Bayesian statistical inference addressed to share prices dynamics' theory

This paper examines the Osborne' Brownian motion theory to prices dynamics. Osborne's assumption is modified to account for the asymmetry of opportunity due to agents' update of the probability of profit overtime. We provide numerical illustrations to demonstrate the underlying behavior of these dynamics by considering the change in prices under an assumed conservative system and a dissipative system. Under a conservative system, results showed that the dynamics quickly converge to a global equilibrium, which is the marginal probability of profit in a fair game. Under a dissipative system, the dynamics can be described by a superposition of distributions in local equilibrium with constant variance satisfying locally the implications of Osborne's theory. Globally, the dynamics do not reach equilibrium, and its distribution exhibits asymmetries of opportunity and is characterized by a changing variance. We finally extend our work and provide empirical evidence that the variance dynamism of the S&P500 index undergoes statistical transition from high to low timeframe. Under high frequency, the lognormal and inverted gamma distributions best explain the variance dynamism; under low frequency, the gamma distribution best explains it. This conclusion paves the way to a new approach to volatility modeling and asset pricing by considering stock returns dynamics as a superposition of statistics with known mean and unknown variance, namely a superstatistics.