A conditional Extreme Value Theory (GARCH-EVT) approach is a two-stage hybrid method that combines a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) filter with the Extreme Value Theory (EVT). The approach requires pre-specification of a threshold separating distribution tails from its middle part. The appropriate choice of a threshold level is a demanding task. In this paper we use four different optimal tail selection algorithms, i.e., the path stability method, the automated Eye-Ball method, the minimization of asymptotic mean squared error method and the distance metric method with a mean absolute penalty function, to estimate out-of-sample Value at Risk (VaR) forecasts and compare them to the fixed threshold approach. Unlike other studies, we update the optimal fraction of the tail for each rolling window of the returns. The research objective is to verify to what extent optimization procedures can improve VaR estimates compared to the fixed threshold approach. Results are presented for a long and a short position applying 10 world stock indices in the period from 2000 to June 2019. Although each approach generates different threshold levels, the GARCH-EVT model produces similar Value at Risk estimates. Therefore, no improvement of VaR accuracy may be observed relative to the conservative approach taking the 95th quantile of returns as a threshold.

This study investigates the dependence between extreme returns of West Texas Intermediate (WTI) crude oil prices and the Crude Oil Volatility Index (OVX) changes as well as the predictive power of OVX to generate accurate Value at Risk (VaR) forecasts for crude oil. We focus on the COVID-19 pandemic period as the most violate in the history of the oil market. The static and dynamic conditional copula methodology is used to measure the tail dependence coefficient (TDC) between the variables. We found a strong relationship in the tail dependence between negative returns on crude oil and OVX changes and the tail independence for positive returns. The time-varying copula discloses the strongest tail dependence of negative oil price shocks and the index changes during the COVID-19 health crisis. The findings indicate the ability of the OVX index to be a fear gauge with respect to the oil market. However, we cannot confirm the ability of OVX to improve one day-ahead forecasts of the Value at Risk. The impact of investors’ expectations embedded in OVX on VaR forecasts seems to be negligible.

The aim of the paper is to examine commonality in liquidity indices across emerging European stock markets. Five markets are included in the study: Hungarian, Czech, Polish, Russian and Turkish, in the period from 2008 to 2017. We propose liquidity indices that are based on low-frequency liquidity proxies and capture both the dynamics coming from volume and price changes. We find strong commonality of the liquidity indices across all examined markets which is robust to the choice of liquidity proxy. The dependence between indices enhances in times of crisis and large market declines, and weakens when markets become stable. We also examine the interdependency between liquidity and volatility estimates and find that liquidity on the European emerging markets is related to CBOE Volatility Index (VIX). Liquidity in the whole region decreases when VIX increases, and vice versa. The liquidity indices based on the extreme market movements show that there are no differences in commonality in time of extreme negative and positive returns.