We study price connectedness between the green bond and financial markets using a structural vector autoregressive (VAR) model that captures direct and indirect transmission of financial shocks across markets. Using heteroskedasticity to identify the structural VAR model parameters, our empirical findings reveal that the green bond market is closely linked to the fixed-income and currency markets , receiving sizeable price spillovers from those markets and transmitting negligible reverse effects. We also show that, in contrast, the green bond market is weakly tied to the stock, energy and high-yield corporate bond markets. These findings have implications in terms of portfolio and risk management decisions for environmentally aware investors holding positions in green bonds.