High-frequency Uniswap v3 crypto data show non-quadratic potentials, with double-well shapes at short sampling frequencies that the author links to market stress.
Estimating Stable Fixed Points and Langevin Potentials for Financial Dynamics
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abstract
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.
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Non-Linear and Meta-Stable Dynamics in Financial Markets: Evidence from High Frequency Crypto Currency Market Makers
High-frequency Uniswap v3 crypto data show non-quadratic potentials, with double-well shapes at short sampling frequencies that the author links to market stress.