A low intelligence model which can explain market liquidity

Classical economists often assume perfect rationality of traders when they study financial markets. Though such theory can prove the existence of equilibrium prices, it cannot say anything about the quantities that are important for attendees in real stock markets, such as the spread (the size of gap between ask and bid) and market impact function (which describes the response of quoted prices to the arrival of new orders). On the other hand, recently, it has been shown that so-called ‘zero intelligence model’, in which traders have no intelligence and issue orders randomly (Poisson processes), can predict the spread and the diffusion rate of real stock markets. However, zero intelligence model cannot predict market impact such as Kyle's lambda, which shows the average price change when a unit order arrives. In our study, first, we clarified the nature of order arrival pattern observed in the empirical data (for example, order arriving rate depends on the distribution of limit orders in the order book). Second, we introduced the nature of order arrival pattern into the zero intelligence model. We call such a model ‘low intelligence model’. We showed that low intelligence model can explain, in addition to spread and diffusion rate, Kyle's lambda, explanation of which is difficult for either general equilibrium theory or the zero intelligence model. This result implies that, in order to know liquidity in a stock market, it is important to understand the interaction between orders and the book, and also that between some orders and other orders.