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Wavelet Optimized Valuation Of Financial Derivatives


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    (Centre for Financial Research, Statistical Laboratory, University of Cambridge, Cambridge CB3 0WA, UK; Equity Derivatives, Citigroup, 390 Greenwich Street, New York, NY 10013, USA)


    (Centre for Financial Research, Statistical Laboratory, University of Cambridge, Cambridge CB3 0WA, UK; Cambridge System Associates Limited, 5-7 Portugal Place, Cambridge CB5 8AF, UK)

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    We introduce a simple but efficient PDE method that makes use of interpolation wavelets for their advantages in compression and interpolation in order to define a sparse computational domain. It uses finite difference filters for approximate differentiation, which provide us with a simple and sparse stiffness matrix for the discrete system. Since the method only uses a nodal basis, the application of non-constant terms, boundary conditions and free-boundary conditions is straightforward. We give empirical results for financial products from the equity and fixed income markets in 1, 2 and 3 dimensions and show a speed-up factor between 2 and 4 with no significant reduction of precision.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 07 ()
    Pages: 1113-1137

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:07:p:1113-1137

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    Keywords: Derivative pricing; partial differential equations; interpolating wavelets; sparse domain; adaptive methods;


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