TY - JOUR
AU - Ait-Sahalia,Yacine
TI - Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approach
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 222
PY - 1998
Y2 - February 1998
DO - 10.3386/t0222
UR - http://www.nber.org/papers/t0222
L1 - http://www.nber.org/papers/t0222.pdf
N1 - Author contact info:
Yacine Aït-Sahalia
Department of Economics
Bendheim Center for Finance
Princeton University
Princeton, NJ 08540
Tel: 609/258-4015
Fax: 609/258-0719
E-Mail: yacine@princeton.edu
AB - When 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.
ER -