Quintile regression based approach for dynamical VaR and CVaR forecasting using metalog distribution





VaR, CVaR, Expected Shortfall, dynamic risk measures, forecast, Quantile LGARCH model, metalog distribution


The paper proposes a new method of dynamic VaR and CVaR (ES) risk measures forecasting. Quantile linear GARCH model is chosen as the main forecasting model for time series quantiles. To build a forecast, the values of quantiles are approximated by the metalog distribution, which makes it possible to use analytical formulas to evaluate risk measures. The method of VaR and CVaR forecasting is formulated as a step-by-step algorithm. At the first stage, an initial model is built to obtain variance estimates. The predicted variance values obtained from the constructed model are used at the second stage to find the QLGARCH model coefficients by solving the minimization problem. At the third stage, the QLGARCH models are estimated on a non uniform quantile grid. The obtained predicted values of quantiles are used to estimate the approximating metalog distribution. The investigated theory is applied to VaR and CVaR forecasting for time series of daily log return of the DJI index.

Author Biographies

Grigoriy Zrazhevsky, Taras Shevchenko National University of Kyiv, Kyiv

Grigoriy M. Zrazhevsky, Candidate of Physical and Mathematical Sciences (Ph.D.), an associate professor at the Department of Theoretical and Applied Mechanics of the Faculty of Mechanics and Mathematics of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

Vira Zrazhevska, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Vira F. Zrazhevska, Candidate of Physical and Mathematical Sciences (Ph.D.), an associate professor at the Department of Differential Equations of the Faculty of Physics and Mathematics of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.


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New methods in system analysis, computer science and theory of decision making