This paper uses a straightforward application of alpha-stable distributions for Romanian Stock Market, showing how a relatively simple implementation in the real world of a complex mathematical tool can be much more reliable in risk management than the classical Gaussian or log-normal distributions. In this paper we use a SAS macro for estimating the parameters of an alpha-stable distribution, using the time-series regression method from Kogon and Williams (1998). Using the Fast Fourier Transform, we estimate the probability density function, the cumulative distribution function and consequently, the VaR (99.5%) and TVaR (99%). For numerical illustration we are using daily logreturns of the BET Index; the measures of market risk, estimated on rolling windows using alpha-stable distributions and Gaussian distribution, are then compared to the actual logreturns of the BET Index. Numerical experiments show that using alpha-stable distributions for estimating VaR and TVaR can be a better alternative for managing the risk of financial assets.