Contagion risk refers to the propagation of shocks originating in a specific economic sector (or country) to other sectors or regions. During periods of crisis, this risk tends to intensify, such that a localized adverse event can generate significant losses throughout the system. Traditionally, contagion has been measured through intersectoral dependence, usually assessed using correlations. However, although correlations capture the intensity of dependence, they present important limitations, particularly their symmetry, which prevents the identification of contagion direction. To overcome these limitations, this study proposes a robust approach to identify and measure contagion risk by combining asymmetric dependence measures, causal inference via vine copulas, and wavelet coherence analysis. This combination allows for the following: (i) capturing nonlinear coherences through the flexibility of vine copulas; (ii) incorporating causal and temporal relationships into contagion dynamics; (iii) measuring contagion intensity while removing dependence symmetry; and (iv) analyzing contagion direction across multiple time scales. The methodology was applied to intraday data from various segments of the U.S. economy between 2005 and 2025, focusing on the interactions between the banking and insurance sectors, which are central to the propagation of financial shocks. The results indicate that the banking sector tends to transmit long-term shocks to the insurance sector during crises, whereas in stable periods, both sectors jointly absorb shocks from other parts of the system. In the short term, both sectors respond to shocks originating in areas directly associated with the epicenters of crises, such as the real estate sector during the subprime crisis and the pharmaceutical sector during the COVID-19 pandemic.