Bio-energy has the potential to be a key mitigation option if combined with carbon capture and sequestration (BECCS) because it generates electricity and absorbs emissions at the same time. However, biomass is not distributed evenly across the globe, and regions with a potentially high demand might be constrained by limited domestic supply. Therefore, climate mitigation policies might create the incentive to trade biomass internationally. This paper uses scenarios generated by the integrated assessment model WITCH to study trade of woody biomass from multiple perspectives: the volume of biomass traded, its value, the impact on other power generation technologies and on marginal abatement costs. The policy scenarios consist of three representative carbon tax policies (4.8 W/m2, 3.8 W/m2 and 3.2 W/m2 radiative forcing in 2100) and a cap-and-trade scheme (3.8 W/m2 in 2100). Results show that the incentive to trade biomass is high: at least 50% of biomass consumed globally is from the international market. Regions trade 13-69 EJ/yr of woody biomass in 2050 and 55-81 EJ/yr in 2100. In 2100 the value of biomass traded is equal to US$ 0.7-7.2 Trillion. Trade of woody biomass sensibly reduces marginal abatement costs. In the tax scenarios, abatement increases by 120-323 Gt CO2 over the century. In the cap-and-trade scenario biomass trade reduces the price of emission allowances by 34% in 2100 and cumulative discounted policy costs by 14%.