Bias in the Estimation of Mean Reversion in Continuous-Time Lévy Processes

This paper develops the approximate bias of the ordinary least squares estimator of the mean reversion parameter in continuous-time Lévy processes. Several cases are considered, depending on whether the long-run mean is known or unknown and whether the initial condition is fixed or random. The approximate bias is used to construct a bias corrected estimator. The performance of the approximate bias and the bias corrected estimator is examined using simulated data