We analyze the components of the bid-ask spread in the Athens Stock Exchange (ASE), which was recently characterized as a developed market. For large and medium capitalization stocks, we estimate the adverse selection and the order handling component of the spreads as well as the probability of a trade continuation on the same side of either the bid or the ask price, using the Madhavan et al.~(1997) model. We extend it by incorporating the traded volume and we find that the adverse selection component exhibits U-shape patterns, while the cost component pattern depends on the stock price. For high priced stocks, the usual U-shape applies, while for low-priced ones, it is an increasing function of time, mainly due to the order handling spread component. Furthermore, the expected price change and the liquidity adjustment to Value-at-Risk that is needed is higher in the low capitalization stocks, while the most liquid stocks are the high priced ones. Moreover, by estimating the Madhavan et al.~(1997) model for two distinct periods we explain why there are differences in the components of the bid-ask spread.