Abstract
We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade stock (or any other risky asset for that matter) at the market price or place a limit order, i.e., an instruction to buy (sell) a certain amount of the stock if its price falls below (raises above) a predefined level. The choice between these two options is purely random (there are no strategies involved), and the execution price of a limit order is determined simply by offsetting the most recent market price by a random amount. Numerical simulations of this model revealed that despite such minimalistic rules the price pattern generated by this model has such realistic features as “fat” tails of the probability distribution of price fluctuations, characterized by a crossover between two power law exponents, long range correlations of the volatility, and a non-trivial Hurst exponent of the price signal.
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