The Mathematical Institute, University of Oxford, Eprints Archive

Adaptive Finite Element Solution of 1D European Option Pricing Problems

Jackson, Nicholas and Suli, Endre (1997) Adaptive Finite Element Solution of 1D European Option Pricing Problems. Technical Report. Unspecified. (Submitted)

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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 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.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1318
Deposited By:Lotti Ekert
Deposited On:09 Jun 2011 08:22
Last Modified:09 Jun 2011 08:22

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