Fat tails arise endogenously from modeling of price change based on  a quotient of arbitrarily correlated demand and supply (i.e., excess demand) whether or not jump discontinuities are present. The assumption is that supply and demand are described by drift terms, Brownian (i.e., Gaussians or normals ) 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  excess demand, \mathcal{D \left( \% -S}\right) /S -1 (where D and 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( D/S\right) . For G\left( x\right) \sim\left\vert x\right\vert ^{1/q} one has \zeta=q. The value, q\tilde{=} \in\left[ 3,5\right] is in agreement with empirical data. While many theoretical explanations have been offered for the paradox of fat tails, we show that this issue never arises if one models price dynamics using basic economics methodology,  rather than the usual starting point for classical finance which assumes a normal distribution of price changes. The function , G , can be calibrated in the absence of rare events . The results establish a simple link between the decay exponent of the density function and the price adjustment function, a feature that can improve methodology for risk assessment  .
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\% -S}\right) /S (where D and 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( D/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 arises if one models price dynamics using basic economics methodology, i.e., generalized Walrasian adjustment, rather than the usual starting point for classical finance which assumes a normal distribution of price changes. The function G is deterministic, and can be calibrated with a smaller data set . The results establish a simple link between the decay exponent of the density function and the price adjustment function, a feature that can improve methodology for risk assessment . The mathematical results can be applied to other problems involving the relative difference or quotient of Levy processes of jump-diffusion type .
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Fat
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
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an excess demand analysis resulting in
D
(i.e., excess demand)
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Gaussians or normals
Gaussian
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relative
D
\mathcal{D
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\mathcal{D
D
-1
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value, q
empirical data for assets typically yields a value, \zeta
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3, or \ \zeta
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is in agreement with empirical data. While many theoretical explanations have been offered for the paradox of fat tails, we show that this issue
for some markets. The discrepancy between the empirical result and theory
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i.e., generalized Walrasian adjustment,
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, G ,
G is deterministic, and
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in the absence of rare events
with a smaller data set
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. The mathematical results can be applied to other problems involving the relative difference or quotient of Levy processes of jump-diffusion type