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

Estimating Stable Fixed Points and Langevin Potentials for Financial Dynamics