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Keywords:

  • Bayesian procedures;
  • GMM;
  • Indirect inference;
  • Kalman filter;
  • Leverage effect;
  • Long-memory;
  • Maximum likelihood;
  • Monte Carlo Markov Chain;
  • QML;
  • SV-M

Abstract.  Although stochastic volatility (SV) models have an intuitive appeal, their empirical application has been limited mainly due to difficulties involved in their estimation. The main problem is that the likelihood function is hard to evaluate. However, recently, several new estimation methods have been introduced and the literature on SV models has grown substantially. In this article, we review this literature. We describe the main estimators of the parameters and the underlying volatilities focusing on their advantages and limitations both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.