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A theoretical comparison between integrated and realized volatility

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Author Info
Nour Meddahi (Département de sciences économiques, CIREQ, CIRANO, Université de Montréal, succursale Centre-ville, Montréal Québec H3C 3J7, Canada)
Abstract

In this paper we provide both qualitative and quantitative measures of the precision of measuring integrated volatility by realized volatility for a fixed frequency of observation. We start by characterizing for a general diffusion the difference between realized and integrated volatility for a given frequency of observation. Then we compute the mean and variance of this noise and the correlation between the noise and the integrated volatility in the Eigenfunction Stochastic Volatility model of Meddahi (2001a). This model has as special cases log-normal, affine and GARCH diffusion models. Using previous empirical results, we show that the noise is substantial compared with the unconditional mean and variance of integrated volatility, even if one employs five-minute returns. We also propose a simple approach to capture the information about integrated volatility contained in the returns through the leverage effect. We show that in practice, the leverage effect does not matter. Copyright © 2002 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.689
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 17 (2002)
Issue (Month): 5 ()
Pages: 479-508
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Handle: RePEc:jae:japmet:v:17:y:2002:i:5:p:479-508

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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. Ole Barndorff-Nielsen & Neil Shephard, 2000. "Non-Gaussian OU based models and some of their uses in financial economics," OFRC Working Papers Series 2000mf01, Oxford Financial Research Centre. [Downloadable!]
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  12. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO. [Downloadable!]
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  17. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September. [Downloadable!] (restricted)
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  20. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June. [Downloadable!] (restricted)
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  23. 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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