Bias-corrected estimators for the Vasicek model: an application in risk measure estimation

Zi-Yi Guo

Abstract

We evaluate the usefulness of bias-correction methods in enhancing the Vasicek model for market risk and counterparty risk management practices. The naive bias-corrected estimator, the Tang and Chen bias-corrected estimator and the Bao et al bias-corrected estimator are selected to be compared against the benchmark least squares (LS) estimator. Our Monte Carlo experiment shows that the bias-corrected estimators substantially reduce the small sample bias of the LS estimator for the Vasicek model and project much more accurate value-at-risk and potential future exposure estimations. Even if the sample length is as long as 30 years, the improvements are still significant, especially for the cases where the mean-reversion parameter is close to zero. The applications to real data further demonstrate that the small sample bias of the LS estimator cannot be ignored and one should consider bias-corrected estimators for the Vasicek model.