In 2007 Lasry & Lions introduced a price formation model that describes the evolution of price by a system of parabolic equations for the trader densities (as functions of the bid-ask price), with the agreed price entering as a free boundary. The authors motivated the model using mean field game theory, but the detailed microscopic origin remained unclear. In this talk we provide a simple agent based trade model with standard stochas-
tic price fluctuations together with discrete trading events. By modelling trading events between vendors and buyers as kinetic collisions we obtain a Boltzmann-type model for the densities. Then we prove rigorously that in the limit of large trading frequencies, the proposed Boltzmann model converges to the Lasry and Lions free boundary problem. We also analyse other asymptotics beyond the scales that the free boundary model can describe and illustrate our analytical results with numerical simulations.