Valuing European Options using the Finite Element Method

The main objective of this paper is to develop an adaptive finite element method for computation of the values and different sensitivity measures of European options. The options are priced using the Black-Scholes PDE-model, and the resulting PDE´s are of parabolic type in one spatial dimension with different boundary conditions and jump conditions at monitoring dates. The adaptive finite element method is based on a posteriori estimates of the error in desired quantities, the suggested adaptive finite element method is stable and gives fast and accurate results.