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    Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme

    Chan, R.T.L. and Hubbert, Simon (2014) Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme. Review of Derivatives Research 17 (2), pp. 161-189. ISSN ISSN: 1380-6645.

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    Abstract

    This paper will demonstrate how European and American option prices can be computed under the jump-diffusion model using the radial basis function (RBF) interpolation scheme. The RBF interpolation scheme is demonstrated by solving an option pricing formula, a one-dimensional partial integro-differential equation (PIDE). We select the cubic spline radial basis function and adopt a simple numerical algorithm (Briani et al. in Calcolo 44:33–57, 2007) to establish a finite computational range for the improper integral of the PIDE. This algorithm reduces the truncation error of approximating the improper integral. As a result, we are able to achieve a higher approximation accuracy of the integral with the application of any quadrature. Moreover, we a numerical technique termed cubic spline factorisation (Bos and Salkauskas in J Approx Theory 51:81–88, 1987) to solve the inversion of an ill-conditioned RBF interpolant, which is a well-known research problem in the RBF field. Finally, our numerical experiments show that in the European case, our RBF-interpolation solution is second-order accurate for spatial variables, while in the American case, it is second-order accurate for spatial variables and first-order accurate for time variables.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): European options, American options, Jump-diffusion models, Radial basis functions, Cubic spline
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Simon Hubbert
    Date Deposited: 14 Jan 2016 14:31
    Last Modified: 14 Jan 2016 14:31
    URI: http://eprints.bbk.ac.uk/id/eprint/13991

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