Laplace Estimator of Integrated Volatility When Sampling Times Are Endogenous

Abstract

We study a class of nonparametric volatility estimators based on the Laplace transform, which are robust to the presence of the endogeneity of observation times. Asymptotic properties and feasible central limit theorems are established. In the presence of time endogeneity, our bias-corrected Laplace estimator takes advantage of the informational content of time endogeneity, which leads to narrower confidence bounds. The finite sample properties of the estimator are studied through Monte Carlo simulations. Through the simulation study, we also find that due to the presence of the kernel, Laplace estimator could be adopted in a model with microstructure noise. The performance of the Laplace estimator is compared with other commonly used estimators through forecasting exercises by employing high frequency data. We conclude that the bias-corrected Laplace estimator performs better than most estimators in terms of forecasting equity return volatility in the presence of both time endogeneity and market microstructure noise.