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Purpose The purpose of this paper is to examine the dependence structure between the US conventional stock market and each Islamic and conventional stock market provided by the Dow Jones index, namely, for the UK, Canada, Europe, the emerging countries and Asia-Pacific. This paper considers both the bearish and bullish market phases of the 2008 global financial crisis to analyze the financial contagion. Design/methodology/approach The authors implement the copula framework-based GJR-GARCH-t model for the period from December 31, 2004 to September 30, 2016. Findings The marginal models suggest a strong persistence of volatility in all stock markets. The dependence structure for stock market pairs under-consideration is not all strictly symmetrical. Moreover, the Islamic stock markets witness the same behavior as their conventional counterparts. Finally, the resilience and the decoupling hypotheses are not all around upheld by the empirical proof. Originality/value The findings of this paper are very important for global investors in their risk management during extreme market events. As the Sukuk is considered as a safe haven during crisis episodes, the investors are invited to take it into account for further portfolio diversification.

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