We examine the spillovers between green bond (GB), oil, and US and European stock markets during different volatility regimes. Using MS-VAR and the spillover index models, we show that all markets are affected by their own shocks, mainly during high-volatility regime. The transition from low (high) to high (low) regime is more persistent in US (Europe). GB and oil (US stock market) shift from net contributors (receivers) during low-volatility regime to net receivers (contributors) of spillovers during high-volatility regime. For European case, the ability to transmit risk increases for GB and stoxx600 index at high regime. Implications for portfolio management are analyzed.