Brownian trading excursions

We study a parsimonious model of the latent limit order book where orders get placed according to some volume density function relative to a center price process, and get executed whenever this center price reaches their... [ view full abstract ]

We study a parsimonious model of the latent limit order book where orders get placed according to some volume density function relative to a center price process, and get executed whenever this center price reaches their level. This mechanism corresponds to the solution of the stochastic heat equation with multiplicative noise for the relative order volume distribution which we relate to some local time functional. We classify various types of trades, and introduce the trading excursion process which is a Poisson point process.