Estimation of Diffusions using Wavelet scaling methods

Abstract

In continuous time, diffusion processes have been used for modelling financial dynamics for a long time. For example the Ornstein-Uhlenbeck process (the simplest mean-reverting process)has been used to model non-speculative price processes. The Cox-Ingersoll-Ross process is widely used to model interest rate dynamics. We discuss parameter estimation of these processes using a new method, namely a Wavelet filter method. This approach is useful as it turns out that the resulting covariance function is decorrelated. We use Monte Carlo simulation to report the distribution of estimates.Ornstein-Uhlenbeck process, CIR model, Wavelet transform