Relative Volume as a Doubly Stochastic Binomial Point Process

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 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 binomial point process and closely related Cox point process. This is useful for Volume Weighted Average Price (VWAP) traders who require a stochastic model of relative intra-day cumulative volume to implement risk-optimal VWAP trading strategies.