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The Generalised Pareto Distribution Model Approach to Comparing Extreme Risk in the Exchange Rate Risk of BitCoin/US Dollar and South African Rand/US Dollar Returns

Author

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  • Thabani Ndlovu

    (Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein 9300, South Africa)

  • Delson Chikobvu

    (Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein 9300, South Africa)

Abstract

Cryptocurrencies are said to be very risky, and so are the currencies of emerging economies, including the South African rand. The steady rise in the movement of South Africans’ investments between the rand and BitCoin warrants an investigation as to which of the two currencies is riskier. In this paper, the Generalised Pareto Distribution (GPD) model is employed to estimate the Value at Risk (VaR) and the Expected Shortfall (ES) for the two exchange rates, BitCoin/US dollar (BitCoin) and the South African rand/US dollar (ZAR/USD). The estimated risk measures are used to compare the riskiness of the two exchange rates. The Maximum Likelihood Estimation (MLE) method is used to find the optimal parameters of the GPD model. The higher extreme value index estimate associated with the BTC/USD when compared with the ZAR/USD estimate, suggests that the BTC/USD is riskier than the ZAR/USD. The computed VaR estimates for losses of $0.07, $0.09, and $0.16 per dollar invested in the BTC/USD at 90%, 95%, and 99% compared to the ZAR/USD’s $0.02, $0.02, and $0.03 at the respective levels of significance, confirm that BitCoin is riskier than the rand. The ES (average losses) of $0.11, $0.13, and $0.21 per dollar invested in the BTC/USD at 90%, 95%, and 99% compared to the ZAR/USD’s $0.02, $0.02, and $0.03 at the respective levels of significance further confirm the higher risk associated with BitCoin. Model adequacy is confirmed using the Kupiec test procedure. These findings are helpful to risk managers when making adequate risk-based capital requirements more rational between the two currencies. The argument is for more capital requirements for BitCoin than for the South African rand.

Suggested Citation

  • Thabani Ndlovu & Delson Chikobvu, 2023. "The Generalised Pareto Distribution Model Approach to Comparing Extreme Risk in the Exchange Rate Risk of BitCoin/US Dollar and South African Rand/US Dollar Returns," Risks, MDPI, vol. 11(6), pages 1-16, May.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:6:p:100-:d:1160157
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    References listed on IDEAS

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    1. Mohamed Ibrahim & Walid Emam & Yusra Tashkandy & M. Masoom Ali & Haitham M. Yousof, 2023. "Bayesian and Non-Bayesian Risk Analysis and Assessment under Left-Skewed Insurance Data and a Novel Compound Reciprocal Rayleigh Extension," Mathematics, MDPI, vol. 11(7), pages 1-26, March.
    2. Bouri, Elie & Molnár, Peter & Azzi, Georges & Roubaud, David & Hagfors, Lars Ivar, 2017. "On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier?," Finance Research Letters, Elsevier, vol. 20(C), pages 192-198.
    3. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    4. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
    5. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    6. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    7. Delson Chikobvu & Thabani Ndlovu, 2023. "The Generalised Extreme Value Distribution Approach to Comparing the Riskiness of BitCoin/US Dollar and South African Rand/US Dollar Returns," JRFM, MDPI, vol. 16(4), pages 1-16, April.
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