Dynamics of stock prices

We show that the dynamics of stock prices can be accurately described as a continuous time random walk with a time dependent diffusion coefficient. The time evolution of the diffusion coefficient can be derived from tick by tick databases provided the stock price is characterized in terms of a couple of values describing the best ask and the best bid. We are then led to a finding and, namely, that the transition rate of the random walk process is different from the frequency of transactions. Our results allow us to obtain a fast and reliable determination of the diffusion coefficient and precisely confirm that fat tails in the distribution of price variations are due to volatility fluctuations.