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

Article


Chan, R. 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.
AuthorsChan, R. and Hubbert, Simon
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.

JournalReview of Derivatives Research
Journal citation17 (2), pp. 161-189
ISSN1380-6645
Year2014
PublisherSpringer
Accepted author manuscript
Digital Object Identifier (DOI)doi:10.1007/s11147-013-9095-3
Web address (URL)https://doi.org/10.1007/s11147-013-9095-3
Publication dates
Online08 Dec 2013
Print01 Jul 2014
Publication process dates
Deposited01 Dec 2017
Copyright information© 2013 Springer Science+Business Media New York. This is a post-peer-review, pre-copyedit version of an article published in Review of Derivatives Research. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11147-013-9095-3.
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https://repository.uel.ac.uk/item/85981

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