Standard risk measures, such as the value-at-risk (VaR), or the expected shortfall, have to be estimated, and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on n observations of the profit and loss variable induces an asymptotic bias of order 1/ n in the coverage probabilities. This paper shows how to correct for this bias by introducing a new estimator of the VaR, called estimation-adjusted VaR (EVaR). This adjustment allows for a joint treatment of theoretical and estimation risks, taking into account their possible dependence. The estimator is derived for a general parametric dynamic model and is particularized to stochastic drift and volatility models. The finite sample properties of the EVaR estimator are studied by simulation and an empirical study of the S&P index is proposed.
Volume (Year): 29 (2013)
Issue (Month): 04 (August)
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- J. Carlos Escanciano & Jose Olmo, 2011. "Robust Backtesting Tests for Value-at-risk Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 132-161, Winter.
- Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2005.
"Evaluating Value-at-Risk models with desk-level data,"
Working Paper Series
010, North Carolina State University, Department of Economics, revised Dec 2006.
- Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
- Peter Christoffersen & Jeremy Berkowitz & Denis Pelletier, 2008. "Evaluating Value-at-Risk Models with Desk-Level Data," CREATES Research Papers 2009-35, Department of Economics and Business Economics, Aarhus University.
- Dufour, J.M. & Kiviet, J.F., 1995.
"Exact Tests in Single Equation Autoregressive Distributed Lag Models,"
Cahiers de recherche
9549, Universite de Montreal, Departement de sciences economiques.
- Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
- Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche 9549, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Chambers, Marcus J., 2013.
"Jackknife estimation of stationary autoregressive models,"
Journal of Econometrics,
Elsevier, vol. 172(1), pages 142-157.
- Chambers, Marcus J, 2010. "Jackknife Estimation of Stationary Autoregressive Models," Economics Discussion Papers 2786, University of Essex, Department of Economics.
- Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
- Juan Carlos Escanciano & Jose Olmo, 2007.
"Backtesting Parametric Value-at-Risk with Estimation Risk,"
Caepr Working Papers
2007-005_updated, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
- Escanciano, J. Carlos & Olmo, Jose, 2010. "Backtesting Parametric Value-at-Risk With Estimation Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 36-51.
- Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
- Bao, Yong & Ullah, Aman, 2004. "Bias of a Value-at-Risk estimator," Finance Research Letters, Elsevier, vol. 1(4), pages 241-249, December.
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