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An Efficient Method for Option Pricing with Finite Elements: An Endogenous Element Length Approach

In: Operations Research Proceedings 2012

Author

Listed:
  • Tomoya Horiuchi

    (Graduate School of Waseda University)

  • Kei Takahashi

    (School of Science and Engineering, Waseda University)

  • Takahiro Ohno

    (School of Science and Engineering, Waseda University)

Abstract

This paper proposes an efficient version of the finite element method (FEM) in option pricing. In this study, we determine element lengths from the curvature of the PDE endogenously. Our method consists of two algorithms, the coarsening and the refinement of the elements. The model makes the element larger if the curvature of the local domain is low, and smaller if it is high at each time step. We apply this approach to one-dimensional options, a European up-and-out call option, and an American put option. As a result, we find that this method is able to reduce the experiment time while the accuracy remains at a comparable level.

Suggested Citation

  • Tomoya Horiuchi & Kei Takahashi & Takahiro Ohno, 2014. "An Efficient Method for Option Pricing with Finite Elements: An Endogenous Element Length Approach," Operations Research Proceedings, in: Stefan Helber & Michael Breitner & Daniel Rösch & Cornelia Schön & Johann-Matthias Graf von der Schu (ed.), Operations Research Proceedings 2012, edition 127, pages 203-208, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-00795-3_30
    DOI: 10.1007/978-3-319-00795-3_30
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