Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach

Posted: 15 Jul 2002

See all articles by Yacine Ait-Sahalia

Yacine Ait-Sahalia

Princeton University - Department of Economics; National Bureau of Economic Research (NBER)

Abstract

When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.

Suggested Citation

Ait-Sahalia, Yacine, Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach. Econometrica, Vol. 70, pp. 223-262, January 2002. Available at SSRN: https://ssrn.com/abstract=312230

Yacine Ait-Sahalia (Contact Author)

Princeton University - Department of Economics ( email )

Fisher Hall
Princeton, NJ 08544
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National Bureau of Economic Research (NBER)

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