2002/05/01 by Yacine Aït-Sahalia, Yacine Aı̈t-Sahalia · 2 citations
Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Stochastic processes and financial applications #math.ST #msc:60H10 #msc:60J60 #msc:62F12 #msc:62M05 #stat.TH
paper · pdf · doi:10.1214/009053607000000622
published as Annals of Statistics 2008, Vol. 36, No. 2, 906-937 · Published in at http://dx.doi.org/10.1214/009053607000000622 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2002/05/01 · arxiv created 2008/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper provides closed-form expansions for the transition density and likelihood function of arbitrary multivariate diffusions. The expansions are based on a Hermite series, whose coefficients are calculated explicitly by exploiting the special structure afforded by the diffusion hypothesis. Because the transition function for most diffusion models is not known explicitly, the expansions of this paper can help make maximum-likelihood a practical estimation method for discretely sampled multivariate diffusions. Examples of interest in financial econometrics are included.