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Efficient solution of a partial integro-differential equation in finance
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Sachs, E. W. and Strauss, Arne (2008) Efficient solution of a partial integro-differential equation in finance. Applied Numerical Mathematics, Vol.58 (no.11). pp. 1687-1703. doi:10.1016/j.apnum.2007.11.002 ISSN 0168-9274.
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Official URL: http://dx.doi.org/10.1016/j.apnum.2007.11.002
Abstract
Jump-diffusion models for the pricing of derivatives lead under certain assumptions to partial integro-differential equations (PIDE). Such a PIDE typically involves a convection term and a non-local integral. We transform the PIDE to eliminate the convection term, discretize it implicitly, and use finite differences on a uniform grid. The resulting dense linear system exhibits so much structure that it can be solved very efficiently by a circulant preconditioned conjugate gradient method. Therefore, this fully implicit scheme requires only on the order of O(nlogn) operations. Second order accuracy is obtained numerically on the whole computational domain for Merton's model.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School |
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Journal or Publication Title: | Applied Numerical Mathematics | ||||
Publisher: | Elsevier BV | ||||
ISSN: | 0168-9274 | ||||
Official Date: | November 2008 | ||||
Dates: |
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Volume: | Vol.58 | ||||
Number: | no.11 | ||||
Page Range: | pp. 1687-1703 | ||||
DOI: | 10.1016/j.apnum.2007.11.002 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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