https://doi.org/10.1140/epjs/s11734-026-02323-w
Regular Article
Jump-diffusion models of parametric volume–price distributions
1
Department of Computer Science, OsloMet–Oslo Metropolitan University, Pilestredet 52, 0166, Oslo, Norway
2
Department of Environmental Sciences, Faculty of Science, Open University of The Netherlands, 6419AT, Heerlen, The Netherlands
3
Faculty of Science and Technology, Norwegian University of Life Sciences, 1432, Ås, Norway
4
School of Economics, Innovation and Technology, Kristiania University of Applied Sciences, Kirkegata 24-26, 0153, Oslo, Norway
a
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Received:
27
November
2025
Accepted:
15
April
2026
Published online:
7
May
2026
Abstract
We present a data-driven framework to model the stochastic evolution of volume–price distribution from the New York Stock Exchange (NYSE) equities. The empirical distributions are sampled every 10 min over 976 trading days, and fitted to different models, namely Gamma, Inverse Gamma, Weibull, and Log-Normal distributions. Each of these models is parameterized by a shape parameter, 
, and a scale parameter, 
, which are detrended from their daily average behavior. The time series of the detrended parameters is analyzed using adaptive binning and regression-based extraction of the Kramers–Moyal (KM) coefficients, up to their sixth order, enabling the classification of its intrinsic dynamics. We show that (i) is well described as a pure diffusion with a linear mean regression for the Gamma, Inverse Gamma, and Weibull models, while shows dominant jump-diffusion dynamics, with an elevated fourth- and sixth-order moment contributions; (ii) the log-normal model shows however the opposite: is predominantly diffusive, with showing weak jump signatures; (iii) global moment inversion yields jump rates and amplitudes that account for a large share of total variance for , confirming that rare discontinuities dominate volatility.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
