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5 - Evaluation of Value-at-Risk Models: An Empirical Likelihood Approach

Published online by Cambridge University Press:  02 March 2023

David Lynch
Affiliation:
Federal Reserve Board of Governors
Iftekhar Hasan
Affiliation:
Fordham University Graduate Schools of Business
Akhtar Siddique
Affiliation:
Office of the Comptroller of the Currency
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Summary

This chapter provides an alternative to exceedance or density-based evaluation of VaR models. This alternative is based on empirical likelihood. We also outline a method to infer the risk exposure, by assessing whether some measure of interval forecast error (e.g., distance between the empirical distribution of the PITs and the posited uniform distribution) is related to some measure of risk exposure, such as the volatility of given risk factors.

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Publisher: Cambridge University Press
Print publication year: 2023

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References

Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193212.CrossRefGoogle Scholar
Berkowitz, Jeremy. (2001). Testing density forecasts, with applications to risk management. Journal of Business & Economic Statistics, 19, 465474.Google Scholar
Christoffersen, Peter F. (1998). Evaluating interval forecasts. International Economic Review, 39, 841862.CrossRefGoogle Scholar
Diebold, Francis X., Gunther, Todd A. and Tay, Anthony S. (1998). Evaluating density forecasts with applications to financial risk management. International Economic Review, 39, 863883.Google Scholar
Gordy, M. B. and McNeil, A. (2018). Spectral backtests of forecast distributions with application to risk management, Unpublished Manuscript,Google Scholar
Kitamura, Y. (2006). Empirical likelihood methods in econometrics: theory and practice. Cowles Foundation Discussion Paper, 1569.Google Scholar
Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione. Giornale dell’Istituto Italiano degli Attuari, 4, 8391.Google Scholar
Lopez, J. A. (1998). Methods for Evaluating Value-at-Risk Estimates, Economic Policy Review, 4(3), 2–18.Google Scholar
Owen, Art B. (2001). Empirical likelihood. (Chapman and Hall/CRC Boca Raton).Google Scholar
Post, Thierry, and Potì, Valerio. (2017). Portfolio analysis using stochastic dominance, relative entropy, and empirical likelihood. Management Science, 63, 153165.Google Scholar
Rosenblatt, Murray. (1952). Remarks on a multivariate transformation. The Annals of Mathematical Statistics, 23, 470472.Google Scholar
Smirnov, N. (1948). Table for estimating the goodness of fit of empirical distributions. The Annals of Mathematical Statistics, 19, 279281.Google Scholar
Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics, 9, 6062.Google Scholar

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