A Comparative Study of GARCH and EVT Model in Modeling Value-at-Risk

Li, Longqing (2017): A Comparative Study of GARCH and EVT Model in Modeling Value-at-Risk. Published in: Journal of Applied Business and Economics , Vol. 19, No. 7 : pp. 27-48.

Abstract

The paper addresses an inefficiency of the traditional approach in modeling the tail risk, particularly the 1-day ahead forecast of Value-at-Risk (VaR), using Extreme Value Theory (EVT) and GARCH model. Specifically, I apply both models onto major countries stock markets daily loss, including U.S., U.K., China and Hong Kong between 2006 and 2015, and compare the relative forecasting performance. The paper differs from other studies in two important ways. First, it incorporates an asymmetric shock of volatility in the financial time series. Second, it applies a skewed fat-tailed return distribution using the Generalized Error Distribution (GED). The back-testing result shows that, on one hand, the conditional EVT performs equally well relative to GARCH model under the Generalized Error Distribution. On the other hand, the Exponential GARCH based model is the best performing one in Value-at-Risk forecasting, because it not only correctly identifies the future extreme loss, but more importantly, its occurrence is independent.

• Item Type: MPRA Paper
• Language: English
• Keywords: Value-at-Risk,Extreme Value Theory, Backtesting, Risk Forecasting
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill

References

Abad, P., S. Benito, and C. López. (2014). A comprehensive review of Value-at-Risk methodologies. The Spanish Review of Financial Economics 12: 15--32.

Allen, D. E., A. K. Singh, and R. J. Powell. (2013). EVT and tail-risk modeling: Evidence from market indices and volatility series. The North American Journal of Economics and Finance 26: 355--369.

Angelidis, T., A. Benos, and S. Degiannakis. (2004). The use of GARCH models in Value-at-Risk estimation. Statistical Methodology 1:105–128.

Bali, T. G., and S. N. Neftci. (2003). Disturbing extremal behavior of spot rate dynamics. Journal of Empirical Finance 10: 455--477.

Bali T. G. (2007). A Generalized Extreme Value Approach to Financial Risk Measurement. J Money Credit Banking 39: 1613--1649.

Balkema, A. A., and L. de Haan. (1974). Residual Life Time at Great Age. Ann. Probability. 2:792–804.

Bekiros, S. D., and D. A. Georgoutsos. (2005). Estimation of Value-at-Risk by extreme value and conventional methods: a comparative evaluation of their predictive performance. Journal of International Financial Markets, Institutions and Money 15: 209--28.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31:307–327.

Christoffersen, P. F. (1998). Evaluating Interval Forecasts. International Economic Review 39:841.

Dahlen, K. E., R. Huisman, and S. Westgaard. (2015). Risk Modeling of Energy Futures: A Comparison of RiskMetrics, Historical Simulation, Filtered Historical Simulation, and Quantile Regression. Stochastic Models, Statistics and Their Applications: 283--291.

Danielsson, J .,& de Vries,C.(2000). Value-at-risk and extreme returns. Annales d’Economie et de Statistique,60, 239-270

Embrechts, P., C. Klüppelberg, and T. Mikosch. (1997). Modeling Extremal Events.

Embrechts, P., S. I. Resnick, and G. Samorodnitsky.(1999). Extreme Value Theory as a Risk Management Tool. North American Actuarial Journal 3:30–41.

Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the variance of United Kingdom Inflation. Econometrica 50:987.

Fernandez, V. (2005). Risk management under extreme events. International Review of Financial Analysis 14:113--148.

Gençay, R., F. Selçuk, and A. Ulugülyaǧci. (2003). High volatility, thick tails and extreme value theory in value-at-risk estimation. Insurance: Mathematics and Economics 33:337--356.

Gaye Gencer, H., and S. Demiralay. (2015). Volatility Modeling and Value-at-Risk (VaR) Forecasting of Emerging Stock Markets in the Presence of Long Memory, Asymmetry and Skewed Heavy Tails. Emerging Markets Finance and Trade:1--19.

Ghorbel, A., and A. Trabelsi. (2008). Predictive performance of conditional Extreme Value Theory in Value-at-Risk estimation. International Journal of Monetary Economics and Finance 1:121.

Gilli, M., and E.këllezi (2006). An Application of Extreme Value Theory for Measuring Financial Risk. Computational Economics 27:207--228.

Giot, P., and S. Laurent. (2004). Modeling daily Value-at-Risk using realized volatility and ARCH type models. Journal of Empirical Finance 11:379--398.

Glantz, M., and R. Kissell. (2014). Extreme Value Theory and Application to Market Shocks for Stress Testing and Extreme Value-at-Risk. Multi-asset Risk Modeling:437--476.

Glosten, L. R., R. Jagannathan, and D. E. Runkle (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance 48:1779--1801.

Karmakar, M., and G. K. Shukla. (2015). Managing extreme risk in some major stock markets: An extreme value approach. International Review of Economics & Finance 35:1--25.

Kittiakarasakun, J., and Y. Tse. (2011). Modeling the fat tails in Asian stock markets. International Review of Economics & Finance 20:430--440.

Kuester, K. (2005). Value-at-Risk Prediction: A Comparison of Alternative Strategies. Journal of Financial Econometrics 4:53--89.

Kupiec, P. H. (1995). Techniques for Verifying the Accuracy of Risk Measurement Models. Derivatives 3:73--84.

Lieberman, G. J., and E. J. Gumbel. (1960). Statistics of Extremes. Journal of the American Statistical Association 55:383

Lin, C., and S. Shen. (2006). Can the Student-t distribution provide accurate Value-at-Risk? The Journal of Risk Finance 7:292--300.

Longin, F. M. (2000). From Value-at-Risk to stress testing: The extreme value approach. Journal of Banking & Finance 24:1097--1130.

Marimoutou, V., B. Raggad, and A. Trabelsi. (2009). Extreme Value Theory and Value-at-Risk: Application to oil market. Energy Economics 31:519--530.

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

Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica 59:347.

Pickands, J.III, (1975). Statistical Inference Using Extreme Order Statistics. The Annals of Statistics 3:119–131.

Poon, S.-H., and C. W. J. Granger. (2002). Forecasting Volatility in Financial Markets: A Review (revised edition). SSRN Journal.

Smith, R. L. (2002). Measuring Risk with Extreme Value Theory. Value-at-Risk and Beyond:224--246.

Theodossiou, P. (2015). Skewed Generalized Error Distribution of Financial Assets and Option Pricing. MFJ 19:223–266.