In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the L\'evy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predictions on the long-time behaviour of the waiting-time probability density are presented. Finally, a general scaling form is given, based on the solution of the fractional diffusion equation.Comment: 11 pages, no figures, LaTeX2e, submitted to Physica

We complement the theory of tick-by-tick dynamics of financial markets based on a continuous-time random walk (CTRW) model recently proposed by Scalas ct al. (Physica A 284 (2000) 376), and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London