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.

Studies on the economic development of government units are among the key challenges for authorities at different levels and an issue often investigated by economists. In spite of a considerable interest in the issue, there is no standard procedure for the assessment of economic development level of units at different levels of government (national, regional, sub-regional). This assessment needs a complex system of methods and techniques applicable to the various types of data. So, adequate methods must be used at each level. This paper proposes a complex procedure for a synthetic indicator. The units are assessed at different government levels. Each level (national, regional, and sub-regional) may be described with a particular type of variables. Set of data may include variables with a normal or near-normal distribution, a strong asymmetry or extreme values. The objective of this paper is to present the potential behind the application of a complex Multi-Criteria Decision Making (MCDM) procedure based on the tail selection method used in the Extreme Value Theory (EVT), i.e., Mean Excess Function (MEF) together with one of the most popular MCDM methods, namely the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), to assess the economic development level of units at different government levels. MEF is helpful to identify extreme values of variables and limit their impact on the ranking of local administrative units (LAUs). TOPSIS is suitable in ranking units described with multidimensional data set. The study explored the use of two types of TOPSIS (classical and positional) depending on the type of variables. These approaches were used in the assessment of economic development level of LAUs at national, regional and sub-regional levels in Poland in 2017.

The dynamic development of commodity derivatives markets has been observed since the mid-2000s. It is related to the development of e-commerce, the inflow of financial investors’ capital, and the emergence of exchange-traded funds and passively managed index funds focused on commodities. These advances are accompanied by changes in dependence structure in the markets. The main purpose of this study is to assess the conditional dependence structure in various commodity futures markets (energy, metals, grains and oilseeds, soft commodities, agricultural commodities) in the period from the beginning of 2000 to the end of 2018. The specific purpose is to identify the states of the market corresponding to typical patterns of the conditional dependency structure, and to determine the time of transition from one state to another. The copula-based Multivariate Generalized Autoregressive Conditional Heteroskedasticity models were used to describe the dynamics of dependencies between the rates of return on prices of commodity futures, while the dynamic Kendall’s tau correlation coefficients were applied to measure the strength of dependencies. The daily changes in the conditional dependence structure in the markets (changes in states of the markets) were identified with the fuzzy c-means clustering method. In 2000–2018, the conditional dependence structure in commodity futures markets was not stable, as evidenced by the different states of markets identified (two states in the grains and oilseeds market, the agricultural market, the soft commodities market and the metals market, and three states in the energy market).

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.