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Extreme Value Theory Modelling of the Behaviour of Johannesburg Stock Exchange Financial Market Data

Author

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  • Maashele Kholofelo Metwane

    (Department of Statistics and Operations Research, University of Limpopo, Private Bag X1106, Sovenga 0727, South Africa)

  • Daniel Maposa

    (Department of Statistics and Operations Research, University of Limpopo, Private Bag X1106, Sovenga 0727, South Africa)

Abstract

Financial market data are abundant with outliers, and the search for an appropriate extreme value theory (EVT) approach to apply is an endless debate in the statistics of extremes research. This paper uses EVT methods to model the five-year daily all-share total return index (ALSTRI) and the daily United States dollar (USD) against the South African rand (ZAR) exchange rate of the Johannesburg stock exchange (JSE). The study compares the block maxima approach and the peaks-over-threshold (POT) approach in terms of their ability to model financial market data. The 100-year return levels for the block maxima approach were found to be almost equal to the maximum observations of the financial markets of 10,860 and R18.99 for the ALSTRI and the USD–ZAR, respectively. For the peaks-over-threshold (POT) approach, the results show that the ALSTRI and the USD–ZAR exchange rate will surpass 17,501.63 and R23.72, respectively, at least once in 100 years. The findings in this study reveal a clear distinction between block maxima and POT return level estimates. The POT approach return level estimates were comparably higher than the block maxima estimates. The study further revealed that the blended generalised extreme value (bGEVD) is more suitable for relatively short-term forecasting, since it cuts off at the 50-year return level. Therefore, this study will add value to the literature and knowledge of statistics and econometrics. In the future, more studies on bGEVD, vine copulas, and the r -largest-order bGEVD can be conducted in the financial markets.

Suggested Citation

  • Maashele Kholofelo Metwane & Daniel Maposa, 2023. "Extreme Value Theory Modelling of the Behaviour of Johannesburg Stock Exchange Financial Market Data," IJFS, MDPI, vol. 11(4), pages 1-27, November.
    • Handle: RePEc:gam:jijfss:v:11:y:2023:i:4:p:130-:d:1273741
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    References listed on IDEAS

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    1. Emmanuel Afuecheta & Chigozie Utazi & Edmore Ranganai & Chibuzor Nnanatu, 2023. "An Application of Extreme Value Theory for Measuring Financial Risk in BRICS Economies," Annals of Data Science, Springer, vol. 10(2), pages 251-290, April.
    2. Silius M. Vandeskog & Sara Martino & Daniela Castro-Camilo & Håvard Rue, 2022. "Modelling Sub-daily Precipitation Extremes with the Blended Generalised Extreme Value Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 598-621, December.
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    6. Iyke, Bernard Njindan & Ho, Sin-Yu, 2021. "Exchange rate exposure in the South African stock market before and during the COVID-19 pandemic," Finance Research Letters, Elsevier, vol. 43(C).
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    Cited by:

    1. Aubain Nzokem & Daniel Maposa, 2024. "Fitting the seven-parameter Generalized Tempered Stable distribution to the financial data," Papers 2410.19751, arXiv.org, revised Jan 2025.

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