The asymmetric contagion effect between stock market and cryptocurrency market

•We examine asymmetric contagion effects between stock markets and cryptocurrency markets.•The time-varying symmetrized Joe-Clayton copula GARCH model and nonlinear Granger causality test are used for studying.•We identify a time-varying tail dependence.•We find that the lower tail dependences are more significant than the upper ones.•We find the existence of asymmetric contagion effect between these two markets.