A Theory of Fluctuations in Stock Prices

TL;DR

This paper develops an analytical model for stock return distributions based on uncorrelated diffusive dynamics influenced by a consensus value, providing insights into fluctuations and their dependence on changing market consensus.

Contribution

It introduces a new analytical expression for return distributions considering a dynamic diffusion rate linked to deviation from a consensus stock value.

Findings

Analytical expression matches histograms in simple cases.

Distribution depends on the diffusion rate and consensus stability.

Qualitative explanations for effects of changing consensus value.

Abstract

The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the deviation of the stock price from the consensus value. We find an analytical expression for the distribution of returns in terms of the diffusion rate, when the consensus value is assumed to be fixed in time. The analytical solution is shown to match computed histograms in two simple cases. Differences that result when the consensus value is allowed to change with time are presented qualitative explanations.