選擇權隱含波動率對未來波動率之資訊內涵

The Information Content of Option-Implied Volatility for Realized Volatility

莊明霖(Ming-Lin Chuang)

指導教授 ： 王耀輝

國立臺灣大學/管理學院/財務金融學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.01654

摘要

本研究是以S&P 500 日內五分鐘報酬平方和計算實現波動率(Realized Volatility)，分別以單變量與包含迴歸(Encompassing Regressions)，分析比較1997年至2005 年期間，B-S 評價模型隱含波動率(Black-Scholes Implied Volatility)與無模型設定隱含波動率(Model-Free Implied Volatility)，在7、30、60 與90 天等四個
S&P 500 選擇權到期循環與每天最短到期日之預測能力，本研究著重於不同模型、不同資料型態(買權、賣權與加權平均)預測能力與資訊內涵之比較。
實證結果發現，在上述兩種方法下，短期而言，賣權隱含波動率的預測能力優於買權隱含波動率，但並未完全包含買權隱含波動率的資訊；長期而言，買權隱含波動率則優於賣權隱含波動率，但並未完全包含賣權隱含波度率的資訊。其次，不管是在哪一種方法下，利用成交量加權平均之隱含波動率皆優於單獨利用買權及賣權資料所計算出之隱含波動率。最後，比較上述兩種方法，經過成交量加權平均後，B-S 評價模型隱含波動率優於無模型設定波動率，並且完全包含無模
型設定隱含波動率的資訊。本實證結果，有助於市場投資人能以更有效率之選擇權隱含波動率資訊去評估實現波動率，制定其投資策略。

關鍵字

選擇權 ； B-S 隱含波動率 ； 無模型設定隱含波動率 ； 加權平均波動率 ； 實現波動率

並列摘要

We use 5-minute high frequency index returns to stimate realized volatility of S&P 500 index. Our sample period is from May 1997 to December 2005. We employ both univariate and encompassing regressions to analyze the information content of B-S and model-free Implied Volatility calculated over 7-day, 30-day 60-days, 90-day and shortest maturity horizons. We focus on the comparison of prediction ability and the information content between different models as well as different data, including call option, put option and weighted average.
We find the prediction ability of implied volatility of put option exceeds that of call option in the short run, though it does not subsume all the information contained in call option. However, the prediction ability of implied volatility of call option is better than that of put option in the long run, though it does not subsume all the information contained in put option. In addition, the average implied volatility weighted by volume is better than either call option or put option. Finally, we find that if we use the weighted average data, the B-S Implied Volatility beats the model-free implied volatility. We hope
investors can benefit from the empirical results by choosing effective implied volatility of option to assess realized volatility and thus form their investment strategy.

並列關鍵字

options ； Black-Scholes implied volatility ； model-free implied volatility ； weighted average volatility ； realized volatility

參考文獻

2. 袁淑芳，「台灣市場隱含波動率指標之資訊內涵探究」，私立淡江大學財務金融所博士論文，民國九十七年一月。

1. 李佳玲，「台指選擇權波動度指標與景氣指標之關係性研究」，國立中央大學企業管理研究所碩士論文，民國九十五年六月。

1. Ait-Sahalia, Y., and A.W. Lo, 1998, “Nonparametric Estimation of State-price Densities Implicit in Financial Asset Prices,”Journal of Finance, 53, 499-547.

2. Bakshi, G., C. Cao, and Z. Chen, 1997, “Empirical Performance of Alternative Option Pricing Models,”Journal of Finance, 52, 2003-2049.

3. Bakshi, G., C. Cao, and Z. Chen, 2000, “Pricing and Hedging Long-Term Options,”Journal of Econometrics, 94, 277-318.