This paper studies the estimation of copula-based semi parametric stationary Markov models. Described models allow us evaluate the parameters of copula, which has the best fit to previously selected model (simple estimators of the marginal distribution and the copula parameter are provided). These copula-based models are characterized by nonparametric marginal distributions and parametric copula functions, while the copulas capture all the scale-free temporal dependence of the processes. In our copula dependence study we used MatLab, which help to evaluate copula parameters and choose the best copula class, based on loglikelihood estimation, for the selected financial market data. Also, using this MatLab we made VIX option index simulation - found the best copula fit under our condition and show the evaluation steps for copula based semi parametric autoregression.