Publication: A dominance approach for comparing the performance of VaR forecasting models
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2019
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Facultad de Ciencias Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE)
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We introduce three dominance criteria to compare the performance of alternative VaR forecasting models. The three criteria use the information provided by a battery of VaR validation tests based on the frequency and size of exceedances, offering the possibility of efficiently summarizing a large amount of statistical information. They do not require the use of any loss function defined on the difference between VaR forecasts and observed returns, and two of the criteria are not conditioned on any significance level for the VaR tests. We use them to explore the potential for 1-day ahead VaR forecasting of some recently proposed asymmetric probability distributions for return innovations, as well as to compare the APARCH and FGARCH volatility specifications with more standard alternatives. Using 19 assets of different nature, the three criteria lead to similar conclusions, suggesting that the unbounded Johnson SU, the skewed Student-t and the skewed Generalized-t distributions seem to produce the best VaR forecasts. The added flexibility of a free power parameter in the conditional volatility in the APARCH and FGARCH models leads to a better fit to return data, but it does not improve upon the VaR forecasts provided by GARCH and GJR-GARCH volatilities.
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Preprint submitted to Journal of International Financial Markets, Institutions & Money. May 6, 2019.
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Aas, K., and Haff, I.H. (2006). The generalized hyperbolic skew student’st-distribution. Journal of Financial Econometrics, 4(2), 275-309.
Abad, P., Benito, S., Lopez, C., and Sanchez-Granero, M.A. (2016). Evaluating the performance of the skewed distributions to forecast value-at-risk in the global financial crisis. Journal of Risk, 18(5), 1-28.
Abramowitz, M., and Stegun, I. A. (1972). Handbook of mathematical functions with formulas, graphs, and mathematical tables (Vol. 9). Dover: New York.
Acerbi, C. and Szekely, B. (2014). Backtesting Expected Shortfall. Publication of MSCI. https://www.msci.com/www/research-paper/research-insight-backtesting/0128184734.
Bali, T.G., and Theodossiou, P. (2007). A conditional-SGT-VaR approach with alternative GARCH model. Annals of Operations Research, 151, 241-267.
Basel Committee on Banking Supervision, Standards: Minimum Capital requirements for mar- ket risk (2016). Bank for International Settlements.
Bao, Y., Lee, T., and Saltoglu, B. (2006). Evaluating predictive performance of value-at-risk models in emerging markets: a reality check. Journal of Forecasting, 25, 101-128.
Bhattacharyya, M., and Ritolia, G. (2008). Conditional VaR using EVT: towards a planned margin scheme. International Review of Financial Analysis, 17(2), 382-395.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.
Braione, M., and Scholtes, N.K. (2016). Forecasting Value-at-Risk under different distributional Assumptions. Econometrics, 4(3).
Cai, Y., and Krishnamoorthy, K. (2006). Exact size and power properties of five tests for multi- nomial proportions. Communications in Statistics-Simulation and Computation, 35(1), 149-160.
Caporin, M. (2008). Evaluating Value-at-Risk measures in the presence of long memory condi- tional volatility. The Journal of Risk, 10(3), 79-110.
Choi, P., and Nam, K. (2008). Asymmetric and leptokurtic distribution for heteroscedastic asset returns: the SU-normal distribution. Journal of Empirical finance, 15(1), 41-63.
Colletaz, G., Hurlin, C., and Pe´rignon, C. (2013). The Risk Map: A new tool for validating risk models. Journal of Banking and Finance, 37(10), 3843-3854.
Corlu, C.G., Meterelliyoz, M., and Tinic¸, M. (2016). Empirical distributions of daily equity index returns: A comparison. Expert System with Applications, 54, 170-192.
Diamandis, P.F., Drakos, A.A., Kouretas, G.P., and Zarangas, L. (2011). Value-at-Risk for long and short trading positions: Evidence from developed and emerging equity markets. Interna- tional Review of Financial Analysis, 20, 165-176.
Ding, Z., Granger, C.W.J., and Engle, R.F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83-106.
Du, Z. and Escanciano, J.C. (2016). Backtesting Expected Shortfall: Accounting for Tail Risk. Management Science, 63(4), 940-958.
Engle R.F., and Manganelli, S. (2004). CAViaR: conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics, 22, 367-381.
Fernandez, C., and Steel, M. (1998). On bayesian modelling of fat tails and skewness. Journal of the American Statistical Association, 93(441), 359-371.
Gerlach, R., Chen, C.W.S., Lin, E.M.H., and Lee, W.C.W. (2011). Bayesian forecasting for financial risk management, pre and post the global financial crisis. Journal of Forecasting, 31(8), 661-687.
Giacomini, R., and Komunjer, I. (2005). Evaluation and combination of conditional quantile forecasts. Journal of Business and Economic Statistics, 23(4), 416-431.
Giot, P., and Laurent, S. (2003a). Value-at-Risk for long and short trading positions. Journal of Applied Econometrics, 18, 641-664.
Glosten, L., Jagannathan R., and Runkle, D. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779-1801.
Hentschel, L. (1995). All in the family nesting symmetric and asymmetric GARCH models. Journal of Financial Economics, 39, 71-104.
Hu, W. (2005). Calibration of multivariate generalized hyperbolic distributions using the EM algorithm, with applications in risk management, portfolio opti- mization and portfolio credit risk. Dissertation in the Florida State University. http://diginole.lib.fsu.edu/islandora/object/fsu:181953/datastream/PDF/view
Johnson, N.L. (1949). Systems of frequency curves generated by methods of translations. Biometrika, 36, 149-176.
Kratz, M., Lok, Y.H., and McNeil, A.J. (2018). Multinomial VaR Backtests: A simple implicit approach to backtesting expected shortfall. Journal of Banking and Finance, 88, 393-407.
Kupiec, P. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, 2, 174-184.
Lambert, P., and Laurent, S. (2001). Modelling financial time series using GARCH-type models with a skewed student distribution for the innovations. Mimeo, Universite´ de Liege.
Leccadito, A., Boffelli, S., and Urga, G. (2014). Evaluating the accuracy of value-at-risk fore- casts: New multilevel tests. International Journal of Forecasting, 30, 206-216.
Lee, C.F., and Su, J.B. (2015). Value-at-Risk estimation via a semiparametric approach: Ev- idence from the stock markets. Handbook of Financial Econometrics and Statistics. Springer Science Business Media: New York.
Lopez, J.A. (1998). Testing your risk tests. Financial Survey (May-Jun), 18-20.
Lopez, J.A. (1999). Methods for evaluating Value-at-Risk estimates. Federal Reserve Bank of San Francisco Economic Review, 2, 3-17.
Louzis, D.P., Xanthopoulos-Sisinis, S., and Refenes, A.P. (2014). Realized volatility models and alternative Value-at-Risk prediction strategies. Economic Modelling, 40, 101-116.
McDonald, J. B., and Newey, W. K. (1988). Partially adaptive estimation of regression models via the generalized t distribution. Econometric theory, 4(3), 428-457.
Mittnik, S., and Paolella, M. (2000). Conditional density and value-at-risk prediction of Asian currency exchange rates. Journal of Forecasting, 19, 313-333.
Nakajima, J., and Omori, Y. (2012). Stochastic volatility model with leverage and asymmetri- cally heavy-tailed error using GH skew Student’s t-distribution. Computational Statistics and Data Analysis, 56(11), 690-3704.
Nelson, D.B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econo- metrica, 59(2), 347-370.
Nozari, M., Raei, S., Jahanguin, P., and Bahramgiri, M. (2010). A comparison of heavy-tailed estimates and filtered historical simulation: evidence from emerging markets. International Re- view of Business Papers, 6(4), 347-359.
Ozun, A., Cifter, A., and Yilmazer, S. (2010). Filtered extreme-value theory for value-at-risk estimation: evidence from Turkey. The Journal of Risk Finance, 11(2), 164-179.
Novales, A., and Garcia-Jorcano, L. (2019). Backtesting extreme value theory models of ex- pected shortfall. Quantitative Finance, 19(5), 799-825. DOI: 10.1080/14697688.2018.1535182
Paolella, M. S., and Polak, P. (2015). COMFORT: A common market factor non-Gaussian re- turns model. Journal of Econometrics, 187(2), 593-605.
Righi, M.B. and Ceretta, P.S. (2013). Individual and flexible Expected Shortfall backtesting. Journal of Risk Model Validation, 7(3), 3-20.
Riskmetrics, T. M. (1996). JP Morgan Technical Document.
Sarma, M., Thomas, S., and Shah, A. (2003). Selection of value at risk models. Journal of Forecasting, 22, 337-358.
Schwert, W. (1990). Stock volatility and the crash of ’87. Review of Financial Studies, 3, 77-102.
Simonato, J. G. (2011). The performance of Johnson distributions for computing value at risk and expected shortfall. The Journal of Derivatives, 19(1), 7-24.
Taylor, S.J. (1986). Modelling Financial Time Series. John Wiley and Sons, Inc.
Theodossiou, P. (1998). Financial data and skewed generalized t distribution. Management Sci- ence, 44, 1650-1661.
Yu, P.L.H., Li, W.K., and Jin, S., (2010). On some models for value-at-risk. Econometric Re- views, 29(5-6), 622-641.
Zangari, P. (1996). An improved methodology for measuring VaR. RiskMetrics Monitor, 2nd quarter, 7-25.