Generalized approach for estimatingand forecasting of dynamical varand cvar based on metalog distribution

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.