A Semiparametric Model of Estimating Volatility of Diffusion Processes

This article provides a semiparametric model to estimate the diffusion coefficient of a stochastic differential equation from discretely observed data without assuming any functional form of the diffusion coefficient. It is shown that the model has the consistency such that estimated states of the diffusion coefficient converge to the true ones as the number of observations (N) goes to infinity and the sampling time interval (Δt) goes to zero while NΔt going to infinity.