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Modifications of the Cont-Bouchaud percolation model for price fluctuations give an asymmetry for time-reversal, an asymmetry between high and low prices, volatility clustering, effective multifractality, correlations between volatility and traded volume, and a power law tail with exponent near 3 for the cumulative distribution function of price changes. Combining them together still gives the same power law. Using Ising-correlated percolation does not change these results. Different modifications give log-periodic oscillations before a crash, arising from nonlinear feedback between random fluctuations.

ASYMMETRIES, CORRELATIONS AND FAT TAILS IN PERCOLATION MARKET MODEL