We present a novel approach to the pricing of financial instruments in emission markets---for example, the European Union Emissions Trading Scheme (EU ETS). The proposed structural model is positioned between existing complex full equilibrium models and pure reduced-form models. Using an exogenously specified demand for a polluting good, it gives a causal explanation for the accumulation of CO$_2$ emissions and takes into account the feedback effect from the cost of carbon to the rate at which the market emits CO$_2$. We derive a forward-backward stochastic differential equation for the price process of the allowance certificate and solve the associated semilinear partial differential equation numerically. We also show that derivatives written on the allowance certificate satisfy a linear partial differential equation. The model is extended to emission markets with multiple compliance periods, and we analyze the impact different intertemporal connecting mechanisms, such as borrowing, banking, and withdrawal, have on the allowance price.

CEMAT - Center for Computational and Stochastic Mathematics