Invasion–percolation and statistics of US Treasury bonds

Using a model of analytic branching cascades on fractal clusters it is shown that US Treasury securities returns fluctuations exhibit three types of stochastic behaviors: (a) quasi-Brownian type for a very small cluster consisting of just a single bond; (b) lognormal type for a medium-size very compact cluster (branching dimension d=1); and (c) a stretched lognormal distribution (corresponding to branching dimension d=2) for the largest cluster. An analogy with multifractality at the onset of chaos is also discussed.