日內資料對黃金指數型基金波動性的增量預測價值

Incremental Value of Intraday Data in Improving Volatility Forecasts of GLD Returns

10.6736/JPSR.201110_8(2).0002

劉洪鈞(Hung-Chun Liu)；姜淑美(Shu-Mei Chiang)；白東岳(Tung-Yueh Pai)

GLD ； 變幅 ； 已實現變幅 ； 已實現波動 ； 已實現雙冪次變異 ； GLD ； Range ； Realized range ； Realized volatility ； Realized bipower variation

績效與策略研究

8卷2期（2011 / 10 / 01）

11 - 29

繁體中文

金融史上看似不可能發生，但實際卻又發生的黑天鵝事件，凸顯資產波動預測的重要性及市場風險管理的必要性。近年美元持續走弱，加上美國幾波量化寬鬆政策，遂使得黃金指數基金成為亂世的最佳避險金融商品。同時，資訊科技發達使得金融商品日內交易資料的取得漸趨便利。因此，如何善用這些資訊提升現存波動模型的預測效益，值得進一步探討。本文以GLD為研究標的，使用GARCH（1,1）為波動模型架構，在其條件變異數方程式中加入PK、RV、RBP、RRV等波動估計式，探討前述各種交易資訊能否提升GARCH模型對GLD樣本外波動預測的準確性。實證結果指出RRV為最具效率的日真實波動代理變數。其次，各種波動估計式，對GARCH模型的波動預測存在不同程度的提升效果。多數情況下，GARCH-RBP表現最佳、依序為GARCH-RV、GARCH-RRV、GARCH-PK及GARCH模型，隱含日內交易資訊能有效增進GARCH模型的樣本外預測績效，而日交易資訊，其提升效果較不明顯。最後，選擇權的交易者可應用GARCH-RBP模型來增進其投資部位的操作績效。本研究結果可使市場參與者瞭解各波動估計式所隱含之資訊內容的潛在價值，有助於提升資產的波動預測效率，更可應用風險值相關分析尋求最適的風險管理模型，以提供投資人進行風險計提的模型基礎。

Various financial crises over the past few decades, which are typically regarded as the black swan events, have highlighted the significance of volatility forecasting and the necessity of market risk management. Recently, given the relative weakness of the U.S. dollar along with the quantitative easing monetary policy by the US government, the SPDR Gold Shares (Ticker: GLD) has become increasingly prevalent among global investors as a financial hedging instrument during troubled times. In the meanwhile, the broad availability of financial market data at intraday frequency has inspired research into their potential value as a source of information for volatility forecasting. Thus, it deserves to further examine the promotion in expected benefit of existing volatility model by making good use of this information. This study aims to propose the introduction of various daily- and intraday-based volatility estimators (PK, RV, RBP and RRV) into the conditional variance of GARCH(1,1) framework to explore the benefit and incremental value of the intraday trading information that is embodied in those estimators for improving out-of-sample volatility forecasts of GLD returns at daily horizon over the period from 2005 to 2010. Empirical results indicate that the realized range (RRV) is the most efficient proxy for daily volatility. Secondly, the inclusion of each volatility estimator considered shows an improvement in the GARCH model with certain degree. Specifically, the GARCH-RBP model generates the most accurate daily volatility forecasts, followed by the GARCH-RV, GARCH-RRV, GARCH-PK and GARCH (the benchmark) in most cases. Such evidence indicates that the GARCH volatility forecasts can be improved much more with the additional information contained in intraday-based volatility estimators than in daily-based one. Finally, the mean mixed error criterion (MME) suggests that the GARCH-RBP model facilitates option traders for improving the performance of their trading position.These results can enable the market participants understand the potential values of information content in various volatility estimators. It can not only help to heave the volatility forecasting efficiency of assets, but also apply related analysis of Value-at-Risk to seek optimum risk management model to provide the investors with the base of risk- models.

1. Alexander, C.,Barbosa, A.(2008).Hedging index exchange traded funds.Journal of Banking and Finance,32,326-337.
2. Andersen, T. G.,Bollerslev, T.(1998).Answering the skeptics: yes, standard volatility models do provide accurate forecasts.International Economic Review,39,885-905.
3. Bali, T. G.,Weinbaum, D.(2005).A comparative study of alternative extreme-value volatility estimators.Journal of Futures Markets,25,873-892.
4. Bamdorff-Nielsen, O. E.,Shephard, N.(2004).Power and bipower variation with stochastic volatility and jumps.Journal of Financial Econometrics,2,1-37.
5. Black, F.,Scholes, M.(1973).The pricing of options and corporate liabilities.Journal of Political Economy,81,637-654.
6. Bollerslev, T.,Wooldridge, J. M.(1992).Quasi-maximum likelihood estimation and inference in dynamic models with time varying covariances.Econometric Review,11,143-172.
7. Brailsford, T. J.,Faff, R. W.(1996).An evaluation of volatility forecasting techniques.Journal of Banking and Finance,20,419-438.
8. Brooks, C.(1998).Predicting stock index volatility using GARCH models: can market volume help?.Journal of Forecasting,17,59-80.
9. Christensen, K.,Podolskij, M.(2007).Realized range-based estimation of integrated variance.Journal of Econometrics,141,323-349.
10. Chu, Q. C.,Hsieh, W. L.(2002).Pricing efficiency of the S&P 500 index market: evidence from the standard & poor's depositary receipts.Journal of Futures Markets,22,877-900.
11. Corrado, C.,Truong, C.(2007).Forecasting stock index volatility: comparing implied volatility and the intraday high-low price range.Journal of Financial Research,30,201-215.
12. Franses, P. H.,van Dijk, D. V.(1996).Forecasting stock market volatility using (non-linear) GARCH models.Journal of Forecasting,15,229-235.
13. Garman, M.,Klass, M.(1980).On the estimation of security price volatilities from historical data.Journal of Business,53,67-78.
14. Giosten, L.,Jagannathan, R.,Runkle, D.(1993).On the relation between the expected value and the volatility nominal excess return on stocks.Journal of Finance,46,1779-1801.
15. Hansen, P. R.,Lunde, A.(2005).A forecast comparison of volatility models: does anything beat a GARCH(1,1)?.Journal of Applied Econometrics,20,873-889.
16. Harper, J. T.,Madura, J.,Schnusenberg, O.(2006).Performance comparison between exchange-traded funds and closed-end country funds.Journal of International Financial Markets, Institutions and Money,16,104-122.
17. Jacob, J.,Vipul(2008).Estimation and forecasting of stock volatility with range-based estimators.Journal of Futures Markets,28,561-581.
18. Koopman, S. J.,Jungbacker, B.,Hol, E.(2005).Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements.Journal of Empirical Finance,12,445-475.
19. Martens, M.,van Dijk, D. V.(2007).Measuring volatility with the realized range.Journal of Econometrics,138,181-207.
20. Mincer, J.(Ed.)(1969).Economic Forecasts and Expectations.New York:National Bureau of Economic Research.
21. Nelson, D. B.(1991).Conditional heteroskedasticity in asset returns: a new approach.Econometrica,59,347-370.
22. Olienyk, J. P.,Schwebach, R. G.,Zumwalt, J. K.(1999).WEBS, SPDRs and country funds: analysis of international cointegration.Journal of Multinational Financial Management,9,217-232.
23. Parkinson, M.(1980).The extreme value method for estimating the variance of the rate of return.Journal of Business,53,61-65.
24. Phillips, P. C. B.,Perron, P.(1988).Testing for a unit root in time series regression.Biometrika,75,335-346.
25. Rogers, L. C. G.,Satchell, S. E.(1991).Estimating variance from high, low and closing prices.Annals of Applied Probability,1,504-512.
26. Theodossiou, P.(1998).Financial data and the skewed generalized t distribution.Management Science,44,1650-1661.
27. Tse, Y.,Martinez, V.(2007).Price discovery and informational efficiency of international ishares funds.Global Finance Journal,18,1-15.
28. Vipul,Jacob, J.(2007).Forecasting performance of extreme-value volatility estimators.Journal of Futures Markets,27,1085-1105.
29. 周詩婷(2008)。碩士論文(碩士論文)。臺灣大學財務金融學研究所。
30. 邱懷義(2004)。碩士論文(碩士論文)。淡江大學財務金融研究所。
31. 連欣儀(2008)。碩士論文(碩士論文)。臺灣大學財務金融學研究所。
32. 陳冠臻(2004)。碩士論文(碩士論文)。淡江大學財務金融研究所。