選擇權隱含波動性與標的資產歷史波動性及選擇權參數之關聯性

The Relationship between Implied Volatilities of Options and Historical Volatilities of the Underlying Asset and Option Parameters

許溪南(Hsi-Nan Hsu) ； 詹世煌(Shin-Huang Chan) ； 謝宗祐(Tzung-Yuan Hsieh)

《Asia Pacific Management Review》 5卷4期 (2000/12) Pp. 385-401

https://doi.org/10.6126/APMR.2000.5.4.01

摘要

隱含波動性常被學界及投資人作為選擇權定價中標的物價格波動性的估計值。然而，選擇權中所隱含的股價波動性與股價的歷史波動性關聯性有多高？此外，尚有哪些因素可解釋選擇權的隱含波動性的變動？這不但是投資人所關心的課題，也是學術界急於探討的課題。本研究藉由分析隱含波動性與歷史波動性、到期日長短及股價水準之間的自我迴歸來探討彼此之間的關聯性及1987年股市崩盤前後的差異。實證結果顯示（1）.隱含波動性皆會受歷史波動性的影響，且其關係為正向關係；（2）.僅有價外的選擇權，隱含波動性才具有序列相關，其關係為正向關係；（3）.對於價平的選擇權，隱含波動性並不會受到期日長短的影響;但對於價外及價內的選擇權而言，到期日長短皆與隱含波動性成負相關；（4）.除了價內賣權外，對於其他型態的選擇權，股價水準皆與隱含波動性無顯著的關係；（5）.對於所有的選擇權，在崩盤前後隱含波動性顯著增加，約20%至60%，但歷史波動性卻些微下降，而且經濟結構發生了改變。

關鍵字

隱含波動性 ； 歷史波動性 ； 價位狀況 ； 到期日 ； 股價水準

並列摘要

Implied Volatilities are often used by academic researchers as well as investors as the estimates of the underlying assets volatilities in option pricing. Yet, how much association between implied volatilities and historical volatilities of the underlying asset? In addition, can factors other than historical volatility used be explained the variation of implied volatility? These issues are important for investors as well as academic researchers. The purposes of this paper are (1) to investigate the association between implied volatilities of option prices and the volatilities of the underlying asset, time to maturity, moneyness, and price level of the underlying asset; and (2) to detect if any structural change during the 1987 Crash, Results indicate that: (1) implied volatility is positively related to historical volatility; (2) implied volatilities show positively serial correlation for out of the money options. (3) For at-the-money options, implied volatilities are not influenced by the time to maturity; however, for out-of-money and in-the-money options, implied volatility and time to maturity are negatively correlated. (4) except in-the-money put options, implied volatilities and price level of underlying asset are not significantly correlated. Finally, (5) for all options, implied raised 20%-60 %, while historical volatilities remained unchanged; and all regression structures have changed during the 1987 Crash.

並列關鍵字

implied volatility ； historical volatility ； moneyness ； time to maturity ； stock price level.

參考文獻

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