In the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error bounds. The nature of the local Shannon wavelets basis enables us to adaptively determine the proper size of the computational interval. Numerical experiments on European-style options show exponential convergence and confirm the bounds, robustness, and efficiency.
SIAM Journal on Scientific Computing
Scientific Computing

Ortiz Gracia, L., & Oosterlee, K. (2016). A highly efficient Shannon wavelet inverse Fourier technique for pricing European options. SIAM Journal on Scientific Computing, 38(1), B118–B143. doi:10.1137/15M1014164