Maximum penalized quasi-likelihood estimation of the diffusion function

TL;DR

This paper introduces a maximum penalized quasi-likelihood method for nonparametric estimation of diffusion functions in stochastic processes, providing a computational scheme and asymptotic analysis, with applications to financial data.

Contribution

It presents a novel nonparametric estimation approach using penalized quasi-likelihood, offering an alternative to kernel methods with a practical numerical scheme and asymptotic properties.

Findings

Numerical scheme effectively estimates diffusion functions from simulated data.

Method performs well on financial data such as LIBOR rates and exchange rates.

Asymptotic properties support the estimator's theoretical validity.

Abstract

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.