已實現波動度於動態期貨避險之應用

Applications of Realized Volatility for Futures Hedging

賴雨聖(Yu-Sheng Lai)

指導教授 ： 許和鈞

國立交通大學/管理學院/管理科學系所/博士(2009年)

https://doi.org/10.6842/NCTU.2009.01127

摘要

本論文旨在應用已實現波動度(realized volatility)於動態避險議題上。首先我們提出新的以高頻日內資訊為基礎之多變量波動度模式，並將此模式應用至動態避險比率之估計上。在實證分析上，我們以美國S&P 500期貨為研究對象，探討此新的避險模式是否可以改進期貨避險之績效。與傳統以低頻資訊為基礎之避險模式比較後發現，新的避險模式不但可以大幅降低投資組合在樣本外之風險暴露額，並可為避險者產生正面的經濟價值。探究其主因，主要是因為已實現波動度可以較報酬率平方(return squares)提供更精確之波動度估計值，以致在波動度(或是避險比率)的預測上將得以較傳統方式有較佳的表現。
此外我們亦探討如何將此方法應用於事後(ex-post)避險績效之評估上。將Andersen et al. (2005, 2006)之研究成果應用至期貨避險議題上，我們建構之已實現避險比率得以用於評估各種事前(ex-ante)避險模式之預測能力，同時漸進理論並提供衡量避險比率精確度之方法。另者，已實現避險效果亦可用於衡量期貨避險之績效。
本論文最後探討已實現避險比率之動態性質。藉由門檻自我迴歸模式之分析，我們得以研究避險比率是否存在門檻效果並探討其在不同狀態下之動態性質。應用Hansen (1996)提出之拔靴檢定方法，我們發現門檻效果確實存在於已實現避險比率中。當避險比率高(低)於門檻變數的情況下，避險比率本身將會有較低(高)的波動度。門檻效果以及正向自我迴歸現象的存在均顯示避險比率應是與時變動(time-varying)的，因此實證結果支持動態避險比率假說。
藉由日內高頻資料的應用，已實現波動度提供我們一個不需模式設定(model-free)的方法來估計不可觀測到的波動度指標。本論文的研究成果指出，高頻日內資料的使用將可為許多財務上的議題，例如資產配置或期貨避險等，開啟另一嶄新的研究題材。

關鍵字

動態避險比率 ； 多變量波動度模式 ； 已實現波動度 ； 避險績效

並列摘要

The dissertation applies the realized volatility (RV) approach to the futures hedging problem. Firstly, we propose a new class of multivariate volatility models encompassing RV estimates to estimate the risk-minimizing hedge ratio, and compare the performance of the proposed models with those generated by return-based models. In an out-of-sample context with a daily rebalancing approach, the empirical results show that improvement can be substantial when switching from daily to intraday. This essentially comes from the advantage that the intraday-based RV potentially can provide more accurate daily covariance matrix estimates than RV utilizing daily prices.
Next, we describe ex-post measures for assessing ex-ante hedge ratio estimates. Applying the realized beta framework of Andersen et al. (2005, 2006), the realized hedge ratio, realized hedging effectiveness, and the asymptotic confidence interval are constructed. The realized hedge ratio, which is consistent with the integrated hedge ratio, provides a natural benchmark for assessing the forecasting ability of any ex-ante hedge ratio estimates. Meanwhile, the asymptotic distribution provides insights into the precision of the realized hedge ratio. Furthermore, the realized hedging effectiveness provides an ex-post estimate for the integrated hedging effectiveness.
Then, the dynamics of the realized hedge ratio is investigated via a two-regime Self-Exciting Threshold Autoregressive (SETAR) model. The SETAR is tackled with a linear Autoregressive (AR) model if the threshold effect is not significant. Empirical results conclude the realized daily hedge ratio is characterized as regime-dependent dynamics and is likely to be positively autocorrelated so that the usual assumption of constant hedge ratio seems inappropriate.
The RV approach, which utilizes finer information in intraday high-frequency data, provides a direct and consistent technique for estimating the latent volatility without the need for relying on explicit models. Our investigation may provoke further study on the benefits of utilizing intraday information in volatility modeling, which is relevant to asset allocating and futures hedging.

並列關鍵字

Dynamic Hedge Ratio ； Multivariate Volatility Model ； Realized Volatility ； Hedging Performance

參考文獻

Andersen, T. G., & Bollerslev, T. (1997). Intraday periodicity and volatility persistence in fi-nancial markets. Journal of Empirical Finance, 4, 115-158.

Andersen, T. G., & Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review, 39, 885-905.

Andersen, T. G., Bollerslev, T., Christoffersen, P. F., & Diebold, F. X. (2006). Volatility and correlation forecasting. In G. Elliot, C.W.J. Granger & A. Timmerman (Eds.), Handbook of economic forecasting (pp. 778-878). Amsterdam: North-Holland.

Andersen, T. G., Bollerslev, T., Diebold, F.X., & Ebens, H. (2001a). The distribution of real-ized stock return volatility. Journal of Financial Economics, 61, 43-76.

Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2001b). The distribution of real-ized exchange rate volatility. Journal of the American Statistical Association, 96, 42-55.