Cubic spline wavelets with four vanishing moments on the interval and their applications to option pricing under Kou model

Abstract

The paper is concerned with the construction of a cubic spline wavelet basis on the unit interval and an adaptation of this basis to the first-order homogeneous Dirichlet boundary conditions. The wavelets have four vanishing moments and they have the shortest possible support among all cubic spline wavelets with four vanishing moments corresponding to B-spline scaling functions. We provide a rigorous proof of the stability of the basis in the space [Formula: see text] or its subspace incorporating boundary conditions. To illustrate the applicability of the constructed bases, we apply the wavelet-Galerkin method to option pricing under the double exponential jump-diffusion model and we compare the results with other cubic spline wavelet bases and with other methods.