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.
On the impact of various formulations of the boundary condition within numerical option valuation by DG method
