The continuous time random walk formalism in financial markets

We adapt the continuous time random walk (CTRW) formalism to describe the asset price evolution. We show some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price distribution from high-frequency data; and (ii) the inverse problem, that is, obtaining information on the market microstructure as reflected by high-frequency data knowing only the daily volatility. We apply the formalism to actual financial data and try to show that the CTRW offers alternative tools to deal with several complex issues of financial markets.