The Valuation Of Electricity Options

In recent years, along with the reform of the electricity power industry and the development of electricity drivatives market, many ordinary electricity options and exotic electricity options come to exist. How to price them becomes an exigent problem.Electricity is a kind of common asset, electricity can not be stored effectivesly.,which rules out the traditional spot market, storage-based method of valuing commodity derivatives and traditional traditional no-arbitrage principle method, therefore future based replication is argued to be made necessary by the non-storable nature of electricity. The paper describes the two types of electricity options, one is spark spread option, the other is locational spread option. Both spark and locational spread options are for both geometric Brownian motion and mean reverting price processes. In this paper, we use the futures based approach to derive the partial differential equations, further, by the unit conversion to the analytic solution of spark spread options and locational spread options. In addition, the paper also presented a new finite element method in space direction and a difference method in time direction to solve the PDE equation, finally derive the numerical solution of spark spread call options. Futher, we obtained the error order between the finite element solution and the exact solution of spark spread call option which is for geometric Brownian motion by taking advantage of discontinuity of our approximation space, with the error order being close to2. Final conclusion shows that the numerical solution is very close to the analytical solution of spark spread options, and it can replace the true solution, which further demonstrates the importance of numerical methods described in the paper.