1206.4420 (Thomas Bury)
Thomas Bury
Financial markets are a classical example of complex systems as they are compound by many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics. Here we show that the pairwise model is actually a statistically consistent model with the observed first and second moments of the stocks orientation without making such restrictive assumptions. Our data analysis of six major indices suggests that the actual interaction structure is mathematically equivalent to an Ising model on a complete graph with gaussian interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviors, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.
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http://arxiv.org/abs/1206.4420
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