Cryptocurrencies have become increasingly popular in recent years attracting the attention of the media, academia, investors, speculators, regulators, and governments worldwide. This paper focuses on modelling the volatility dynamics of eight most popular cryptocurrencies in terms of their market capitalization for the period starting from 7th August 2015 to 1st August 2018. In particular, we consider the following cryptocurrencies; Bitcoin, Ethereum, Litecoin, Ripple, Moreno, Dash, Stellar and NEM. The GARCH-type models assuming different distributions for the innovations term are fitted to cryptocurrencies data and their adequacy is evaluated using diagnostic tests. The selected optimal GARCH-type models are then used to simulate out-of-sample volatility forecasts which are in turn utilized to estimate the one-day-ahead VaR forecasts. The empirical results demonstrate that the optimal in-sample GARCH-type specifications vary from the selected out-of-sample VaR forecasts models for all cryptocurrencies. Whilst the empirical results do not guarantee a straightforward preference among GARCH-type models, the asymmetric GARCH models with long memory property and heavy-tailed innovations distributions overall perform better for all cryptocurrencies.

The recent global pandemic of coronavirus (COVID-19) has had an enormous impact on the financial markets across the world. It has created an unprecedented level of risk uncertainty, prompting investors to impetuously dispose of their assets leading to significant losses over a very short period. In this paper, the conditional heteroscedastic models and extreme value theory are combined to examine the extreme tail behaviour of stock indices from major economies over the period before and during the COVID-19 pandemic outbreak. Daily returns data of stock market indices from twelve different countries are used in this study. The paper implements a dynamic method for forecasting a one-day ahead Value at Risk. As a first step, a comprehensive in-sample volatility modelling is implemented with skewed Student's-t distribution assumption and their goodness of fit is determined using information selection criteria. In the second step, the VaR quantiles are estimated with the help of conditional Extreme Value Theory framework and then used to estimate the out-of-sample VaR forecasts. Backtesting results suggest that the conditional EVT based models consistently produce a better 1-day VaR performance compared with conditional models with asymmetric probability distributions for return innovations and maybe a better option in the estimation of VaR. This emphasizes the importance of modelling extreme events in stock markets using conditional extreme value theory and shows that the ability of the model to capture volatility clustering accurately is not sufficient for a correct assessment of risk in these markets.