High-Frequency Returns, Jumps and the Mixture of Normals Hypothesis

51 Pages Posted: 28 Nov 2005

See all articles by Jeff Fleming

Jeff Fleming

Rice University - Jesse H. Jones Graduate School of Business

Bradley S. Paye

Virginia Polytechnic Institute & State University - Department of Finance, Insurance, and Business Law

Date Written: July 28, 2006

Abstract

Previous empirical studies find both evidence of jumps in asset prices and that returns standardized by `realized volatility' are approximately standard normal. These findings appear to be contradictory. Using a sample of high-frequency returns for 20 heavily-traded US stocks, we show that microstructure noise may artificially reduce the variance and increase the kurtosis of returns standardized using realized variance. When we apply a bias-corrected realized variance estimator, standardized returns are platykurtotic and the standard normal distribution is easily rejected. Moreover, when daily returns are standardized using realized bipower variation, an estimator for integrated volatility that is robust to the presence of jumps, the resulting series appear more consistent with the standard normal distribution. These results suggest that there is no empirical contradiction: jumps should be included in stock price models.

Keywords: Realized variance, realized bipower variance, microstructure noise, mixture of normals, jump process

JEL Classification: C22, C12, G12

Suggested Citation

Fleming, Jeff and Paye, Bradley S., High-Frequency Returns, Jumps and the Mixture of Normals Hypothesis (July 28, 2006). Available at SSRN: https://ssrn.com/abstract=855344 or http://dx.doi.org/10.2139/ssrn.855344

Jeff Fleming

Rice University - Jesse H. Jones Graduate School of Business ( email )

6100 South Main Street
P.O. Box 1892
Houston, TX 77005-1892
United States
713-348-4677 (Phone)
713-348-5251 (Fax)

HOME PAGE: http://www.ruf.rice.edu/~jfleming

Bradley S. Paye (Contact Author)

Virginia Polytechnic Institute & State University - Department of Finance, Insurance, and Business Law ( email )

1016 Pamplin Hall (0221)
Blacksburg, VA 24060-0221
United States

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