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### Adaptive Finite Element Solution of 1D European Option Pricing Problems

Abstract:

We present a piecewise Hermite cubic adaptive finite element method for solving a generalised European Black-Scholes problem to guaranteed accuracy. Specifically, we prove a residual-based a posteriori error bound in the $L^{2}(\Omega)$-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 discretisat...

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### Authors

Nicholas Jackson More by this author
Endre Suli More by this author
Publication date:
1997-08-05
URN:
uuid:61481632-b94d-4b8d-a53d-594f456d23aa
Local pid:
oai:eprints.maths.ox.ac.uk:1318