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Wavelet Optimized Valuation Of Financial Derivatives

Author

Listed:
  • B. CARTON DE WIART

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

  • M. A. H. DEMPSTER

    (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)

Abstract

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.

Suggested Citation

  • B. Carton De Wiart & M. A. H. Dempster, 2011. "Wavelet Optimized Valuation Of Financial Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(07), pages 1113-1137.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:07:n:s021902491100667x
    DOI: 10.1142/S021902491100667X
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