Predator-Prey Model for Stock Market Fluctuations
20 Pages Posted: 29 Oct 2008
Date Written: October 27, 2008
We present a dynamical model that describes the evolution of offer and demand in a financial market. The model considers a fully connected network of interacting agents that may be willing to operate in the market, either by selling the stock or by buying it, or that are not interested in operating at that moment. The agents change their mind through self- or mutual influence, and the decision is adopted on a random basis, like in a predator-prey model. One of the most appealing characteristics of such a system is the presence of large oscillations in the number of agents sharing the same perspective. This finite-size effect is self-instigated by an endogenous noise-induced magnification with a characteristic frequency.
This set-up can be used in the modelling of the limit order book. In our case, the difference in population of the two sets of active agents, sellers and buyers, will be directly translated into the evolution of the stock through a simple model of excess demand, that will rise the price when there are more buyers than sellers in the market, and fall it in the opposite case. The random nature of the size of each agent category is responsible for the stochastic component in the asset value evolution, whereas the oscillating behaviour promotes the presence of bullish and bearish periods in the data series in a natural way, with no external interference needed.
We will simulate the time evolution of the system under archetypical market conditions, analyse the most relevant traits, and compare them afterwards with empirically obtained properties.
Keywords: Models of financial markets, Interacting agent models, Stochastic processes
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