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Appraisal of a contour integral method for the Black-Scholes and Heston equations

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  • K. J. in 't Hout
  • J. A. C. Weideman
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    Abstract

    A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parameters are derived theoretically and tested numerically. Test examples presented are the Black-Scholes PDE in one space dimension and the Heston PDE in two dimensions. In the latter case efficiency is compared to ADI splitting schemes for solving this problem. In the examples it is found that the contour integral method is superior for the range of medium to high accuracy requirements. Further improvements to the current implementation of the contour integral method are suggested.

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    File URL: http://arxiv.org/pdf/0912.0434
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0912.0434.

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    Date of creation: Dec 2009
    Date of revision: Apr 2011
    Publication status: Published in SIAM J. Sc. Comp. 33, 763-785 (2011)
    Handle: RePEc:arx:papers:0912.0434

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