To investigate the contagion characteristics of different types of risks in equity markets during major global events, this paper develops a dynamic jump-diffusion two-factor cross-feedback model to decompose the market variance into continuous volatility and discontinuous jump risks. This study conducts the nonlinear Granger causality test to identify the existence of risk contagion and implement the network topology method to quantify the specific degree of volatility spillover and jump risk transmission. The proposed econometric framework allows us to map the contagion network of volatility and jump risks during specific global shocks. The empirical results show that the U.S. and European markets remain the primary risk exporters globally, while the Chinese market acts as a major risk receiver, it also demonstrates persistent volatility spillover and limited jump propagation to other global markets. Furthermore, there is a stronger degree of jump propagation but with shorter duration during unexpected and severe global shocks compared to volatility spillover. Furthermore, the same event exhibits distinct features across different geographical locations, such as the COVID-19 pandemic, where the U.S. exerted significantly risk spillover to China in a unidirectional manner. This study advances the understanding of risk contagion mechanisms between markets and provides theoretical and empirical insights for policymakers to lay out effective regulatory strategies for different risks.