Nonparametric Estimation for Risk in Value-at-Risk Estimator

Abstract

Value-at-Risk (VaR) has become the standard tool used by many financial institutions to measure market risk. However, the performance of a VaR estimator may be affected by sample variation or estimation risk caused from heavy-tailed distributions. After surveying several existing procedures proposed by Jorin (Jorion, P. (1996). Risk²—Measuring the risk in value at risk. Financial Analysis Journal 52:47–56), Huschens (Huschens, S. (1997). Confidence intervals for the value-at-risk. In: Bol, G., Nakhaeizadeh, G., Vollmer, K. H., eds. Risk Measurement, Econometrics and Neural Networks. Heidelberg: Physica-Verlag, pp. 233–244), and Ridder (Ridder, T. (1997). Basics of statistical VaR-estimation. In: Bol, G., Nakhaeizadeh, G., Vollmer, K. H., eds. Risk Measurement, Econometrics and Neural Networks. Heidelberg: Physica-Verlag, pp. 161–187) etc., this article strives to propose several new estimators in measuring the risk involved in VaR estimation. We compare the performance of these VaR models through Monte Carlo simulation studies. We find that the newly proposed methods provide better accuracy and robustness in the estimation of the risk in VaR estimator.

Keywords:

• Value-at-risk (VaR)
• Risk for a VaR estimator
• Confidence interval
• Heavy-tailed distribution

Acknowledgments

The authors would like to thank a referee for helpful comments and suggestions. This research was partially supported by NSC 91-2118-M-031-002 and NSC 90-2745-P-031-003 from the National Science Council, R.O.C.