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In the preceding decade, the South African economy has experienced challenges due to global disruptive events, hence, the implementation of risk mitigation strategies becomes a priority in volatile markets. Stable distributions account for skewness and heavy-tailed behaviour which are frequently observed in financial data. This study aims to investigate the fit of stable distributions for three FTSE/JSE indices and the USD/ZAR currency exchange rate. The maximum likelihood method was applied to fit Nolan’s -parameterization stable distribution. Value at Risk (VaR) is measure assessing market risk, therefore, VaR estimates and Kupiec likelihood test are applied to evaluate the extreme tail behaviour of the fitted stable model. Results show the robustness of stable distributions in the long and short position for each daily returns. This research validates the use of stable distributions aimed at capturing the characteristics financial data. Those concerned with curtailing losses and investigating alternatives for financial modeling in the South African financial industry may benefit the most by using stable distributions.

  Risk management and prediction of market losses of cryptocurrencies are of notable value to risk managers, portfolio managers, financial market researchers and academics. One of the most common measures of an asset’s risk is Value-at-Risk (VaR). This paper evaluates and compares the performance of generalized autoregressive score (GAS) combined with heavy-tailed distributions, in estimating the VaR of two well-known cryptocurrencies’ returns, namely Bitcoin returns and Ethereum returns. In this paper, we proposed a VaR model for Bitcoin and Ethereum returns, namely the GAS model combined with the generalized lambda distribution (GLD), referred to as the GAS-GLD model. The relative performance of the GAS-GLD models was compared to the models proposed by Troster et al. (2018), in other words, GAS models combined with asymmetric Laplace distribution (ALD), the asymmetric Student’s t-distribution (AST) and the skew Student’s t-distribution (SSTD). The Kupiec likelihood ratio test was used to assess the adequacy of the proposed models. The principal findings suggest that the GAS models with heavy-tailed innovation distributions are, in fact, appropriate for modelling cryptocurrency returns, with the GAS-GLD being the most adequate for the Bitcoin returns at various VaR levels, and both GAS-SSTD, GAS-ALD and GAS-GLD models being the most appropriate for the Ethereum returns at the VaR levels used in this study.