A very important area where COVID-19 has seriously disrupted is the global financial markets, where stock markets have experienced great turmoil. To shed light on the nature of this turmoil and to characterize nonlinear dynamics in inter-market risk transmission, we formally test the existence of inter-stock market contagion, identify the main channel once the presence of contagion has been established, and assess the upside and downside risk spillovers dynamically focusing on complexity during pre-COVID-19 and post-COVID-19 periods. Applying multiple measures including time-varying conditional value-at-risk based on copula theory, and sample entropy methods, considering a sample covering seven countries (USA, UK, France, Germany, Japan, Brazil, China) during the period from 4 January 2019 to 30 December 2020, we show that contagion is widely present among analysed stock markets with only a few exceptions and that "portfolio rebalancing" as opposed to "wealth constraint" occurs more as the main channel of transmission. All market pairings exhibit significant bilateral upside and downside spillovers after the outbreak of COVID-19. A significant shift in complexity of risk spillover dynamics is evident for most recipient countries following the shock of COVID-19, among which all but China display a downward shift. The findings of this paper could help regulators, politicians, and portfolio risk managers amid the uncertainty created by the COVID-19 pandemic.
