Maximum likelihood estimation of discretely sampled diffusions: A closed-form approximation approach

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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.

Original languageEnglish (US)
Pages (from-to)223-262
Number of pages40
JournalEconometrica
Volume70
Issue number1
DOIs
StatePublished - Jan 1 2002

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Keywords

  • Continuous-time diffusion
  • Discrete sampling
  • Hermite expansion
  • Maximum-likelihood estimation
  • Transition density

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