35-56

• Giakoumatos, Stefanos, G.

The phenomenon of changing variance and covariance is often encountered in financial time series. As a result, the last years researchers move their interests from the homoscedastic time series models to conditional heteroscedastic time series models. In general, the models of changing variance and covariance are called Volatility Models. The main representatives of this class of models are the Autoregressive Conditional Heteroscedasticity (ARCH) models (Engle, 1982), the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models (Bollerslev, 1986; Bollerslev et al, 1992), and the Stochastic Volatility (SV) models (Taylor, 1986). The SV model is a very promising alternative of the ARCH and GARCH models and has been the focus of considerable attention in the recent years. From the classical view of the Statistics the SV models have been investigated by Taylor (1986) and Vetzal (1992). On the other hand, from the Bayesian approach (Bernardo and Smith 1995) little work has been done. A paper of Jacquier et al (1994) was the first step to this direction and Giakoumatos (2010) provide same elegant MCMC algorithms. In this study we focus our interest on the Stochastic Volatility models using the Bayesian framework. We develop an MCMC algorithm (Gilks et al, 1992) that converges to the joint posterior distribution of the parameters of the SV model. The MCMC algorithm that has been proposed by Jacquier et al (1994) has been studied and we have evidence that it is not very efficient. In our proposed MCMC algorithm, we use some techniques so that the algorithm achieves better convergence characteristics. Our experience show that the random-scan MCMC algorithm converges faster than the general MCMC algorithm. In addition to that a reparameterisation is used which gives better performance than the random-scan MCMC algorithm. Finally, we illustrate our methodology by modelling the weekly rate of return of the General Index of the Athens Stock Exchange Market.

• Economics and Business

• Economics

Stochastic Volatility, MCMC, Volatility Clustering, Gibbs, Metropolis, Athens Stock Exchange Market

JEL classification: C11, C15, C53, C01

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