摘要內容
本篇論文使用Jarrow-Rudd選擇權評價模型，以臺指選擇權(TXO)之日內資料做實證研究，資料期間為2002年4月1日至2003年12月31日。實證結果發現以下結論。第一，利用市場上觀察到的選擇權價格，再以Jarrow-Rudd模型反推標的指數之報酬分配，我們發現臺股指數之報酬分配呈現右偏及高峽峰之情形。透過高階動差的調整，Jarrow-Rudd模型無論在樣本內或樣本外的預測誤差都改善了Black-Scholes模型在笑狀波幅上的偏誤。其次，則著重在隱含波動率之預測能力，結果發現從兩模型所得到之隱含波動率都包含了對實際波動率的資訊，但隱含波動率是一個偏的估計子。第三、主要檢定偏態及峰態是否能解釋笑狀波幅。結果顯示偏態及峰態對笑狀波幅在價平時之斜率有顯著之解釋能力，而笑狀波幅之曲度主要則由峰態所解釋。另外，風險中立的偏態則可以被一些市場變數、如交易量、隱含波幅、指數報酬率以及賣權對買權之未平倉量相對比例所解釋。第四，我們使用了CBOE在2003年九月所公佈的新方法，以臺指選擇權買賣權之收盤價編制了一波動率指標，稱為TVIX。與Whaley(2000)的結果一致，波動率指標--TVIX和指數間呈現高度之負相關，且其對指數報酬有顯著之解釋能力。利用回歸分析，我們更進一步的探討從Jarrow-Rudd模型所反推出來的偏態及峰態是否對股價報酬有解釋能力，再與行為財務學上可視為投資人情緒指標的因子比較，結果發現行為財務學上之情緒指標對於股價報酬較具有解釋能力。最後，我們試著創造一個可衡量投資者恐懼程度的指標，並期望該指標可與VIX有相同之效果。結果發現，當我們以指數報酬分配之左尾計算投資者實際損失幅度為指標時，能夠達到與指數呈負相關且對指數報酬有解釋能力之效果。

Abstract
This study empirically investigates the TAIEX index options (called TXO) by adopting the Jarrow and Rudd option pricing model. Using the intraday data from April 1, 2002 to December 31, 2003, we got several conclusions. First, recover the risk-neutral distribution from observable option price, we find positive skews and leptokurtosis do exist and give rise to volatility skews. Through adjustment of higher moments, Jarrow-Rudd model shows less misspecification. Second, we focus on the forecast ability of implied volatility. Evidence reveals that implied volatilites from Jarrow-Rudd model and Black-Scholes model both contain information about realized volatility but they are biased predictors. Third, we also test whether the implied skewness or kurtosis are the sources of volatility skews. Empirical results suggest the slope of volatility smile can be explained by the implied skewness and kurtosis while the curvature of that is primarily explained by the fourth moment of RND. In addition, regression analysis shows that risk-neutral skewness is influenced by market-wide factors such as trading volume, implied volatility, index return or put/call ratio. Fourth, we construct TVIX by using the new-VIX calculation methodology produced by CBOE in 2003. Consistent with Whaley (2000), TVIX is negatively related to TAIEX and changes of positive in TVIX can help explain the index return. Moreover, regard Whaley’s regression as the benchmark, empirical implement suggests that sentimental indicators in behavior finance such as trading volume or put/call ratio do have explanatory power on the realized return while implied parameters recovered from Jarrow-Rudd model show less evidence on that. Finally, a discussion about constructing a new fear gauge index is proposed. Our goal is to obtain an indicator that can gauge the investors’ risk-aversion. The new fear gauge index which measures the investors’ realistic expected loss performs better for its negative related to the index level and explanatory power on index return.

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