Heavy-tailed distributions of volume and price-change resulting from strategy coordination and decision noise

Abstract

An agent-based model is created to determine the distribution of volume and price change resulting from orders to purchase a stock from high-frequency/short-term, boundedly rational trading agents. The agents who place the orders follow different strategies. Agents who follow the same strategy have coordinated behavior, even if they do not share information—this is tacit collusion (explicit collusion happened during the GameStop and other short squeezes). We look at incoming orders that are composed of a given number of agents that can range from one to ten thousand. It is assumed that each incoming order is a result of a trigger from a particular strategy. A square root price impact function is used to determine the effect on price as a result of the order. The profit of an agent is determined from this price change since they are high-frequency traders. The model produces power-law distributions for individual quantity, aggregate quantity, and price-change, and we fit three stocks to the model by adjusting the temperature. When the market reflects reversion-to-the-mean behavior, the distributions appear to have lighter tails than when the market reflects the hot-hand behavior. The higher risk of heavier tails is seen to be a result of hot-hand trading behavior for this model. The model also has a phase transition in the hot-hand component, in the sense of a nonanalyticity, where the order parameter is the exponent of the power-law tail of the c.d.f. function for aggregate quantity Q. This order parameter is a function of the temperature, varies linearly with inverse temperature in a high-temperature region, and varies nonlinearly in a low-temperature region. The relationship predicted between temperature and aggregate volume has been validated by data from the GameStop short squeeze.