Asset flow model for a homogeneous group of investors: High-frequency trading limit

Abstract

Deterministic and stochastic asset flow models have been designed to study the effects of behavioral components on market dynamics. These models have been successful in explaining the mechanisms behind price overshoots, oscillations, reversals, liquidity- and value-induced market bubbles and oscillations, and flash crashes. While these models are originally nonlinear, we demonstrate here that, in the case of a market consisting of a homogeneous group of investors with identical trading sentiments, natural modifications of the response functions yield a version that can be represented by a linear dynamical system across the entire state space of the system. We show that this linear version exhibits all types of price behavior, just like the nonlinear version, while also having the benefit of being explicitly integrable even with time-varying parameters. We present a limiting case of the model that corresponds to fast trading, which is appropriate for modern electronic markets, and provide examples illustrating the differences in the response of the price to variability in the intrinsic value of shares or liquidity.