A fitted finite volume method for real option valuation of risks in climate change

In this paper, we first regard the sea level and the temperature as the underlying assets, and then develop a real option model to evaluate potential sea level rising risk management opportunities. In the case of American real options, we reformulate the problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. It is shown that the nonlinear partial differential equation (PDE) is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O(λ−k2). A so-called fitted finite volume method is proposed to solve the nonlinear PDE in both cases of European and American options, and the convergence of the fully discrete system of equations is obtained. Finally, some numerical experiments are performed to illustrate the theoretical results of this method.