The stochastic nature of price volatility, as an important issue in stock markets, significantly affects decision makers’ decisions. In this paper, a new multivariate fractionally integratedgeneralized autoregressive conditional heteroscedasticity (MVFIGARCH) model is proposed. Being more comprehensive in comparison with the models in the literature, the proposed model considers long term parameter which is estimated simultaneously with other parameters. One of the well-known methods of MVFIGARCH estimation is the Gaussian quasi-maximum likelihood method. The Gaussian quasi-maximum likelihood estimator of MVFIGARCH model is known to be sensitive to data outliers. To correct the vulnerability of this method to outliers in data, robust M-estimators are introduced for MVFIGARCH models. Volatility models with bounded innovation propagation property are introduced to increase the robustness of the estimations. The applicability of the proposed model is justified by the volatility transmission among Tehran stock index, Dubai stock index and oil global price index using MVFIGARCH model within the time span from December 5, 2006 to January 30, 2012 is investigated. The result of estimation in different models generally shows volatility transmission from oil global market to Tehran and Dubai markets. Volatility transmission from Dubai market to Tehran was meaningfully observed as well. However, the effect of transmission was not observed in reverse direction.