Title: Asymptotic expansion formulas for diffusion processes based on the perturbation method
Authors: Emanuele Guidotti - University of Neuchatel (Switzerland) [presenting]
Nakahiro Yoshida - University of Tokyo (Japan)
Abstract: Asymptotic expansion formulas for arbitrary diffusion processes are provided in a form that facilitates implementation. The implementation in the R package YUIMA is presented. The user can now efficiently compute expected values of diffusion processes with theoretically any degree of accuracy. Between $10^9-10^10$ Monte Carlo simulations were required to distinguish between the true expected value of an Asian option payoff and the approximation computed in 0s-10s by the proposed expansion. The method finds applications in option pricing and other fields where expectations, moments, density estimation, filtering, and functionals of diffusion processes are involved.