Abstract
The work is devoted to the development of methods for dynamic risk measures VaR and CVaR estimating. As a basic model, a heteroscedastic time series model is considered. The methods proposed in the article are designed for obtaining the forecast estimates of risk measures for volatile time series taking into account the long-range dependence presence. The method of smoothing of the autocorrelation function based on an optimization procedure is used for variance modeling. A metalog distribution is proposed to use for risk measures model residuals estimating. This distribution allows to describe the behavior of the tail part of the distribution with different characteristics. The paper proposes two methods of metalog distribution estimating. The first method is based on an empirical distribution function and the second one on its approximation by sample quantiles. For VaR and CVaR modeling and forecasting, explicit analytical formulas were obtained with different number of members of the metalog distribution. The procedure for obtaining the forecast values of dynamic risk measures VaR and CVaR is formulated as an algorithm. The proposed approach is applied to the time series of the Russian Trading System index for the period 14/10/2005–10/02/2020. For comparison, the forecast of dynamic risk measures is built using well known methods of risk estimation based on the GEV distribution, GPD and historical modeling. Quantitative and qualitative analyzes of the obtained estimates confirmed the high quality of the obtained estimates.
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References
Acerbi, C., Tasche, D.: Expected shortfall: a natural coherent alternative to value at risk. Econ. Notes 31(2), 379–388 (2002). https://doi.org/10.1111/1468-0300.00091
Chrisman, L.: Estimating US Deaths from COVID-19 Coronavirus in 2020 (2020). https://lumina.com/estimating-us-deaths-from-covid-19-coronavirus-in-2020
Echaust, K., Just, M.: Value at risk estimation using the GARCH-EVT approach with optimal tail selection. Mathematics 8(1), 114 (2020). https://doi.org/10.3390/math8010114
Keelin, T.W.: The metalog distributions. Decis. Anal. 13(4), 223–293 (2016). https://doi.org/10.1287/deca.2016.0338
Khokhlov, V.: Conditional value-at-risk for uncommon distributions. SSRN Electron. J. (2018). https://doi.org/10.2139/ssrn.3200629, https://ssrn.com/abstract=3200629
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts Techniques and Tools. Princeton University Press, Princeton (2005)
Norton, M., Khokhlov, V., Uryasev, S.: Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation. Ann. Oper. Res. pp. 1–35 (2019). https://doi.org/10.1007/s10479-019-03373-1
Omari, C., Mwita, P., Waititu, A.: Using conditional extreme value theory to estimate value-at-risk for daily currency exchange rates. J. Math. Finan. 7(4), 846–870 (2017). https://doi.org/10.4236/jmf.2017.74045
Osei, J., Sarpong, P., Amoako, S.: Comparing historical simulation and Monte Carlo simulation in calculating var. Dama Int. J. Res. 3(6), 22–35 (2018)
Pankratova, N.D., Zrazhevskaja, N.G.: Method of dynamic VaR and CVaR risk measures forecasting for long range dependent time series on the base of the heteroscedastic model. Intell. Control Autom. J. 8(2), 126–138 (2017). https://doi.org/10.4236/ica.2017.82010
Pratiwi, N., Iswahyudi, C., Safitri, R.: Generalized extreme value distribution for value at risk analysis on gold price. J. Phys: Conf. Ser. 1217, 012090 (2019). https://doi.org/10.1088/1742-6596/1217/1/012090
Tabasi, H., Yousefi, V., Tamosaitiene, J., Ghasemi, F.: Estimating conditional value at risk in the Tehran stock exchange based on the extreme value theory using Garch models. Adm. Sci. 9(2), 40 (2019)
Zrazhevska, N.: Construction and application of the classification scheme of dynamic risk measures estimating. Eureka: Phys. Eng. 5, 67–80 (2016). https://doi.org/10.21303/2461-4262.2016.00162
Zrazhevskaja, N.G., Zrazhevskij, A.G.: Classification of methods for risk measures VaR and CVaR calculation and estimation. Syst. Res. Inf. Technol. 3, 118–125 (2016). https://doi.org/10.20535/SRIT.2308-8893.2016.3.11
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Zrazhevska, V., Zrazhevsky, G. (2021). Generalized Approach for Estimatingand Forecasting of Dynamical VaRand CVaR Based on Metalog Distribution. In: Babichev, S., Lytvynenko, V., Wójcik, W., Vyshemyrskaya, S. (eds) Lecture Notes in Computational Intelligence and Decision Making. ISDMCI 2020. Advances in Intelligent Systems and Computing, vol 1246. Springer, Cham. https://doi.org/10.1007/978-3-030-54215-3_15
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