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

Thabani Ndlovu () and Delson Chikobvu
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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

Risks, 2023, vol. 11, issue 6, 1-16

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.

Keywords: BitCoin; cryptocurrency; Extreme Value Theory; Generalised Pareto Distribution; exchange rates; rand (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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