A Dynamical Model for Financial Market: Among Common Market Strategies Who and How Moves the Price to Fluctuate, Inflate, and Burst?

Abstract

A piecewise linear dynamical model is proposed for a stock price. The model considers the price is driven by three rather standard demand components: chartist, fundamental and market makers. The chartist demand component is related to the study of differences between moving averages. This generates a high order system characterized by a piecewise linear map not trivial to study. The model has been studied analytically in its fixed points and dynamics and then numerically. Results are in line with the related literature: the fundamental demand component helps the stability of the system and keeps prices bounded; market makers satisfy their role of restoring stability, while the chartist demand component produces irregularity and chaos. However, in some cases, the chartist demand component assumes the role to compensate the fundamental demand component, felt in an autogenerated loop, and pushes the dynamics to equilibrium. This fact suggests that the instability must not be searched into the nature of the different investment styles rather in the relative proportion of the contribution of market actors.