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.

REFERENCES

Acereda, B., Leon, A., Mora, J., (2020). Estimating the expected shortfall of cryptocurrencies: An evaluation based on backtesting. Finance Research Letters, 33, 101181.

Alexander, C., Sarabia, J. M., (2012). Quantile uncertainty and Value-at-Risk model risk. Risk Anal. Int. J., 32 (8), pp. 1293–1308.

Argyropoulos, Ch., Panopoulou, E., (2019). Backtesting VaR and ES under the magnifying glass. International Review of Financial Analysis, 64, pp. 22–37.

Artzner, P., Delbaen, F., Eber, J. M., Heath, D., (1999). Coherent Measures of Risk, Mathematical Finance, Vol. 9(3), pp. 203–228.

Bu, D., Liao, Y., Shi, J., Peng, H., (2019). Dynamic expected shortfall: A spectral decomposition of tail risk across time horizons. Journal of Economic Dynamics & Control, 108, 103753.

Cheng, W-H., Hung, J-C., (2011). Skewness and leptokurtosis in GARCH-typed VaR estimation of petroleum and metal asset returns. Journal of Empirical Finance, 18, pp. 160–173.

Cheung, K. C., Yuen F. L., (2020). On the uncertainty of VaR of individual risk. Journal of Computational and Applied Mathematics, 367, 112468.

Clift, S. S., Costanzino, N., Curran, M., (2016). Empirical Performance of Backtesting Methods for Expected Shortfall, http://dx.doi.org/10.2139/ssrn.2618345.

Daníelsson, J., Jorgensen, B. N., Samorodnitsky, G., Sarma, M., de Vries, C. G., (2013). Fat tails, VaR and subadditivity. Journal of Econometrics, 172, pp. 283–291.

Del Brio, E. B., Mora-Valencia, A., Perote, J., (2020). Risk quantification for commodity ETFs: Backtesting Value-at-Risk and Expected Shortfall. International Review of Financial Analysis, 70, 101163.

Ding, Z., Granger, C. W. J., Engle, R. F., (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1, pp. 83–106.

Doman, M., Doman, R., (2009). Modelowanie zmienności i ryzyka. Metody ekonometrii finansowej, Wolters Kluwer Polska, Kraków.

Dowd, K., (1999). Beyond Value at Risk: The New Science of Risk Management, John Wiley & Sons, Chichester.

Eling, M., (2014). Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?. Insurance: Mathematics and Economics, 59, pp. 45–56.

Elsayed, A. H., Gozgor, G., Yarovaya, L., (2022). Volatility and return connectedness of cryptocurrency, gold, and uncertainty: Evidence from the cryptocurrency uncertainty indices. Finance Research Letters, 47, 102732.

Fałdziński, M., (2014). Teoría wartości ekstremalnych w ekonometrii finansowej. Wydawnictwo Naukowe Uniwersytetu Mikołaja Kopernika w Toruniu, Toruń.

Fernandez-Perez, A., Frijns, B., Fuertes, A-M., Miffre J., (2018). The skewness of commodity futures returns. Journal of Banking and Finance, 86, pp. 143–158.

Fiszeder, P., Fałdziński, M., Molnár, P., (2019). Range-Based DCC Models for Covariance and Value-at-Risk Forecasting. Journal of Empirical Finance, 54, pp. 58–76

Gumbel, E. J., (2004). Statistics of Extremes. Dover Publications, Inc, Mineola, New York.

Hill, B. M., (1975). A simple general approach to inference about the tail of the distribution. The Annals of Statistics, 3(5), pp. 1163–1174.

Huang, C. K., Huang, C. S., Chikobvu, D., Chinhamu, K., (2015). Extreme risk, Valueat- Risk and Expected Shortfall in the gold market. Int. Bus. Econ. Res. J., 14(1), pp. 91–107.

Jajuga, K., (2008). Zarządzanie ryzykiem. Polskie Wydawnictwo Naukowe PWN, Warszawa.

Jalal, A., Rockinger, M., (2018). Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data. Journal of Empirical Finance, 15, pp. 868–877.

Jorion, P., (2001). Value-at-Risk, The New Benchmark for Managing Financial Risk, 2nd Edition, McGraw-Hill, New York.

Li, X., Guo Q., Liang Ch., Umar M., (2022). Forecasting gold volatility with geopolitical risk indices. Research in International Business and Finance, 64, 101857.

Kayla, P., Maheswaran, S., (2021). A study of excess volatility of gold and silver. IIMB Management Review, 33, pp. 133–145.

Kratz, M., Lok, Y. H., McNeil, A. J., (2018). Multinomial VaR backtests: A simple implicit approach to backtesting expected shortfall. Journal of Banking and Finance, 88, pp. 393–407.

Lazar, E., Zhang, N., (2019). Model risk of expected shortfall. Journal of Banking and Finance, 105, pp. 74–93.

McNeil, A., Frey R., (2000): Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Journal of Empirical Finance, 7, pp. 271–300.

Mensi, V., Vinh, Vo X., Hoon Kang, S., (2022). COVID-19 pandemic’s impact on intraday volatility spillover between oil, gold, and stock markets. Economic Analysis and Policy, 74, pp. 702–715.

Morales, L., Andreosso-O’Callaghan, B., (2011). Comparative analysis on the effects of the Asian and global financial crises on precious metal markets. Research in International Business and Finance, 25(2), pp. 203–227.

Naeem, M., Tiwari, A. K., Mubashra, S., Shahbaz, M., (2019). Modeling volatility of precious metals markets by using regime-switching GARCH models. Resources Policy, 64, 101497.

Righi M. B., Ceretta P. S., (2015). A comparison of Expected Shortfall estimation models. Journal of Economics and Business, 78, pp. 14–47.

Trzpiot, G., (2004). O wybranych własnościach miar ryzyka. Badania Operacyjne i Decyzje, no. 3-4, pp. 91–98.

Walid, C., Shawkat, H., Khuong, N. D., (2014). Volatility forecasting and risk management for commodity markets in the presence of asymmetry and long memory. Energy Econ., 41, pp. 1–18.

Włodarczyk, B., (2017). Prognozowanie zmienności stóp zwrotu na rynkach złota i srebra z uwzględnieniem efektu asymetrii i długiej pamięci. Studia i Prace WNEiZ US, no. 50, T. 1, pp. 231–247.

Vidal, A., Kristjanpoller, W., (2020). Gold volatility prediction using a CNN-LSTM approach. Expert Systems with Applications, 157, 113481.

Yu, W., Yang, K., Wei, Y., Lei, L., (2018). Measuring Value-at-Risk and Expected Shortfall of crude oil portfolio using extreme value theory and vine copula. Physica A, 490, pp. 1423–1433.

Zijing, Z., Zhang, H. K., (2016). The dynamics of precious metal markets VaR: A GARCH-EVT approach. Journal of Commodity Markets, 4, pp. 14–27.