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We show that the quotient of Levy processes of jump-diffusion type has a fat-tailed distribution. An application is to price theory in economics. We show that fat tails arise endogenously from modeling of price change based on an excess demand analysis resulting in a quotient of arbitrarily correlated demand and supply whether or not jump discontinuities are present. The assumption is that supply and demand are described by drift terms, Brownian (i.e., Gaussian) and compound Poisson jump processes. If $P^{-1}dP/dt$ (the relative price change in an interval $dt$) is given by a suitable function of relative excess demand, $\left( \mathcal{D}% -\mathcal{S}\right) /\mathcal{S}$ (where $\mathcal{D}$ and $\mathcal{S}$ are demand and supply), then the distribution has tail behavior $F\left( x\right) \sim x^{-\zeta}$ for a power $\zeta$ that depends on the function $G$ in $P^{-1}dP/dt=G\left( \mathcal{D}/\mathcal{S}\right) $. For $G\left( x\right) \sim\left\vert x\right\vert ^{1/q}$ one has $\zeta=q.$ The empirical data for assets typically yields a value, $\zeta\tilde{=}3,$ or $\ \zeta \in\left[ 3,5\right] $ for some markets. The discrepancy between the empirical result and theory never a

Author

Caginalp, Gunduz

Published

2020

Language

EN