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