Self-organized percolation model for stock market fluctuations

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Abstract

In the Cont–Bouchaud model [cond-mat/9712318] of stock markets, percolation clusters act as buying or selling investors and their statistics controls that of the price variations. Rather than fixing the concentration controlling each cluster connectivity artificially at or close to the critical value, we propose that clusters shatter and aggregate continuously as the concentration evolves randomly, reflecting the incessant time evolution of groups of opinions and market moods. By the mechanism of “sweeping of an instability” [Sornette, J. Phys. I 4, 209 (1994)], this market model spontaneously exhibits reasonable power-law statistics for the distribution of price changes and accounts for the other important stylized facts of stock market price 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 p to pc 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 p controlling the connectivity/influence 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 interaction/connectivity parameter p, i.e. a continuous increase up to the critical value pc 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 1999). 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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