Maximum likelihood estimation of stochastic volatility models

Yacine Aït-Sahalia, Robert Kimmel

Research output: Contribution to journalArticlepeer-review

258 Scopus citations


We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a short-dated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.

Original languageEnglish (US)
Pages (from-to)413-452
Number of pages40
JournalJournal of Financial Economics
Issue number2
StatePublished - Feb 2007

All Science Journal Classification (ASJC) codes

  • Accounting
  • Finance
  • Economics and Econometrics
  • Strategy and Management


  • CEV model
  • Closed-form likelihood expansions
  • GARCH model
  • Heston model
  • Volatility proxies


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