A restricted B-spline estimation of diffusion processes with applications to financial data

Abstract

Time-homogeneous diffusion process plays an important role in the financial market, and it is widely used for describing the stochastic dynamics of the underlying economic variables. In this work, we study nonparametric estimation of the drift and diffusion functions for the time-homogeneous diffusion process, and propose a new nonparametric regression technique based on higher-order approximations, which is called B-spline approach. The nonnegativity of the diffusion function is guaranteed by the restricted B-spline method. Our simulation results show that our method indeed outperforms the local polynomial method.