An analysis of the dependence structure among certain European indices (FTSE100, CAC40, DAX30, ATX20, PX, BUX and BIST) has been conducted. The main features of the financial data were studied: asymmetry, fat-tailedness (leptokurtosis), variability and mutual dependence. We have fitted a regime switching copula based model including asymmetric and fat-tailed copulas. All the indices are left-skewed and fat-tailed. Large indices are more skewed and less fail-tailed. The findings suggest that size of a market has an influence on its properties. A particular behaviour of the Turkish market suggests the importance of geographical factors. It is also suggested that the maturity of a market is insignificant in the analysis. Another important conclusion drawn from our empirical investigation is that VaR is a less exact risk measure than ES. However, the dynamics of the temporal and statistical properties of both measures are similar
In this study, we use daily gold log-returns to analyse the quality of forecasting expected shortfalls (ES) using volatility and models based on the extreme value theory (EVT). ES forecasts were calculated for conditional APARCH models formed on the entire distribution of returns, as well as for EVT models. The results of ES forecasts for each model were verified using the backtesting procedure proposed by Acerbi and Szekely. The results show that EVT models provide more accurate one-day ahead ES forecasts compared to the other models. Moreover, the asymmetric theoretical distributions for innovations of EVT models allow the improvement of the accuracy of ES forecasting.
We investigate the sum of dependent random variables. The dependent structure is modeled by copulas. The risk measures, VaR and ES of such sums, are calculated. We present the lower and upper border of VaR. The examples when the marginals have exponential and Pareto distribution are investigated. The influence of the degree of dependence on the value of VaR of the sum of dependent random variables is analysed.
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