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    A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing

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    Authors
    Chen, W.
    Wang, Song
    Date
    2017
    Type
    Journal Article
    
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    Citation
    Chen, W. and Wang, S. 2017. A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing. Applied Mathematics and Computation. 305: pp. 174-187.
    Source Title
    Applied Mathematics and Computation
    DOI
    10.1016/j.amc.2017.01.069
    ISSN
    0096-3003
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/52000
    Collection
    • Curtin Research Publications
    Abstract

    © 2017 Elsevier Inc.In this paper we propose a power penalty method for a linear complementarity problem (LCP) involving a fractional partial differential operator in two spatial dimensions arising in pricing American options on two underlying assets whose prices follow two independent geometric Lévy processes. We first approximate the LCP by a nonlinear 2D fractional partial differential equation (fPDE) with a penalty term. We then prove that the solution to the fPDE converges to that of the LCP in a Sobolev norm at an exponential rate depending on the parameters used in the penalty term. The 2D fPDE is discretized by a 2nd-order finite difference method in space and Crank–Nicolson method in time. Numerical experiments on a model Basket Option pricing problem were performed to demonstrate the convergent rates and the effectiveness of the penalty method.

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