Understanding the cubic and half-cubic laws of financial fluctuations

Recent empirical research has uncovered regularities in financial fluctuations. Those are: (i) the cubic law of returns: returns follow a power law distribution with exponent 3; (ii) the half cubic law of volumes: volumes follow a power law distribution with exponent 32; (iii) Approximate cubic law of number of trades: the number of trades in a given time intervals follows a power law distribution with exponent around 3. We discuss a new theory that explains them, as well as some related facts.