Realized Kernel Estimation of Quadratic Volatility with Irregular Sampling Times

• Activity Number: 15
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Michael Levine*+ and Jian Zou and Xiaoguang Wang
• Companies: Purdue University and Indiana University-Purdue University Indianapolis and Purdue University
• Keywords: Quadratic volatility ; Non-equispaced sampling times ; Realized kernel volatility estimator ; high-frequencey financial data ; limit theorems

Abstract

Estimating quadratic volatility of high-frequency financial data is rather common today. It is, in its essence, a nonparametric approach to the estimation problem and, as such, is sharply different from the more traditional maximum likelihood estimation of quadratic volatility. One of the most popular ways to estimate quadratic volatility is the so-called realized kernel volatility estimator that has been defined first in the work of Barndorff-Nielsen, Shephard and others. Usually, the price process is assumed to be of the Brownian semimartingale type and the sampling times are assumed to be regularly spaced. The latter assumption, arguably, does not reflect the reality of discrete sampling. In our research, we a)obtain a new quadratic variation estimator that generalizes the original realized kernel estimator to the case of discrete non-equispaced sampling case and b)obtain several new limit theorems for the sums of a functions of Brownian semimartingale increments under non-equidistant sampling assumption that are of independent interest. This is joint work with Jian (Frank) Zou and Xiaoguang Wang.