A mechanism for the latent liquidity revealing into the limit order book

Latent order book models have allowed for significant progress in the understanding of price formation in financial markets. In particular they were able to reproduce a number of stylized facts such as the square root impact of metaorders. An important question that is raised – if one wants to bring such models closer to real market data – is that of the connection between the latent order book and the revealed order book, observable and quantifiable. It is here suggested a self-consistent mechanism for the revelation of latent liquidity that allows for quantitative estimation of the latent order book from real market data. In particular, our setup allows to track the revealed liquidity as function of revelation rates and incentive to give away information by revealing one’s intentions. We confront our results to real market data and discuss market stability. Finally we run a numerical simulation to compute the price impact and discuss different regimes.