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This paper investigates the impact of COVID-19 on financial markets. Itfocuses on the evolution of the market efficiency, using two efficiencyindicators: the Hurst exponent and the memory parameter of a fractionalL\'evy-stable motion. The second approach combines, in the same model ofdynamic, an alpha-stable distribution and a dependence structure between pricereturns. We provide a dynamic estimation method for the two efficiencyindicators. This method introduces a free parameter, the discount factor, whichwe select so as to get the best alpha-stable density forecasts for observedprice returns. The application to stock indices during the COVID-19 crisisshows a strong loss of efficiency for US indices. On the opposite, Asian andAustralian indices seem less affected and the inefficiency of these marketsduring the COVID-19 crisis is even questionable.

Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics