Fractional calculus and continuous-time finance. II: The waiting-time distribution

The continuous time random walk (CTRW) is a good phenomenological description of the tick-by-tick dynamics in a financial market. It can naturally take into account the pathological time evolution of financial markets, which is non-Markovian and/or non-local. The CTRW can be tested against empirical data, thus providing useful information on the restrictions of the premises. There is an implication for microscopic market models. The model should, at least phenomenologically, take into account the agents in the market decide to sell and buy an asset at randomly distributed instants. It would be a success to derive the `right' waiting-time distribution from first principles, whatever these first principles will be.