On the non-linear stochastic price adjustment of securities

Abstract

We introduce a type of Itô process that models the adjustment of the market price of a traded security to new information affecting supply and demand. It is based on supply and demand functions and the Walrasian price adjustment assumption that proportional price increase is driven by excess demand. When supply and demand curves are linearised about the equilibrium point, the process turns out to be a logistic form of Brownian motion with random element of the Wiener type.

Keywords: Excess demand function, Walrasian price adjustment process, Logistic Brownian motion.

> East African Journal of Statistics Vol. 1 (1) 2005: pp. 109-116