Adaptive Finite Element Solution of 1 D European Option Pricing Problems

We present a piecewise Hermite cubic adaptive nite element method for solving a generalised European Black-Scholes problem to guaranteed accuracy. Speciically, we prove a residual-based a posteriori error bound in the L 2 (()-norm, at contract issue, for a continuous Galerkin approximation to the solution using Galerkin orthogonality and weighted strong stability of an associated dual problem. We use this bound to construct an adaptive algorithm to generate a space-time discretisation which ensures that the error norm is less than a given tolerance. We demonstrate the speed and accuracy of our method through example pricings. The rst author would like to acknowledge the nancial support of the EPSRC and the investment bank BZW, and to thank Sam Howison for helpful comments.