Wavelet Methods in PDE Valuation of Financial Derivatives

摘要

We investigate the application of a wavelet method of lines solution method to financial PDEs. We demonstrate the suitability of a numerical scheme based on biorthogonal interpolating wavelets to financial PDE problems where there are discontinuities or regions of sharp transitions in the solution. The examples treated are the Black Scholes PDE with discontinuous payoffs and a 3-dimensional cross currency swap PDE for which a speedup over standard finite difference methods of two orders of magnitude is reported.