We develop a spatial model of climate risks when goods markets across regions are economically integrated but firms can only insure against local climate shocks. We show that firms' insurance demands across regions can be strategic complements or substitutes depending on the correlation of climate shocks across regions. Strategic complementarity can result in equilibrium multiplicity when regions are highly integrated, leading to underinsurance traps. Underinsurance can persist even at actuarially fair insurance premiums and can be Pareto dominated by an economy without insurance markets. We show that insurance market collapse in one region creates contagion effects, potentially contracting insurance markets in other regions. Insurance subsidies can paradoxically worsen the underinsurance problem.