Estimating Stable Fixed Points and Langevin Potentials for Financial Dynamics
Statistical Finance
2023-11-29 v2 Data Analysis, Statistics and Probability
Applications
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.
Cite
@article{arxiv.2309.12082,
title = {Estimating Stable Fixed Points and Langevin Potentials for Financial Dynamics},
author = {Tobias Wand and Timo Wiedemann and Jan Harren and Oliver Kamps},
journal= {arXiv preprint arXiv:2309.12082},
year = {2023}
}
Comments
10 pages, 6 figures