本研究利用Jarrow-Rudd模型獲得每天股價報酬分配隱含的波動性、偏態係數、 峰態係數。因為這些參數隱含著某些資訊在其中，因此我們將利用這些參數進行一連串的實證研究。從我們的實證結果，我們可以得知：(1) 我們延伸Bakshi、Kapadia和Madan的研究，加以探討隱含偏態係數、峰態係數對波動性微笑曲線的曲度的影響。我們發現隱含偏態係數及峰態係數的確在解釋波動性微笑曲線上有其解釋力。我們的實證結果也驗證了Zhang的數學推論：微笑曲線的斜率相關於隱含偏態係數，而曲度則相關於隱含峰態係數。(2) 從JR模型計算出來的隱含波動性是未來波動性的一個偏誤估計值，但是它仍然包含有預測未來波動性的資訊。(3) 隱含偏態係數包含市場情緒的特性在其中。投資者愈樂觀，則隱含偏態係數愈正。(4) 隱含偏態係數、隱含峰態係數及IIS指標對報酬皆有其解釋力。另外，當報酬率是正的情況時，VIX的正向變動愈大，則投資者愈感到樂觀。相反的，當報酬率是負的情況，VIX的正向變動愈大，則投資者是其為一個不好的現象，會愈悲觀。(5) 我們試圖利用隱含波動性、隱含偏態係數、隱含峰態係數來建立一個新的投資者恐懼衡量指標。新的指標的確有其衡量恐懼的效果存在，但是相對於VIX的效果而言，仍然是比較差的。

This paper uses the Jarrow and Rudd model (1982) to obtain implied volatility, implied skewness, and implied kurtosis. Then we use these implied parameters to do a series of empirical test. From our empirical results, we can obtain some conclusions. First, we extend Bakshi, Kapadia, and Madan’s research (2003) .We find that implied skewness and implied kurtosis have explanatory power for the slope and the curvature of smile. Our empirical results also verify Zhang’s conclusions (2004): the slope is related with risk-neutral skewness, and the curvature is related with risk-neutral kurtosis. Second, the implied volatility from the Jarrow and Rudd model is a biased estimator of the future volatility, but the implied volatility still contains information in forecasting the future volatility. Third, implied skewness contains the effect of market sentiment. The more optimistic the investors are, the more positive the skewness is. Fourth, implied skewness, implied kurtosis, and IIS (Investors intelligence sentiment survey) have effects on explaining the return. When the return is positive, the result shows the larger the positive change of the VIX is, the more optimistic the investors are. On the contrary, when the return is negative, the result shows the larger the positive change of the VIX is, the more pessimistic the investors are. Finally, we utilize implied volatility, implied skewness, and implied kurtosis to construct a new fear gauge index. The new index indeed has certain effect on measuring the level of the investors’ fear.

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