  We develop a maximum penalized quasi-likelihood estimator for estimating in a
nonparametric 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 1-month, 3-month, and 30-year Treasury bond yields are
generated by diffusion processes, we use our numerical scheme to estimate the
diffusion function.
