationships between implied volatility indexes and stock index returns. Journal of Portfolio Management 31, 92-100.
20. Goodell, J. W., Vähämaa, S., 2013. US presidential elections and implied volatility: the role of political uncertainty. Journal of Banking & Finance 37, 1108-1117.
21. Granger, C. W. J., Newbold, P., 1974. Spurious regressions in econometrics. Journal of Econometrics 2, 111-120.
22. Granger, C. W. J., 1981. Some properties of time series data and their use in econometric model specification. Journal of Econometrics 16, 121-130.
23.Honcoop, D., Lehnert, T., 2007. Can sentiment be predicted to have Cross-Sectional effects? Journal of Financial Forecasting 1, 55-62. 
24.Iwatsubo, K., Inagaki, K., 2007. Measuring financial market contagion using dually-traded stocks of Asian firms. Journal of Asian Economics 18, 217-236.
25.Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231-254.
26.Johansen, S., Juselius, K., 1990. Maximum likelihood estimation and inference on cointegration-with application to the demand for money. Oxford Bulletin of Economics and Statistic 52, 169-210. 
27.Kliger, D., Kudryavtsev, A., 2013. Volatility expectations and the reaction to analyst recommendations. Journal of Economic Psychology 37, 1-6.
28.Konstantinidi, E., Skiadopoulos, G., Tzagkaraki, E., 2008. Can the evolution of implied volatility be forecasted? evidence from European and US implied volatility indices. Journal of Banking and Finance 32, 2401-2411. 
29.Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54, 159-178.
30.Lee, C., Ryu, D., 2014. The volatility index and style rotation: evidence from the Korean stock market and VKOSPI. Investment Analysts Journal 43, 29-39.
31.MacKinnon, J. G., 1996. Numerical distribution functions for unit root and cointegration tests. Journal of Applied Econometrics 11, 601-618.
32.Osterwald-Lenum, M., 1992. A Note with quantiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics. Oxford Bulletin of Economics and Statistics 54, 461-472.
33.Phillips, P. C. B., Perron, P., 1988. Testing for a unit root in time series regression. Biometrika 75, 335-346.
34.Said, S. E., Dickey, D. A., 1984. Testing for unit roots in autoregressive- moving average models of unknown order. Biometrika 71, 599-607.
35.Sarwar, G., 2012. Is VIX an investor fear gauge in BRIC equity markets. Journal of Multinational Financial Management 22, 55-65.
36.Simon, D. P., Wiggins III, R. A., 2001. S&P futures returns and contrary sentiment indicators. Journal of Futures Markets 21, 447-462. 
37.Smales, L. A., 2014. News sentiment and the investor fear gauge. Finance Research Letters 11, 122-130.
38.Whaley, R. E., 1993. Derivatives on market volatility: hedging tools long overdue. Journal of Derivatives 1, 71-84. 
39.Whaley, R. E., 2000. The investor fear gauge. Journal of Portfolio Management 26, 12-17. 
40.Yang, M. J., Liu, M.-Y., 2012. The forecasting power of the volatility index in emerging markets: evidence from the Taiwan stock market. International Journal of Economics and Finance 4, 217-231.