2016/11/20 by Michael Levine, Xiaoguang Wang, Levine, Michael +2
Economics, Econometrics and Finance · #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #Complex Systems and Time Series Analysis
paper · pdf · doi:10.48550/arxiv.1611.06566
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is thought of as a financial asset price process, a general sampling scheme like the one employed in this paper is capable of reflecting what happens whenever the financial trading data are recorded in a tick-by-tick fashion. A law of large numbers and a central limit theorem are proved after an appropriate normalization. One application of our result is an extension of the realized kernel estimator of integrated volatility to the case of random sampling times.