Partial Differential Equations for pricing in Carbon markets

In this thesis we present a numerical pricing method for allowance certificates in the European Union Emissions Trading Scheme (EU ETS). The presented approach lies in-between an equilibrium model that are already widely used in this field and a simplistic risk-neutral model. Using an exogenously stated demand process for a polluting good, it gives a causal explanation for the accumulation of CO2 emissions and takes into account the feedback effect from the cost of carbon to the rate at which the market emits CO2. We develop a Forward-Backward Stochastic Differential Equation (FBSDE) and numerically present a Crank-Nicolson approximation scheme for the associated semilinear Partial Differential Equation (PDE) for the price of the allowance certificate while also showing that the derivatives specified on the allowance certificate satisfy a linear Partial Differential Equation.