02237cam a22002537 4500001000600000003000500006005001700011008004100028100002500069245013800094260006600232490005100298500001900349520106400368530006101432538007201493538003601565690011201601690006901713710004201782830008601824856003701910856003601947t0222NBER20161027041218.0161027s1998 mau||||fs|||| 000 0 eng d1 aAit-Sahalia, Yacine.10aMaximum Likelihood Estimation of Discretely Sampled Diffusionsh[electronic resource]:bA Closed-Form Approach /cYacine Ait-Sahalia. aCambridge, Mass.bNational Bureau of Economic Researchc1998.1 aNBER technical working paper seriesvno. t0222 aFebruary 1998.3 aWhen a continuous-time diffusion is observed only at discrete dates, not necessarily close together, the likelihood function of the observations is in most cases not explicitly computable. Researchers have relied on simulations of sample paths in between the observations points, or numerical solutions of partial differential equations, to obtain estimates of the function to be maximized. By contrast, we construct a sequence of fully explicit functions which we show converge under very general conditions, including non-ergodicity, to the true (but unknown) likelihood function of the discretely-sampled diffusion. We document that the rate of convergence of the sequence is extremely fast for a number of examples relevant in finance. We then show that maximizing the sequence instead of the true function results in an estimator which converges to the true maximum-likelihood estimator and shares its asymptotic properties of consistency, asymptotic normality and efficiency. Applications to the valuation of derivative securities are also discussed. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aG12 - Asset Pricing • Trading Volume • Bond Interest Rates2Journal of Economic Literature class. 7aC13 - Estimation: General2Journal of Economic Literature class.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0222.4 uhttp://www.nber.org/papers/t022241uhttp://dx.doi.org/10.3386/t0222