Abstract:
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 knowledge of final volume, it is shown that relative intra-day volume
conditionally has a binomial distribution and is a novel generalization of a binomial point
process: the doubly stochastic binomial point process. Re-scaling the intra-day traded volume
to a relative volume between 0 (no volume traded) and 1 (daily trading completed) allows
empirical intra-day volume distribution information for all stocks to be used collectively
to estimate and identify the random intensity component of the doubly stochastic binomial
point process and closely related Cox point process.
