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  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.    

This rapid propagation of the Novel Coronavirus Disease (COVID-19) has caused the global healthcare system to break down. The infectious disease originated from East Asia and spread to the world. This unprecedented pandemic further damages the global economy. It seems highly probable that the COVID-19 recession changes stock market volatility. Therefore, this study resorts to the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model with a smooth transition method to capture the influences of the COVID-19 pandemic on the dynamic structure of the stock market index volatilities for some Asian countries (the Four Asian Tigers and Japan). The empirical results show that the shocks of the COVID-19 change the dynamic volatility structure for all stock market indices. Moreover, we acquire the transition function for all stock market index volatilities and find out that most of their regime adjustment processes start following the outbreak of the COVID-19 pandemic in the Four Asian Tigers except South Korea and Japan. Additionally, the estimated transition functions show that the stock market index volatilities contain U-shaped patterns of structural changes. This article also computes the corresponding calendar dates of structure change about dynamic volatility patterns. In the light of estimation of location parameters, we demonstrate that the structure changing the date of stock market index volatility for South Korea and Japan has occurred in late 2019.