Emrah Altun, Hüseyin Tatlidil
1.981 457


In this study, wavelet based GARCH-Extreme Value Theory (EVT) is proposed to model financial return series to forecast daily value-at-risk. Wavelets based GARCH-EVT is hybrid model combining the wavelet analysis and EVT. Proposed model contains three stages. In first stage, return series is decomposed into wavelet series and approximation series by applying the maximal overlap discrete wavelet transform. Second stage, detrended return series and approximation series are obtained by using wavelet series and scaling series. GARCH model is fitted to each obtained series to forecast daily volatility. Final stage, EVT is used to estimate quantile estimation of standardized residuals of GARCH model obtained for detrended return series and daily VaR value is forecasted by using volatility forecasts and quantile estimation. Daily VaR forecasting accuracy of proposed hybrid model is compared with the GARCH models specified under heavy-tailed distributions and GARCH-EVT model. Empirical findings show that wavelet based GARCH-EVT model is outperformed at high quantiles according to backtesting results.

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McNeil, A. J., & Frey, R., Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Journal of empirical finance, 7(3), (2000), 271-300.

Gencay, R., & Selcuk, F., Extreme value theory and Value-at-Risk: Relative performance in emerging markets. International Journal of Forecasting, 20(2), (2004), 287-303.

Gilli, M., An application of extreme value theory for measuring financial risk. Computational Economics, 27(2-3), (2006), 207-228.

Onour, I. A., Extreme risk and fat-tails distribution model: empirical analysis. Journal of Money, Investment and Banking, (13), (2010).

Singh, A. K., Allen, D. E., & Robert, P. J., Extreme market risk and extreme value theory. Mathematics and computers in simulation, 94, (2013), 310-328.

Soltane, H. B., Karaa, A., & Bellalah, M., Conditional VaR Using GARCH-EVT Approach: Forecasting Volatility in Tunisian Financial Market.Journal of Computations & Modelling, 2(2), (2012), 95-115.

Chan, K. F., & Gray, P., Using extreme value theory to measure value-at-risk for daily electricity spot prices. International Journal of Forecasting,22(2), (2006), 283-300.

Karmakar, M., Estimation of tail-related risk measures in the Indian stock market: An extreme value approach. Review of Financial Economics,22(3), (2013), 79-85.

Altun, E., & Tatlidil, H., A Comparison of Extreme Value Theory with Heavy-tailed Distributions in Modeling Daily VAR. Journal of Finance and Investment Analysis, 4(2), (2015),69-83

Venkataraman, S., Value at risk for a mixture of normal distributions: the use of quasi-Bayesian estimation techniques. Economic Perspectives-Federal Reserve Bank of Chicago, 21, (1997), 2-13.

Zangari, P., An improved methodology for measuring VaR. RiskMetrics Monitor, 2(1), (1996), 7-25.

Lee, M. C., Su, J. B., & Liu, H. C., Value-at-risk in US stock indices with skewed generalized error distribution. Applied Financial Economics Letters, 4(6), (2008), 425-431.

Angelidis, T., Benos, A., & Degiannakis, S., The use of GARCH models in VaR estimation. Statistical methodology, 1(1), (2004), 105-128.

Daubechies, I., Ten lectures on wavelets, Philadelphia: Society for industrial and applied mathematics, 61, (1992), 198-202.

Chui, C. K. (1992). An Introduction to Wavelets, Philadelphia, SIAM, 38, (1992).

Graps, A., An introduction to wavelets. Computational Science & Engineering, IEEE, 2(2), (1995), 50-61.

Chi, X., & Kai-jian, H., Wavelet denoised value at risk estimate. In Management Science and Engineering, ICMSE'06, IEEE, (2006), 1552-1557

Lai, K. K., He, K., Xie, C., & Chen, S., Market risk measurement for crude oil: a wavelet based var approach. IJCNN'06, IEEE, (2006), 2129-2136.

Samia, M., Dalenda, M., & Saoussen, A., Accuracy and Conservatism of VaR Models: A Wavelet Decomposed VaR Approach Versus Standard ARMA-GARCH Method. International Journal of Economics and Finance, 1(2), (2009).

Tan, Z., Zhang, J., Wang, J., & Xu, J., Day-ahead electricity price forecasting using wavelet transform combined with ARIMA and GARCH models. Applied Energy, 87(11), (2010), 3606-3610.

Cifter, A., Value-at-risk estimation with wavelet-based extreme value theory: Evidence from emerging markets. Physica A: Statistical Mechanics and its Applications, 390(12), (2011), 2356-2367.

Balkema, A. A., & De Haan, L., Residual life time at great age. The Annals of probability, (1974), 792-804.

Pickands III, J., Statistical inference using extreme order statistics. the Annals of Statistics, (1975), 119-131.

Engle, R. F., Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, (1982), 987-1007.

Bollerslev, T., Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3), (1986), 307-327.

Bollerslev, T., A conditionally heteroskedastic time series model for speculative prices and rates of return. The review of economics and statistics, (1987), 542-547.

Nelson, D. B., Conditional heteroskedasticity in asset returns: A new approach. Econometrica: Journal of the Econometric Society, (1991), 347-370.

Lee, M. C., Su, J. B., & Liu, H. C., Value-at-risk in US stock indices with skewed generalized error distribution. Applied Financial Economics Letters, 4(6), (2008), 425-431.

Hamburger, Y., Wavelet-based Value at Risk Estimation: A Multiresolution Approach. Erasmus Universiteit, (2003).

Ramsey, J. B., The contribution of wavelets to the analysis of economic and financial data. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 357(1760), (1999), 2593-2606.

Cornish, C. R., Bretherton, C. S., & Percival, D. B., Maximal overlap wavelet statistical analysis with application to atmospheric turbulence.Boundary-Layer Meteorology, 119(2), (2006), 339-374.

Kupiec, P. H., Techniques for verifying the accuracy of risk measurement models. THE J. OF DERIVATIVES, 3(2), (1995)