Implicit Estimation for the Stochastic Volatility Model

Abstract

Efficient, accurate, and fast Markov Chain Monte Carlo estimation methods based on the Implicit approach are proposed. In this article, we introduced the notion of Implicit method for the estimation of parameters in Stochastic Volatility models.

Implicit estimation offers a substantial computational advantage for learning from observations without prior knowledge and thus provides a good alternative to classical inference in Bayesian method when priors are missing.

Both Implicit and Bayesian approach are illustrated using simulated data and are applied to analyze daily stock returns data on CAC40 index.

Keywords:

• Bayesian analysis
• Gibbs
• Implicit distribution
• MCMC algorithm
• Metropolis Hastings
• Stochastic Volatility model
• Heston model

Notes

(*) Corresponds to parameters estimated by using true values as prior parameters.

(**) Corresponds to parameters estimated by using prior different from true values.

(*) Corresponds to parameters estimated by using true values as prior parameters.

(**) Corresponds to parameters estimated by using prior different from true values.

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsta.