A comparative study of two models sv with mcmc algorithm

Abstract

This paper examines two asymmetric stochastic volatility models used to describe the volatility dependencies found in most financial returns. The first is the autoregressive stochastic volatility model with Student′s t-distribution (ARSV-t), and the second is the basic Svol of JPR (Journal of Business and Economic Statistics 12(4), 371–417, 1994). In order to estimate these models, our analysis is based on the Markov Chain Monte Carlo (MCMC) method. Therefore, the technique used is a Metropolis-Hastings (Hastings, Biometrika 57, 97–109, 1970), and the Gibbs sampler (Casella and George The American Statistician 46(3) 167–174, 1992; Gelfand and Smith, Journal of the American Statistical Association 85, 398–409, 1990; Gilks et al. 1993). The empirical results concerned on the Standard and Poor′s 500 Composite Index (S&P), CAC 40, Nasdaq, Nikkei, and Dow Jones stock price indexes reveal that the ARSV-t model provides a better performance than the Svol model on the mean squared error (MSE) and the maximum likelihood function.​