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The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

Funded by The Danish National Research Foundation

MPS-RR 2004-19
September 2004

Estimating Functions for Discretely Sampled Diffusion-Type Models

by: Martin Jacobsen, Bo Martin Bibby , Michael Sørensen


The theory of estimating functions for diffusion-type models is reviewed with a view to applications in finance. Several types of estimating functions are presented, including some explicit estimating functions. Special attention is given to martingale estimating functions. Also prediction-based estimating functions are considered. Large sample asymptotics is discussed in detail. The theory of optimal estimating functions is presented and applied to di usion models. The classical theory as well as the new theory of small $Delta$-optimality are considered. The focus is on di usion models and stochastic volatility models, but a simple diffusion with jumps is treated too. Several examples are given.

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This paper has now been published in Ait-Sahalia, Y. and Hansen, L.P. (eds.): Handbook of Financial Econometrics, North-Holland, Amsterdam (to appear)