Relative intra-day cumulative volume is intra-day cumulative volume divided by final total volume. If intra-day cumulative volume is modeled as a Cox (doubly stochastic Poisson) point process, then using initial enlargement of filtration with the filtration of the Cox process enlarged by...

If intra-day volume is modelled as a Cox point process, then relative intra-day cumulative volume (intra-day cumulative volume divided by final total volume) is shown to be a novel generalization of a binomial point process; the doubly stochastic binomial point process. Re-scaling the intra-day...