Journal of Risk

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

Zi-Yi Guo

  • Our Monte Carlo simulation results indicate that the widely-used least squares estimations of the Vasicek model suffer significant small-sample biases even if the sample length reaches as long as 30 years.
  • Bias-corrected estimators could substantially reduce the small sample biases of the least squares estimations, and further project much more accurate value-at-risk and potential future exposure estimates.
  • Empirical applications to a variety of time series are in general in line with the Monte Carlo simulation results.

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.

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