For a Stock Market,the critical problem is the maintenance of its liquidity.Market liquidity can be described in various ways,in particular, in terms of the bid/offer spread and the market depth.Model of market liquidity dynamics has been proposed in Schmidt,A.B.'literate.In our study,we improve his model.On one hand,we think that trading volume is determined by the total number of traders,as well as the relations between the numbers of buyers and sellers,while the model of Schmidt only considers the first item.On the other hand,Schmidt assumes that the number of “newcomers”in the market is in proportion to the current number of trades.However,we all know that the continual rise or fall of the price will also attract more buyers or sellers,that is,“newcomers”,into the market,which he has not taken for granted.We also prove it to be a chaos model through analysis of Lyapunov exponent.On the assumption that price variation can be neglected,we discuss the conditions in which chaos will emerge.Finally,we implement a computer simulation of the model in MATLAB,and get more interesting results.
