Volatility and models based on the extreme value theory for gold returns

Dominik Krężołek; Krzysztof Piontek

doi:https://doi.org/10.59170/stattrans-2024-012

Volatility and models based on the extreme value theory for gold returns

Dominik Krężołek University of Economics in Katowice, Poland ORCID:https://orcid.org/0000-0002-4333-9405 , Krzysztof Piontek Wroclaw University of Economics and Business, Poland ORCID: https://orcid.org/0000-0001-9197-561X Statistics in Transition new series, vol. 25, 2024, 2, pages: 1-22 Published online: 5 June 2024 https://doi.org/10.59170/stattrans-2024-012 Citation: Krężołek, D., Piontek, K., 2024. Volatility and models based on the extreme value theory for gold returns. Statistics in Transition new series, 25(2), pp. 1-22. https://doi.org/10.59170/stattrans-2024-012

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ABSTRACT

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.

KEYWORDS

expected shortfall, volatility models, EVT, gold returns, backtesting.

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