Modeling the birth of a liquid market

A continuum market dynamics model with a variable number of traders is proposed. It includes an “impatience” factor that characterizes the frequency of leaving the market by those traders who are not been able to find their counterparts. The market liquidity is defined simply as the presence of traders on both the bid and offer sides of the market. If the price variation is neglected, the deterministic model can be transformed into the Schrodinger equation with a Morse-type potential. It is concluded that the discrete model may be more appropriate for describing a transition to a liquid market. Results of stochastic modeling the birth of a liquid market are discussed.