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.