When Fourier techniques are employed to specific option pricing cases from computational finance with non-smooth functions, the so-called Gibbs phenomenon may become apparent. This seriously impacts the efficiency and accuracy of the pricing. For example, the Variance Gamma asset price process...

We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By...

This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different...