This paper analyzes the arising problems of using MCMC sampling methods under different model parameterizations in a stochastic volatility model. It turns out that the performance of Bayesian inference is dependent on the true parameter values. The standard centered parameterization has shortcomings when the variability of its volatility is relatively small, while the non-centered parameterization presents with complications when the persistence parameter is close to one. This paper uses the recently presented ancillarity-sufficiency interweaving strategy which overcomes the pitfalls of the parameterizations by using both of them in order to update the latent states and the parameters of interest jointly, this way maintaining the dependence between them.