Estimation for stochastic volatility model: Quasi-likelihood and asymptotic quasi-likelihood approaches

Abstract

For estimation of the stochastic volatility model (SVM), this paper suggests the quasi-likelihood (QL) and asymptotic quasi-likelihood (AQL) methods. The QL approach is quite simple and does not require full knowledge of the likelihood functions of the SVM. The AQL technique is based on the QL method and is used when the covariance matrix Σ is unknown. The AQL approach replaces the true variance–covariance matrix Σ by nonparametric kernel estimator of Σ in QL.

Keywords

• Stochastic volatility model (SVM)
• Quasi-likelihood (QL)
• Asymptotic quasi-likelihood (AQL)
• Martingale difference
• Kernel estimator