Abstract
Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and to select the most appropriate one. In this paper, we shall propose to use the empirical likelihood approach to evaluate these models. Simulation results and real life examples show that the empirical likelihood method is more powerful and more robust than some of the asymptotic method available in literature.
Similar content being viewed by others
References
Duffie D, Pan J. An overview of value at risk. J Derivatives, 5: 7–49 (1997)
Alexander C. Risk Management and Analysis, Vol. I & II. Chichester: Wiley, 1998
Dowd K. Beyond Value at Risk: The New Science of Risk Management. New York: Wiley, 1998
Jorion P. Value at Risk: The New Benchmark for Managing Financial Risk, 2nd ed. New York: McGraw-Hill, 2000
Hendricks D. Evaluation of value-at-risk models using historical data. Federal Reserve Bank of New York Economic Policy Review, 2: 39–69 (1996)
Mahoney J M. Forecast biases in value-at-risk estimations: evidence from foreign exchange and global equity portfolios. Working paper, Federal Reserve Bank of New York, 1996
Engle R F. ARCH, Selected Readings. Oxford: Oxford University Press, 1995
Bollerslev T. Generalized autoregressive conditional heteroscedasticity. J Econometrics, 31: 307–327 (1986)
Embrechts P, Kluppelberg C, Mikosch T. Modeling Extremal Events for Insurance and Finance. Berlin: Springer, 1997
Christoffersen P F. Elements of Financial Risk Management. Amsterdam: Academic Press, 2003
Engle R F, Manganelli S. CAViaR: conditional autoregressive value at risk by regression quantiles. J Bus Econom Statist, 22: 367–381 (2004)
Koenker R, Bassett G. Regression quantiles. Econometrica, 46: 33–50 (1978)
Fan J Q, Gu J. Semiparametric estimation of Value-at-Risk. Econometrics J, 6: 261–290 (2003)
Chan K C, Karolyi A G, Longstaff F A, et al. An empirical comparison of alternative models of the short-term interest rate. J Finance, 47: 1209–1227 (1992)
Chen S X, Tang C Y. Nonparametrical inference of Value-at-Risk for dependent financial returns. J Financial Econometrics, 3: 227–255 (2005)
Chen S X, Wong C M. Smoothed block empirical likelihood for quantiles of weakly dependent process. Statist Sinica, to appear (2009)
Kupiec P H. Techniques for verifying the accuracy of risk measurement models. J Derivatives, 3: 73–84 (1995)
Christoffersen P F. Evaluating interval forecasts. Internat Econom Rev, 39: 841–862 (1998)
Crnkovic C, Drachman J. Quality control. Risk, 9: 139–143 (1996)
Lopez J. Regulatory evaluation of value-at-risk models. J Risk, 23: 470–472 (1997)
Christoffersen P, Hahn J, Inoue A. Testing and comparing value-at-risk measures. J Empirical Finance, 8: 325–342 (2001)
Owen A B. Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75: 237–249 (1988)
Owen A B. Empirical likelihood ratio confidence regions. Ann Statist, 18: 90–120 (1990)
Hall P, LaScala B. Methodology and algorithms of empirical likelihood. Internat Statist Rev, 58: 109–127 (1990)
DiCiccio T S, Hall P, Romono J. Empirical likelihood is Bartlett correctable. Ann Statist, 19: 1053–1061 (1991)
Owen A B. Empirical likelihood for linear models. Ann Statist, 19: 1725–1747 (1991)
Chen S X. Empirical likelihood confidence intervals for nonparametric density estimation. Biometrika, 83: 329–341 (1996)
Chen S X, Qin Y S. Empirical likelihood confidence intervals for local linear smoothers. Biometrika, 87: 946–953 (2000)
Chen S X, Hall P. Smoothed empirical likelihood confidence intervals for quantiles. Ann Statist, 21: 1166–1181 (1993)
Owen A B. Empirical Likelihood. London: Chapman and Hall, 2001
Kitamura Y, Stutzer M. An information-theoretic alternative to generalized method of moments estimation. Econometrica, 65: 861–874 (1997)
Morgan J P. Riskmetrics-Technical Document, 4th ed. New York: Morgan Guaranty Trust Company, 1996
Nelson D. Filtering and forecasting with misspecified GARCH models: getting the right variance with the wrong models. J Econometrics, 52: 61–90 (1992)
Author information
Authors and Affiliations
Corresponding author
Additional information
The work was supported by Guangdong Natural Science Foundation (Grant No. 2008276) and a grant from the Research Grants Council of Hong Kong, China
Rights and permissions
About this article
Cite this article
Wei, Z., Wen, S. & Zhu, L. Empirical likelihood-based evaluations of Value at Risk models. Sci. China Ser. A-Math. 52, 1995–2006 (2009). https://doi.org/10.1007/s11425-009-0050-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-009-0050-6