A Theoretical Comparison Between Integrated and Realized Volatilies

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

Abstract: In this paper, we provide both qualitative and quantitative measures of the cost of measuring the integrated volatility by the realized volatility when the frequency of observation is fixed. We start by characterizing for a general diffusion the difference between the realized and the integrated volatilities for a given frequency of observations. 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 examples, log-normal, affine, and GARCH diffusion models. Using some previous empirical works, we show that the standard deviation of the noise is not negligible with respect to the mean and the standard deviation of the integrated volatility, even if one considers returns at five minutes. We also propose a simple approach to capture the information about the integrated volatility contained in the returns through the leverage effect.

Keywords: integrated volatility; realized volatility; infinitesimal generator; eigenfunction stochastic volatility models; leverage effect; exact moments (search for similar items in EconPapers)
JEL-codes: C50 C51 C52 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2001
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Citations: View citations in EconPapers (4)

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http://hdl.handle.net/1866/365 (application/pdf)

Related works:
Journal Article: A theoretical comparison between integrated and realized volatility (2002)
Working Paper: A Theoretical Comparison Between Integrated and Realized Volatilities (2001)
Working Paper: A Theoretical Comparison Between Integrated and Realized Volatilies (2001)
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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:2001-26

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