On the Impact of Various Formulations of the Boundary Condition within Numerical Option Valuation by DG Method

Jiří Hozman, Tomáš Tichý

Options, a crucial type of financial instrument, are very challenging as concerns both, the application and valuation. A key property of (exotic) options is to provide a tool to manage the market risk coming from everyday innovations at the market. Due to the complexity of underlying processes and/or payoff functions valuation via numerical methods is often inevitable. The flexibility in terms of model assumptions 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. Efficient formulation of the boundary conditions of option valuation formula is one of such approaches. In this paper we focus on the impact of Dirichlet, Neumann and transparent boundary conditions when the valuation formula is discretized by the discontinuous Galerkin method combined with the implicit Euler scheme for the temporal discretization. The numerical results are presented using real data of DAX index options.