This paper’s analysis was triggered by the outbreak of the new virus COVID-19. In December 2019, the Chinese officials alerted the World Health Organization (WHO) of the existence of an unknown deadly virus. Coronavirus has rapidly spread across the world - to Europe, Middle East and the USA, forcing the World Health Organization to declare COVID-19 a global pandemic. Its spread has generated major concerns for the health and economic sectors. Meanwhile, all countries hope for the development of a vaccine. Using as a research method the EGARCH model, this paper investigates if it can be applied to model the trend of volatility of the pharmaceuticals and biotechnology markets, especially during the health crisis. More specifically, this paper tries to identify whether different specifications of univariate GARCH models can usefully anticipate volatility in the stock indices market. The study uses estimates from both a symmetric and an asymmetric GARCH models, namely GARCH (1, 1) and EGARCH models, for the Dow Jones Pharmaceuticals and Biotechnology index (DJUSPN). The dataset is extracted from “Investing.com” and covers the period September 2019 - August 2020, resulting in a total of approximately 252 daily closing prices. The data focuses on the response of the highest capitalized pharmaceutical and biotechnology companies from the US to combat the outbreak of the coronavirus. This study concludes that the EGARCH model is better than the unconditional volatility and the conditional GARCH (1, 1) volatility and it is best suited for modelling and forecasting the fluctuations of the stock indexes.