報酬率、交易量、波動性之同步關聯性

Simultaneous Relationships among Return, Volume and Volatility

許硯評(Yen-Ping Hsu)

指導教授 ： 辛敬文

共同指導教授 ： 葉錦徽(Jin-Huie Yeh)

元智大學/管理學院/財務金融學系/碩士(2008年)

https://doi.org/10.6838/YZU.2008.00191

摘要

相較於過去傳統的波動性模型, 近年來發展至臻的已實現波動性得到研究學者們的廣泛討論。在估計波動性上, 用高頻日內資料所得算出的已實現波動性除了可提供更多更完整的資訊外, 其資訊內涵以及不受限於其它模型的特性更可讓原本潛藏的波動性變得能直接觀察到。有鑑於此, 本研究使用向量自我迴歸模型來探討報酬率、交易量、已實現波動性三者之間的關聯性。過去的文獻往往僅探討兩兩變數, 如報酬率與交易量、報酬率與波動性、以及波動性與交易量, 並且控制另一個變數為外生變數, 我們認為這樣的模型可能會有內生偏誤, 且會產生模型誤設的結果。因此在本研究中, 我們透過雙變數以及三變數的向量自我迴歸模型, 來重新證驗那些過去學者們所得到的假說。如同過去的研究所證實的, 我們的實證結果指出, 交易量與波動性之間存在顯著的正相關, 不僅如此, 交易量亦具有傳遞市場訊息的功能。然而在風險溢酬理論中, 波動性對未來的報酬率的正向影響卻已不存在。而在報酬率與波動性不對稱之關係上, 我們不僅驗證了Leverage effect, 即過去報酬率對未來的波動性有顯著的負向影響, 亦在報酬率與交易量的關係中發現同樣的現象。再者, 為了確實地捕捉到Volatility feedback effect, 我們引用在美國芝加哥交易所掛牌的隱含波動率指數(VIX), 並從中萃取出與過去資訊無關、具有前瞻性的波動性變數。在控制了Leverage effect 的三變數之向量自我迴歸模型中, 我們的結果發現Volatility feedback effect 與Leverage effect 是共同存在的。最後, 作為敏感性分析, 我們亦考慮了Jump 對波動性的影響。

關鍵字

向量自我迴歸模型 ； 已實現波動性 ； 波動性之不對稱效果 ； 隱含波動率指數

並列摘要

Contrary to that traditional noisy volatility estimates constructed from GARCH
or stochastic volatility model using daily data, the recent proposed realized volatility calculated via high frequency intraday data has been proven to provide better precision assessing latent volatility. The superior information content along with its model-free and nonparametric nature, has made the realized volatility to make the latent volatility process virtually visible. Taking advantage of the feature, this paper uses vector autoregression model to investigate the simultaneous relationships among return, trading volume and realized volatility. We argue that the past studies addressing the relationships between return/volume (or return/volatility, or volatility/volume) while controlling the volatility (or volume, or return) as an exogenous variable may subject to endogeneity bias (simultaneous bias) and thus produce misleading results. Hence, we re-examine several well-documented hypotheses or relationships among these variables through bivariate and a full of trivariate analysis to verify our concerns. We found that trading volume is positive related to volatility contemporarily, justifying the role trading volume plays in conveying market information. In addition, we found the leverage effect in volatility, as well as in trading volume. The relationship between lagged volatility and current return that relates return-risk trade-off no longer exists. To properly examine the volatility feedback hypothesis explaining the return-volatility asymmetry, controlling the leverage effect, we construct a new forward-looking volatility factor that is unrelated to historical information set by extracting information from the implied volatility index (VIX) traded in CBOE. Our results support the coexistence of both the volatility feedback effect and the leverage effect. In sensitivity analysis, we found our obtained results robust to the jump considerations.

並列關鍵字

Vector AutoRegressive Model ； Realized Volatility ； Leverage Effect ； Volatility Feedback Effect ； VIX

參考文獻

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