مدل سازی تولد یک بازار نقد

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.

Advances of the Internet technology have been promoting the creation of new electronic markets. The critical problem for an emerging market is the maintenance of its liquidity. The market liquidity can be described in various ways, in particular, in terms of the bid/offer spread and the market depth [1], [2] and [3]. The minimal criterion of the market liquidity is the very presence of traders on both the bid and offer sides. In this communication, we formulate the model able to describe the process of establishing liquidity in an emerging market. Several models of the market dynamics derived in terms of different trader strategies have been discussed in the literature [4], [5], [6], [7], [8] and [9] (for a recent review on the agent based computational finance, see Ref. [10]). Usually, these models assume a constant total number of traders partitioned dynamically into different behavior groups, e.g. “chartists” and “fundamentalists”. A combinatorial partitioning model with a variable number of traders was recently described in Ref. [11]. In the next section, we propose a continuum dynamics model with a variable number of traders in terms of observable variables 1. Its deterministic properties are described in Section 3. It is concluded that the discrete model may be more appropriate for describing a transition to a liquid market. Examples of stochastic modeling of the birth of a liquid market are discussed in Section 4.