WAVELET OPTIMIZED VALUATION OF FINANCIAL DERIVATIVES

B. Carton de Wiart () and M. A. H. Dempster ()
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B. Carton de Wiart: Centre for Financial Research, Statistical Laboratory, University of Cambridge, Cambridge CB3 0WA, UK;
M. A. H. Dempster: Centre for Financial Research, Statistical Laboratory, University of Cambridge, Cambridge CB3 0WA, UK;

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 07, 1113-1137

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.

Keywords: Derivative pricing; partial differential equations; interpolating wavelets; sparse domain; adaptive methods (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S021902491100667X

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