The growing interest in sustainable investment instruments in financial markets necessitates an in-depth examination of the sensitivities these assets exhibit toward risk factors. The aim of this study is to empirically investigate the dependency structure between the green bond index and the global volatility indicators - the VIX (equity market volatility), OVX (oil market volatility), and MOVE (bond market volatility) indices. In the analysis process, the Quantile Coherence approach developed by Baruník and Kley was employed in order to simultaneously evaluate the relationship among the variables both across different frequencies (short and long term) through the implicit components and under different market conditions (bear and bull markets). The findings obtained from the research indicate that, although the dependency between green bond returns and the volatility indices remains generally weak, it exhibits a pronounced heterogeneity and asymmetry depending on frequency and market conditions. Notably, the dependencies with the MOVE index are considerably more pronounced and longer-term compared to those with the VIX and OVX, revealing that risks originating from the broader bond market exert a more persistent and profound influence on the green bond market. In contrast, it is striking that the analyzed imaginary components are generally statistically insignificant. This demonstrates that volatility shocks do not exhibit a delayed transmission to the green bond market, and that the interaction in question occurs largely on a simultaneous (instantaneous) basis. The findings suggest that the green bond market is dynamic, changing with frequency and market conditions in response to external volatility shocks, yet it displays a limited dependency mechanism. In this respect, the study offers implications for investors and policymakers regarding portfolio diversification and risk management.