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We present a plausible micro-founded model for the previously postulatedpower law finite time singular form of the crash hazard rate in theJohansen-Ledoit-Sornette model of rational expectation bubbles. The model isbased on a percolation picture of the network of traders and the concept thatclusters of connected traders share the same opinion. The key ingredient is thenotion that a shift of position from buyer to seller of a sufficiently largegroup of traders can trigger a crash. This provides a formula to estimate thecrash hazard rate by summation over percolation clusters above a minimum sizeof a power sa (with a > 1) of the cluster sizes s, similarly to a generalizedpercolation susceptibility. The power sa of cluster sizes emerges from thesuper-linear dependence of group activity as a function of group size,previously documented in the literature. The crash hazard rate exhibitsexplosive finite-time singular behaviors when the control parameter (fractionof occupied sites, or density of traders in the network) approaches thepercolation threshold pc. Realistic dynamics are generated by modelling thedensity of traders on the percolation network by an Ornstein-Uhlenbeck process,whose memory controls the spontaneous excursion of the control parameter closeto the critical region of bubble formation. Our numerical simulations recoverthe main stylized properties of the JLS model with intermittent explosivesuper-exponential bubbles interrupted by crashes.

Micro-foundation using percolation theory of the finite-time singular behavior of the crash hazard rate in a class of rational expectation bubbles