Highlights It is the first work which focuses on three indicators of the financial market, namely volatility expectations, correlation expectations and illiquidity during the COVID-19 crisis. We examine structural breaks in the stock market returns – implied volatility, stock market returns –implied correlation and stock market returns – market illiquidity relations. We detect a structural break in the relationship between stock returns – correlation expectations preceding by one day the structural break in stock returns – volatility expectations. Italy is recognized as the only one country transmitting fears from the data of COVID-19 cases to global fear gauges related to volatility and correlation. Stock market illiquidity does not affect the stock market returns and does not depend on any COVID-19 official announcements of cases and deaths.

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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.

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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.