Comparison of Block Maxima and Peaks Over Threshold Value-at-Risk models for market risk in various economic conditions

Szubzda, Filip; Chlebus, Marcin

doi:10.2478/ceej-2019-0005

Abstract

The aim of the presented study was to assess the quality of VaR forecasts in various states of the economic situation. Two approaches based on the extreme value theory were compared: Block Maxima and the Peaks Over Threshold. Forecasts were made on the daily closing prices of 10 major indices in European countries, divided into two groups: emerging countries (Bulgaria, Czech Republic, Lithuania, Latvia, Poland, Slovakia and Hungary) and developed countries (England, France and Germany). Three states of economic situation were analysed: the pre-crisis (2007), the crisis (2008) and the post-crisis (2009) period as out-of-sample. The main conclusion obtained is the too slow process of adapting static EVT-based forecasts to market movements. While in the pre-crisis period the results were satisfactory, in the period of crisis VaR forecasts were too often exceeded.

References

Abad, P., Benito, S., & Lopez, C. (2013). A comprehensive review of value at risk methodologies. The Spanish Review of Financial Economics, 12(1), 15–32.
Search in Google Scholar Back to article
Allen, D., Singh, A., & Powell, R. (2011). Value at Risk estimation using extreme value theory. ECU Publications. Retrieved from http://ro.ecu.edu.au/ecuworks2011/.
Search in Google Scholar Back to article
Alves, M., & Santos, P. (2013). Conditional EVT for VAR estimation: comparison with a new independence test. In J. Lita da Silva (Ed.), Advances in regression, survival analysis, extreme values, Markov processes and other statistical applications (pp. 183–191). Berlin, Germany: Springer.
Search in Google Scholar Back to article
Angelidis, T., Benos, A., & Degiannakis, S. (2007). A robust VAR model under different time periods and weighting schemes. Review of Quantitative Finance and Accounting, 28, 187–201.
Search in Google Scholar Back to article
Artzner, P., Eber, J.-M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203–228.
Search in Google Scholar Back to article
Balkema, A., & de Haan, L. (1974). Residual lifetime at great age. Annals of Probability, 2, 792–804.
Search in Google Scholar Back to article
Bao, Y., Lee, T.-H., & Saltoglu, B. (2006). Evaluating predictive performance of Value-at-Risk models in emerging markets: a reality check. Journal of Forecasting, 25, 101–128.
Search in Google Scholar Back to article
BCBS. (1996). Supervisory framework for the use of ‘backtesting’ in conjuction with the internal models approach to market risk capital requirements. Basel: Basel Committee on Banking Supervision. Retrieved from https://www.bis.org/publ/bcbs22.htm.
Search in Google Scholar Back to article
Bee, M., & Miorelli, F. (2010). Dynamic VaR models and the peaks over threshold method for market risk measurement: an empirical investigation during a financial crisis. Department of Economics Working Papers 1009, Department of Economics, University of Trento, Italia.
Search in Google Scholar Back to article
Bhattacharyya, M., & Ritolia, G. (2008). Conditional VaR using EVT – towards a planned margin scheme. International Review of Financial Analysis, 17, 382–395.
Search in Google Scholar Back to article
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327.
Search in Google Scholar Back to article
Bollerslev, T., Todorov, V., & Li, S. (2013). Jump tails, extreme dependencies, and the distribution of stock returns. Journal of Econometrics, 172(2), 307–324.
Search in Google Scholar Back to article
Bommier, E. (2014). Peaks-over-threshold modelling of environmental data. Retrieved from https://uu.diva-portal.org/smash/get/diva2:760802/FULLTEXT01.pdf.
Search in Google Scholar Back to article
Bystrom, H. (2001). Managing risks in tranquil and volatile markets using conditional extreme value theory. International Review of Financial Analysis, 13(2), 133–152.
Search in Google Scholar Back to article
Caires, S. (2009). A comparative simulation study of the annual Maxima and the peaks-over-threshold methods. “Hydraulic Engineering Reports” (Deltares Report 1200264-002). Retrieved from https://repository.tudelft.nl/islandora/object/uuid:143b0f1e-f61e-44ab-8da3-9241970d915b?collection=research.
Search in Google Scholar Back to article
Caporin, M. (2008). Evaluating Value-at-Risk measures in the presence of long memory conditional volatility. Journal of Risk, 10, 79–110.
Search in Google Scholar Back to article
Chlebus, M. (2014). Market risk measuring using value at risk – two-step approach (PhD thesis), Faculty of Economic Sciences, University of Warsaw.
Search in Google Scholar Back to article
Christoffersen, P. (1998). Evaluating interval forecasting. International Economic Review, 39, 841–862.
Search in Google Scholar Back to article
Darbha, G. (2001). Value-at-Risk for fixed income portfolios – a comparison of alter-native models. Mumbai: National Stock Exchange. Retrieved from https://www.researchgate.net/publication/228607410_Value-at-Risk_for_Fixed_Income_portfolios-A_comparison_of_alternative_models.
Search in Google Scholar Back to article
Da Silva, A., & de Melo Mendes, B. V. (2003). Value-at-Risk and extreme returns in Asian stock markets. International Journal of Business, 8(1), 24.
Search in Google Scholar Back to article
Embrechts, P., Kluppelberg, C., & Mikosch, T. (1997). Modelling extremal events for Insurance and Finance. Springer-Verlag, 295–305.
Search in Google Scholar Back to article
Engle, R. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50, 987–1007.
Search in Google Scholar Back to article
Engle, R., & Patton, A. (2001). What good is a volatility model? Quantitative Finance, Vol. 1, 237–245.
Search in Google Scholar Back to article
Engle, R. F., & Manganelli, S. (2004). CAViaR: conditional autoregressive value at risk by regression quantiles. Journal of Business & Economic Statistics, 22(4), 367–381.
Search in Google Scholar Back to article
Ergun, T., & Jun, J. (2010). Time-varying higher-order conditional moments and forecasting intraday VaR and expected shortfall. The Quarterly Review of Economics and Finance, 50, 264–272.
Search in Google Scholar Back to article
Fisher, R., & Tippett, L. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proceedings of the Cambridge Philosophical Society, 180–190.
Search in Google Scholar Back to article
Flugentiusson, H. (2012). Push it to the limit. Testing the usefulness of extreme value theory in electricity markets. Lund University Publications. Retrieved from http://lup.lub.lu.se/luur/download?-func=downloadFile&recordOId=3166413&file-OId=3166414.
Search in Google Scholar Back to article
Gencay, R., & Selcuk, F. (2004). Extreme value theory and Value-at-Risk: Relative performance in emerging markets. International Journal of Forecasting, 20, 287–303.
Search in Google Scholar Back to article
Gencay, R., Selcuk, F., & Ulugulyagci, A. (2003). High volatility, thick tails and extreme value theory in Value-at-Risk estimation. Insurance: Mathematics and Economics, 33, 337–356.
Search in Google Scholar Back to article
Kourouma, L., Dupre, D., Sanfilippo, G., & Taramasco, O. (2010). Extreme value at risk and expected shortfall during financial crisis. Retrieved from https://ssrn.com/abstract=1744091;doi:10.2139/ssrn.1744091.
Open DOI Search in Google Scholar Back to article
Kupiec, P. (1995). Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives, 3(2), 73–84.
Search in Google Scholar Back to article
Lopez, J. (1999). Methods for evaluating Value-at-Risk estimates. Federal Reserve Bank of San Francisco Economic Review, 2, 3–17.
Search in Google Scholar Back to article
Manganelli, S., & Engle, R. (2001). Value at Risk Models in Finance. ECB Working Paper No. 75, available at SSRN: https://ssrn.com/abstract=356220
Search in Google Scholar Back to article
Marimoutou, V., Raggad, B., & Trabelsi, A. (2009). Extreme value theory and value at risk: application to oil market. Energy Economics, 31, 519–530.
Search in Google Scholar Back to article
Marinelli C., d’Addona S., & Rachev T. (2007). A comparison of some univariate models for Value-at-Risk and expected shortfall. International Journal of Theoretical and Applied Finance, 10(06), 1043–1075.
Search in Google Scholar Back to article
Mutu, S., Balogh, P., & Moldovan, D. (2011). The efficiency of value at risk models on central and eastern European stock markets. International Journal of Mathematics and Computers in Simulation, 5, 110–117.
Search in Google Scholar Back to article
Nozari, M., Raei, S., Jahanguin, P., & Bahramgiri, M. (2010). A comparison of heavy-tailed estimates and filtered historical simulation: evidence from emerging markets. International Review of Business Papers, 6(4), 347–359.
Search in Google Scholar Back to article
Pagan, A. (1996). The econometrics of financial markets. Journal of Empirical Finance, 3, 15–102.
Search in Google Scholar Back to article
Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, 119–131.
Search in Google Scholar Back to article

Comparison of Block Maxima and Peaks Over Threshold Value-at-Risk models for market risk in various economic conditions

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