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A Theoretical Comparison Between Integrated and Realized Volatilies

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  • MEDDAHI, Nour

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.

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File URL: http://hdl.handle.net/1866/365
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2001-26.

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Length: 30 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:mtl:montde:2001-26

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Keywords: integrated volatility; realized volatility; infinitesimal generator; eigenfunction stochastic volatility models; leverage effect; exact moments;

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