Maximum penalized quasi-likelihood estimation of the diffusion function

We develop a maximum penalized quasi-likelihood estimator for estimating in a non-parametric way the diffusion function of a diffusion process, as an alternative to more traditional kernel-based estimators. After developing a numerical scheme for computing the maximizer of the penalized maximum quasi-likelihood function, we study the asymptotic properties of our estimator by way of simulation. Under the assumption that overnight London Interbank Offered Rates (LIBOR), the USD/EUR, USD/GBP, JPY/USD, and EUR/USD nominal exchange rates, and the 1-month, 3-month Treasury bill yields, and 30-year Treasury bond yields are generated by diffusion processes, we use our numerical scheme to estimate the diffusion function.