Analysis of Financial Time Series, Third Edition

12.8 New Approach to SV Estimation

In this section, we discuss an alternative procedure to estimate stochastic volatility (SV) models. This approach makes use of the technique of forward filtering and backward sampling (FFBS) within the Kalman filter framework to improve the efficiency of Gibbs sampling. It can dramatically reduce the computing time by drawing the volatility process jointly with the help of a mixture of normal distributions. In fact, the approach can be used to estimate many stochastic diffusion models with leverage effects and jumps.

For ease in presentation, we reparameterize the univariate stochastic volatility model in Eqs. (12.20) and (12.21) as

12.40

12.41

where , , σ0 > 0, {zt} is a zero-mean log volatility series, and {ϵt} and {ηt} are bivariate normal distributions with mean zero and covariance matrix

The parameter ρ is the correlation between ϵt and ηt and represents the leverage effect of the asset return rt. Typically, ρ is negative signifying that a negative ...