Physica A: Statistical Mechanics and its Applications
Self-organized percolation model for stock market fluctuations
Section snippets
The Percolation model of stock market prices
A wealth of models [1], [2], [3], [4], [5] (to our knowledge, the first stock market simulation was performed by the economist Stigler in 1964 [6]), partially listed in [7], have been introduced in the financial and more recently in the physical community which attempt to capture the complex behavior of stock market prices and of market participants. Based on the competition between supply and demand, the effort is to model the main observed stylized facts: absence of two-point correlation of
Percolation connectivity evolving with time
We thus return to an alternative mechanism [16] which gives power laws without the need to tune to and which is very robust and simple. The new idea we propose in this context is that there is no reason a priori to expect that the parameter controlling the connectivityinfluence between traders is fixed. The circle of professionals and colleagues to whom a trader is typically connected evolves as a function of time, not only in its structure at fixed average number of connections
Concluding remarks
We have presented what we believe is probably the simplest and most robust model of stock market dynamics without tunable parameters that self-organizes into a regime where the most important empirical characteristics of stock market price dynamics are captured.
In this simplest version, we have chosen the most straightforward dynamics of the interactionconnectivity parameter , i.e. a continuous increase up to the critical value followed by a reset to a low value and so on. Incorporating a
Acknowledgments
This idea originated at the meeting “Facets of Universality in Complex Systems: Climate, Biodynamics and Stock Markets”, organized at Giessen University by Armin Bunde and John Schellnhuber (June ). We thank NIC Jülich for time on their Cray-T3E, T.Lux for ref.3, and A. Johansen for comments. One of us (DS) wishes to point out that all errors are due to the other author (DS).
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