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Since the inception of Bitcoin in 2008, cryptocurrencies have played anincreasing role in the world of e-commerce, but the recent turbulence in thecryptocurrency market in 2018 has raised some concerns about their stabilityand associated risks. For investors, it is crucial to uncover the dependencerelationships between cryptocurrencies for a more resilient portfoliodiversification. Moreover, the stochastic behavior in both tails is important,as long positions are sensitive to a decrease in prices (lower tail), whileshort positions are sensitive to an increase in prices (upper tail). In orderto assess both risk types, we develop in this paper a flexible copula modelwhich is able to distinctively capture asymptotic dependence or independence inits lower and upper tails simultaneously. Our proposed model is parsimoniousand smoothly bridges (in each tail) both extremal dependence classes in theinterior of the parameter space. Inference is performed using a full orcensored likelihood approach, and we investigate by simulation the estimators'efficiency under three different censoring schemes which reduce the impact ofnon-extreme observations. We also develop a local likelihood approach tocapture the temporal dynamics of extremal dependence among two leadingcryptocurrencies. We here apply our model to historical closing prices of fiveleading cryotocurrencies, which share most of the cryptocurrency marketcapitalizations. The results show that our proposed copula model outperformsalternative copula models and that the lower tail dependence level between mostpairs of leading cryptocurrencies -- and in particular Bitcoin and Ethereum --has become stronger over time, smoothly transitioning from an asymptoticindependence regime to an asymptotic dependence regime in recent years, whilstthe upper tail has been relatively more stable overall at a weaker dependencelevel.

Asymmetric tail dependence modeling, with application to cryptocurrency market data