Numerical valuation of options by DG method: A study of boundary condition formulation

Option valuation is obviously the most efficient when done analytically. However, in many cases, including most types of exotic options no closed form of the pricing formula exists. In such cases, some numerical approximation is inevitable. In our recent research we focused on discontinuous Galerkin method to numerical solution of partial differential equations. Obviously, the flexibility in terms of model assumptions and/or additional conditions often brings high time costs so that it can be useful to reduce the space on which the computation is executed in order to keep both the computation time and calculation error at acceptable levels. In this paper we study the impact of various definitions of boundary condition, in particular the Dirichlet, Neumann and transparent one. Similarly to our previous results, we use real data of DAX index options to show the differences among various specifications.