Predator–prey model for stock market fluctuations

We present a dynamical model for the price evolution of financial assets. The model is based on a two-level approach: In the first stage, one finds an agent-based model that describes the current state of investors’ beliefs, perspectives or strategies. The dynamics is inspired by a model for describing predator–prey population evolution: Agents change their mind through self- or mutual interaction, and the decision is adopted on a random basis, with no direct influence of the price itself. One of the most appealing properties of such a system is the presence of large oscillations in the number of agents sharing the same perspective, what may be linked with the existence of bullish and bearish periods in financial markets. In the second stage, one has the pricing mechanism, which will be driven by the relative population in the different groups of investors. The price equation will depend on the specific nature of the species, and thus, it may change from one market to the other: We will present a simple model of excess demand in the first place and then consider a more elaborate liquidity model. The outcomes of both models are analyzed and compared.