Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7375714 | Physica A: Statistical Mechanics and its Applications | 2018 | 15 Pages |
Abstract
The quotient of random variables with normal distributions is examined and proven to have power law decay, with density fxâf0xâ2, with the coefficient depending on the means and variances of the numerator and denominator and their correlation. We also obtain the conditional probability densities for each of the four quadrants given by the signs of the numerator and denominator for arbitrary correlation Ïâ[â1,1). For Ï=â1 we obtain a particularly simple closed form solution for all xâR. The results are applied to a basic issue in economics and finance, namely the density of relative price changes. Classical finance stipulates a normal distribution of relative price changes, though empirical studies suggest a power law at the tail end. By considering the supply and demand in a basic price change model, we prove that the relative price change has density that decays with an xâ2 power law. Various parameter limits are established.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Carey Caginalp, Gunduz Caginalp,