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A new delta expansion for multivariate diffusions via the Itô-Taylor expansion

Nian Yang, Nan Chen and Xiangwei Wan ()

Journal of Econometrics, 2019, vol. 209, issue 2, 256-288

Abstract: In this paper we develop a new delta expansion approach to deriving analytical approximation to the transition densities of multivariate diffusions using the Itô-Taylor expansion of the conditional expectation of the Dirac delta function. Our approach yields an explicit recursive formulas for the expansion coefficients and is universally applicable for a wide spectrum of models, particularly the time-inhomogeneous non-affine irreducible multivariate diffusions. We show that this new approach can be viewed as an extension of Aït-Sahalia (2002) and Lee et al. (2014) to the case of multivariate models. The derived expansions are proved to converge to the true probability density as the observational time interval shrinks. The obtained approximations can thereby be used to carry out the maximum likelihood estimation for the diffusions with discretely observed data. Extensive numerical experiments demonstrate the accuracy and effectiveness of our approach.

Keywords: Closed-form density expansion; Delta expansion; Itô-Taylor expansion; Multivariate diffusions; Maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C13 C32 C63 (search for similar items in EconPapers)
Date: 2019
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Handle: RePEc:eee:econom:v:209:y:2019:i:2:p:256-288