  One of the greatest contributors of the 20th century among all academician in
the field of statistical finance, M. F. M. Osborne published in 1956 [6] an
essential paper and proposed to treat the question of stock market motion
through the prism of both the Law of Weber-Fechner [1, 4] and the branch of
physics developed by James Clerk Maxwell, Ludwig Boltzmann and Josiah Willard
Gibbs [3, 5] namely the statistical mechanics. He proposed an improvement of
the known research made by his predecessor Louis Jean-Baptiste Alphonse
Bachelier, by not considering the arithmetic changes of stock prices as means
of statistical measurement, but by drawing on the Weber-Fechner Law, to treat
the changes of prices. Osborne emphasized that as in statistical mechanics, the
probability distribution of the steady-state of subjective change in prices is
determined by the condition of maximum probability, a statement close to the
Gibbs distribution conditions. However, Osborne also admitted that the
empirical observation of the probability distribution of logarithmic changes of
stock prices was emphasizing obvious asymmetries and consequently could not
perfectly confirm his prior theory. The purpose of this paper is to propose an
explanation to what we could call the Osborne paradox and then address an
alternative approach via Bayesian inference regarding the description of the
probability distribution of changes in logarithms of prices that was
thenceforth under the prism of frequentist inference. We show that the stock
market returns are locally described by equilibrium statistical mechanics with
conserved statistics variables, whereas globally there is yet other statistics
with persistent flowing variables that can be effectively described by a
superposition of several statistics on different time scales, namely, a
superstatistics.
