Multi-population mortality modelling plays a crucial role in the securitization of longevity risk. For example, the payoff of Swiss Re’s Kortis bond involves the mortality improvements of both the U.S. and U.K. male populations. Capturing the mortality dependence between the two populations is critical for accurate longevity risk pricing. Recently, some researchers investigated the use of copula in modelling mortality dependence, and observed that mortality dependence is stronger during mortality deteriorations than during mortality improvements. In order to capture observed asymmetric dependence, we propose to use a multivariate regime-switching copula. We study how the choice of copula affects the risk profile of a longevity security and examine the impact of asymmetric dependence and regime-switching in pricing the security.