1. Title: “The Asymmetric Stochastic Volatility Models and the Multicriteria Decision Methods in Finance” 
2. Objectives: The volatility is a very important variable in the financial market. For this reason it is necessary to study its properties and its behaviour. In this research, we propose some models to estimate the volatility of several types of index returns and to analyse the asymmetric answer of the volatility in the presence of different sign shocks (leverage effect).
3. Data/Methods: The data used are the daily index returns of different countries and the methods used to estimate the volatility are based in maximum likelihood.
For comparing the obtained results of the estimation and for establishing a preference order between the indices we use the discrete multicriteria methods.
4. Results/Expected results: We expect to estimate if there is an asymmetric answer in the analysed indices. Moreover, if the asymmetric answer exists, we would like to show which is the best model to estimate this asymmetric answer.   
5. Conclusion: The GARCH and SV model are able to reproduce the dynamics of volatility and the stylised facts of stock indices return series. However, if there is an asymmetric answer, the asymmetric model to estimate the dynamic of the volatility is necessary.
The partial ranking between the indices is different when we used a GARCH model or when an ARSV model was used.
Keywords: Stochastic volatility, Leverage Effect, Multicriteria Methods.