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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 24: Financial Markets and Risk Management

SOE 24.1: Vortrag

Freitag, 22. März 2024, 10:00–10:15, MA 001

Estimating Stable Fixed Points and Langevin Potentials for Financial Dynamics — •Tobias Wand^1,2, Timo Wiedemann³, Jan Harren³, and Oliver Kamps¹ — ¹Center for Nonlinear Science, Universität Münster — ²Institut für Theoretische Physik, Universität Münster — ³Finance Center Münster, Universität Münster

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. Under strong constraints derived from additional data, evidence has been found that additional correction terms in the SDE's drift potential should be taken into consideration [1]. Our work 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 without requiring any additional constraints [2]. 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.

[1] Halperin and Dixon, Physica A: 537, 122187 (2019) [2] Wand et al., arXiv 2309.12082 (2023)

Keywords: Langevin Equation; Stochastic Differential Equation; Finance; Econophysics; Data-Driven Inference