The Estimation of Leverage Effect with High-Frequency Data

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Dan Wang*+
• Companies: The University of Chicago
• Keywords: leverage effect ; Ito process ; consistency ; stable convergence ; microstructure noise ; discrete observation

Abstract

Leverage effect has become an extensively studied phenomenon which describes the (usually) negative relation between stock returns and their volatility. Although it is well acknowledged, most studies of leverage effect are based on cross-sectional calibration with parametric models, over daily or longer horizons, and usually do not specify the parameter being studied. This paper provides nonparametric estimation for a class of stochastic measures of leverage effect. The theory covers both the cases with and without microstructure noise, and studies the statistical properties of the estimators when the log price process is a continuous semimartingale. Volatility is stochastic, and our asymptotics reflect a high frequency data sampling regime. The consistency and limit distribution of the estimators are derived, and simulation results which corroborate the asymptotic properties are presented. This estimator also provides the opportunity to study high frequency regression, and the theoretical connection between skewness and leverage effect. Adopting similar ideas, it is easy to extend the the study to other important aspects of stock returns, e.g. volatility of volatility.