本研究探討美國波動度指數與標的指數(S&P500)、那斯達克指數和道瓊工業指數之非線性誤差修正平滑移轉效果，運用Pesaran et al. (2001)自我迴歸遞延落差(ARDL)模型之區間測試(Bound Test)法，檢測波動度指數與標的指數、那斯達克指數和道瓊工業指數短期動態調整至長期均衡的調整過程，並將ARDL的誤差修正係數做為轉換變數，配適非線性平滑移轉誤差修正模型，臆測標的指數、那斯達克指數和道瓊工業指數對波動度是否存在非線性平滑移轉效果。 實證結果發現，就短期而言S&P500指數、Nasdaq綜合指數及Dow Jones工業平均指數的走向是與VIX波動度的變動呈反向的關係，表示各指數在偏離均衡後，前期之調整在短期間即可回復至均衡，顯示此市場是有效率。S&P 500指數對於VIX指數的負向關係較Nasdaq綜合指數及Dow Jones工業平均指數為強烈，因S&P500指數為VIX指數之標的資產指數。另外，考量VIX與標的及Nasdaq和Dow Jones指數之非線性特性，以誤差修正做為門檻轉換變數的LSTECM模型，其結果能有效捕捉到線性模型無法觀察到的現象。 The purpose of this research is to test smooth transition for the relationship between volatility and each of its underlying asset and related assets. At the beginning, we use ARDL bounding tests to test the long run and short run relationship between volatility and each of its underlying assets and related assets. Then, we show that the logistic smooth transition error correction model has a better explained than a linear model. We consider the error correction term as the transition variable which is estimated from an underlying cointegrating relationship predicted by the error correction representation of ARDL model. The results as follow: First, not surprisingly, there is a negative and statistically significant relationship between volatility and each of its underlying asset and related assets. Second, VIX and its underlying asset have stronger negative relationship than with other related assets. Finally, the LSTECM model can effectively catch these nonlinear relationships. Thus traders willing to enter oversold markets should wait until extremely high levels of volatility are witnessed, and their strategy should be strictly on a short-term basis.