An Agent‐Based model for Limit Order Book: Estimation and simulation

Abstract

In this article, we introduce an agent‐based model for a Limit Order Book (LOB) market with a price limit and simulate and estimate its parameters. In this framework, we have reached a linear relation between the percentage of the sellers in the market and the changes in the logarithm of the price. Moreover, we demonstrate that in this model if the supply and demand are equal and naturally if the demand is more than the supply, on the average, logarithm of the price strictly increases and this occurs while in the model argued, the inflation is assumed to be zero, no real factor exists in order to increase the value of stocks and no factor‐like rumors enters. This conclusion implies that merely the normal activities of the dealers to gain profit causes a false increase in the stock price. This fact, as being demonstrated in the simulation, has also been proved analytically. We call this phenomenon “the intrinsic bubble”. Finally, we show that if the rules of the market change in the way that the daily price of the stock is calculated by the median of the prices traded, instead of their mean, this intrinsic bubble will more or less disappear.