The Estimation of Leverage Effect with High Frequency Data

Journal of the American Statistical Association, Forthcoming

44 Pages Posted: 30 Aug 2011 Last revised: 13 Nov 2014

See all articles by Christina Dan Wang

Christina Dan Wang

Columbia University - Department of Statistics

Per A. Mykland

University of Chicago - Department of Statistics

Date Written: October 5, 2013

Abstract

Leverage effect has become an extensively studied phenomenon which describes the negative relation between the stock return and its volatility. Although this characteristic of stock returns is well acknowledged, most studies about it are based on cross-sectional calibration with parametric models. Other than that, most previous work are over daily or longer return horizons and usually do not specify the quantitative measure of it. This paper provides nonparametric estimation of a class of stochastic measures of leverage effect for both cases with and without microstructure noise, and studies the statistical properties of the estimators when the log price process is a quite general continuous semimartingale, in the stochastic volatility context and for high frequency data. The consistency and limit distribution of the estimators are derived, and simulation results present the properties accordingly. This estimator also provides the opportunity to study the empirical relation between skewness and leverage effect, which further leads to the prediction of skewness. Furthermore, adopting similar ideas to these in this paper, it is easy to extend the study to other important aspects of the stock returns, e.g. volatility of volatility.

Keywords: consistency, discrete observation, efficiency, Itˆo process, leverage effect, realized volatility, stable convergence, skewness, microstructure noise

JEL Classification: C1, C13, C14

Suggested Citation

Wang, Christina Dan and Mykland, Per A., The Estimation of Leverage Effect with High Frequency Data (October 5, 2013). Journal of the American Statistical Association, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1919138 or http://dx.doi.org/10.2139/ssrn.1919138

Christina Dan Wang (Contact Author)

Columbia University - Department of Statistics ( email )

Mail Code 4403
New York, NY 10027
United States

HOME PAGE: http://stat.columbia.edu/~dwang/

Per A. Mykland

University of Chicago - Department of Statistics ( email )

Chicago, IL 60637-1514
United States
773-702-8044 (Phone)

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