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Original Articles

American option pricing problem transformed on finite interval

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Pages 821-836 | Received 20 Oct 2013, Accepted 14 Mar 2014, Published online: 13 May 2014
 

Abstract

We study the American option pricing linear complementarity problem (LCP), transformed on finite interval as it is initially defined on semi-infinite real axis. We aim to validate this transformation, investigating the well-posedness of the resulting problem in weighted Sobolev spaces. The monotonic penalty method reformulates the LCP as a semi-linear partial differential equation (PDE) and our analysis of the penalized problem results in uniform convergence estimates. The resulting PDE is further discretized by a fitted finite volume method since the transformed partial differential operator degenerates on the boundary. We show solvability of the semi-discrete and fully discrete problems. The Brennan–Schwarz algorithm is also presented for comparison of the numerical experiments, given in support to our theoretical considerations.

2010 AMS Subject Classifications:

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