We modify the Gallant and Tauchen (1996) efficient method of moments (EMM) method to perform exact Bayesian inference, where exact means no reliance on asymptotic approximations.  We use this modification to evaluate the empirical plausibility of recent predictions from high-frequency financial theory regarding the small-time movements of an Ito semimartingale.  The theory indicates that the probability distribution of the small moves should be locally stable around the origin. It makes no predictions regarding large rare jumps, which get filtered out. Our exact Bayesian procedure imposes support conditions on parameters as implied by this theory.  The empirical application uses Index options extending over a wide range of moneyness, including deep out of the money puts. The evidence is consistent with a locally stable distribution valid over most of the support of the observed data while mildly failing in the extreme tails, about which the theory makes no prediction.  We undertake diagnostic checks on all aspects of the procedure.  In particular, we evaluate the distributional assumptions regarding a semi-pivotal statistic, and we test by Monte Carlo that the posterior distribution is properly centered with short credibility intervals.  Taken together, our results suggest a more important role than previously thought for pure jump-like models with diminished, if not absent, diffusive component.

Ron Gallant is a Liberal Arts Professor of Economics at The Pennsylvania State University. Prior to joining the Penn State faculty, he was Hanes Corporation Foundation Professor of Business Administration, Fuqua School of Business, Duke University, with a secondary appointment in the Department of Economics, Duke University, and Distinguished Scientist in Residence, Department of Economics, New York University.

Before joining the Duke faculty, he was Henry A. Latane Distinguished Professor of Economics at the University of North Carolina at Chapel Hill.  He retains emeritus status at UNC.

Previous to UNC he was, successively, Assistant, Associate, Full, and Drexel Professor of Statistics and Economics at North Carolina State University. Gallant has held visiting positions at the l'Ecole Polytechnique, the University of Chicago, and Northwestern University.

He received his A.B. in mathematics from San Diego State University, his M.B.A. in marketing from the University of California at Los Angeles, and his Ph.D. in statistics from Iowa State University.  He is a Fellow of both the Econometric Society and the American Statistical Association.  He has served on the Board of Directors of the NationalBureau of Economic Research, the Board of Directors of the American Statistical Association, and on the Board of Trustees of the National Institute of Statistical Sciences.  He is past co-editor of theJournal of Econometrics and past editor of The Journal of Business and Economic Statistics.