  Since the inception of Bitcoin in 2008, cryptocurrencies have played an
increasing role in the world of e-commerce, but the recent turbulence in the
cryptocurrency market in 2018 has raised some concerns about their stability
and associated risks. For investors, it is crucial to uncover the dependence
relationships between cryptocurrencies for a more resilient portfolio
diversification. Moreover, the stochastic behavior in both tails is important,
as long positions are sensitive to a decrease in prices (lower tail), while
short positions are sensitive to an increase in prices (upper tail). In order
to assess both risk types, we develop in this paper a flexible copula model
which is able to distinctively capture asymptotic dependence or independence in
its lower and upper tails simultaneously. Our proposed model is parsimonious
and smoothly bridges (in each tail) both extremal dependence classes in the
interior of the parameter space. Inference is performed using a full or
censored likelihood approach, and we investigate by simulation the estimators'
efficiency under three different censoring schemes which reduce the impact of
non-extreme observations. We also develop a local likelihood approach to
capture the temporal dynamics of extremal dependence among two leading
cryptocurrencies. We here apply our model to historical closing prices of five
leading cryotocurrencies, which share most of the cryptocurrency market
capitalizations. The results show that our proposed copula model outperforms
alternative copula models and that the lower tail dependence level between most
pairs of leading cryptocurrencies -- and in particular Bitcoin and Ethereum --
has become stronger over time, smoothly transitioning from an asymptotic
independence regime to an asymptotic dependence regime in recent years, whilst
the upper tail has been relatively more stable overall at a weaker dependence
level.
