A New Improvement Scheme for Approximation Methods of Probability Density Functions (Revised version of CARF-F-305; Forthcoming in “Journal of Computational Finance”)

Abstract

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in the Hilbert space projection theorem. Moreover, we apply “Dykstra’s cyclic projections algorithm” for its implementation. Numerical examples for application to an asymptotic expansion method in option pricing demonstrate the effectiveness of our scheme under SABR model.