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Modeling and Forecasting Realized Volatility

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Author Info
Anderson, Torben G.
Bollerslev, Tim
Diebold, Francis X.
Labys, Paul

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Abstract

We provide a general framework for integration of high-frequency intraday data into the measurement, modeling and forecasting of daily and lower frequency return volatilities and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on potentially restrictive and complicated parametric multivariate ARCH or stochastic volatility models. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time-series methods for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we develop formal links between realized volatility and the conditional covariance matrix. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen/Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to a variety of popular daily ARCH and more complicated high-frequency models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, produces well-calibrated density forecasts of future returns, and correspondingly accurate quantile predictions. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

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Paper provided by Duke University, Department of Economics in its series Working Papers with number 02-12.

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Date of creation: 2002
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Handle: RePEc:duk:dukeec:02-12

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  8. Nelson, Daniel B. & Foster, Dean P., 1995. "Filtering and forecasting with misspecified ARCH models II : Making the right forecast with the wrong model," Journal of Econometrics, Elsevier, vol. 67(2), pages 303-335, June. [Downloadable!] (restricted)
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  19. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(06), pages 808-817, December. [Downloadable!]
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  20. Suleyman Basak & Alexander Shapiro, 1999. "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-032, New York University, Leonard N. Stern School of Business-. [Downloadable!]
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  22. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February. [Downloadable!]
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  27. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November. [Downloadable!] (restricted)
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  31. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September. [Downloadable!] (restricted)
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  33. Taylor, Stephen J. & Xu, Xinzhong, 1997. "The incremental volatility information in one million foreign exchange quotations," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 317-340, December. [Downloadable!] (restricted)
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  38. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December. [Downloadable!] (restricted)
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  41. Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, vol. 40(1), pages 87-96, January. [Downloadable!] (restricted)
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