"A New Improvement Scheme for Approximation Methods of Probability Density Functions"

Takahashi, Akihiko and Yukihiro Tsuzuki

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 symptotic expansion method in option pricing demonstrate the effectiveness of our scheme under SABR model.