Narrow Results

We present results of an extension of the market model introduced by Bornholdt to high dimensions. Three and four dimensions are shown to behave similar to two, for suitable parameters.

We study an extension of the Bornholdt spin-market model using configurable network topology. The distribution of returns was studied using the probability plot correlation coefficient and indicates three different behaviors for the tails of the distribution of returns. The price volatility was studied by fitting the magnetization with a Wiener process and a power-law behavior was found for the volatility as a function of the levels of randomness and connectivity of the network. Both parameters have opposing effects on the risk as inferred from the Shannon entropy of the magnetization. Also, we show that trading can spatially auto-organize depending on the conditions of the control space. Finally, we show that there is a range of values of the control space that renders a model that reproduces real-market data.