  The Geometric Brownian Motion (GBM) is a standard model in quantitative
finance, but the potential function of its stochastic differential equation
(SDE) cannot include stable nonzero prices. This article generalises the GBM to
an SDE with polynomial drift of order q and shows via model selection that q=2
is most frequently the optimal model to describe the data. Moreover, Markov
chain Monte Carlo ensembles of the accompanying potential functions show a
clear and pronounced potential well, indicating the existence of a stable
price.
