摘要
本文藉由Black-Scholes的評價模型探討指數選擇權隱含波動率是否有內含均值回歸(mean reversion)之解釋因子。此外，本研究亦考慮均值回歸效果是否對隱含波動率微笑曲線(或偏態)型態變動提供部分的解釋。最後，本文更進一步分析不同的價內、外程度之隱含波動率受均值回歸效果是否會有不同的影響。本文分析台灣指數選擇權以及美國S&P 500指數選擇權，包括買、賣權，並且依循Bollen and Whaley (2004)建議以delta來代替一般價性(價平、內、外程度)，衡量隱含波動率。另外，本文依照Fama and French (1988)與Bali, Demirtas, and Levy (2007)所提出的均值回歸模型，分別求出均值回歸之線性與非線性估計值。實證結果發現，不管在台灣市場或者美國S&P 500的隱含波動率均有內含均值回歸之因子且非常顯著。最後，隱含波動偏態型態之變動也受到線性和非線性均值回歸所影響，其中台股以價平、價內與價外特別顯著。意味市場未來價格變動存在長期價格反轉的現象，亦即均值回歸。
並列摘要
This paper examines whether implied volatility smile derived by Black and Scholes options pricing model includes mean reversion. In addition, we consider whether mean reversion explains a change in the implied volatility smile. Finally, we analyze that the implied volatility across different moneyness would be influenced by the mean reversion. We investigate and compare S&P 500 and Taiwan index options. With the traditional moneyness measure, we apply alternative one suggested by Bollen and Whaley (2004). Moreover, we follow Fama and French (1988) and Bali, Demirtas, and Levy (2007) and estimate the linear and nonlinear estimators of the mean reversion, respectively. We find that the mean reversion is the significant factor and is embed into implied volatilities in the Taiwan and S&P 500 options markets. Specifically, a change in implied volatility skewness is affected by linear and nonlinear mean reversion. It is found more obviously significant evidence in Taiwan than in U.S., with suggesting the long-run price reversal phenomenon in the market.
參考文獻
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