Open AccessQuintile regression based approach for dynamical VaR and CVaR forecasting using metalog distribution
Author(s) -
Grigoriy Zrazhevsky,
V. F. Zrazhevska
Publication year - 2021
Publication title -
sistemnì doslìdžennâ ta ìnformacìjnì tehnologìï
Language(s) - English
Resource type - Journals
eISSN - 2308-8893
pISSN - 1681-6048
DOI - 10.20535/srit.2308-8893.2021.1.12
Subject(s) - cvar , quantile , econometrics , mathematics , quantile regression , variance (accounting) , autoregressive conditional heteroskedasticity , series (stratigraphy) , statistics , expected shortfall , economics , risk management , management , accounting , biology , volatility (finance) , paleontology
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.