The stable tail dependence and influence among the European stock markets: a score-driven dynamic copula approach

This paper studies the time-varying tail dependence among the European stock markets and assesses the influence of individual financial markets. By utilizing two generalized autoregressive score (GAS) copulas, we compute the tail dependence for 11 European stock indexes and 1 American stock index over the last 16 years. Notably, it is found that the dependencies among European stock indexes are generally stable, even during the crisis periods. Then an influence measure is proposed for each individual market based on the tail dependence. Interestingly, the influence ranking is also stable for both the whole period and two big drawdown days in crisis periods. To be specific, AEX (Netherlands), FCHI (France), and GDAXI (Germany) always show the most significant influences, while SPX (USA) is always the least influential one. Finally, an equal-weighted portfolio is built to measure the systemic risk in the European stock markets. It is found that both patterns of risk (VaR) and expected shortfall (ES) are different from the time-varying tail dependence. There exist obvious inverted spikes on 16 October 2008 and 16 March 2020. The results indicate that the extreme portfolio risk does not come from the increase of dependence among European stock markets, but from the individual jumps.