Maximum penalized quasi-likelihood estimation of the diffusion function

Jeff Hamrick, Yifei Huang, Constantinos Kardaras and Murad Taqqu

Quantitative Finance, 2011, vol. 11, issue 11, 1675-1684

Abstract: 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.

Date: 2011
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DOI: 10.1080/14697688.2011.615212

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