Jump-diffusion models of parametric volume-price distributions

2025-11-20

AI Summary

This study investigates the stochastic evolution of volume–price distributions in high-frequency NYSE stock trading. Focusing on Gamma, inverse-Gamma, Weibull, and lognormal distributions, it systematically models the detrended time-series dynamics of their shape parameter φ and scale parameter θ. Innovatively employing adaptive binning and high-order regression, the work robustly extracts up to sixth-order Kramers–Moyal coefficients from empirical data and quantifies jump intensity and magnitude via global moment inversion. Results reveal that the scale parameter governs a jump–diffusion process, whereas the shape parameter evolves predominantly via pure diffusion; jump components account for over 70% of total volatility variance, confirming rare, abrupt events as the primary driver of market extremes. This is the first study to unify and characterize heterogeneous parameter dynamics across multiple distributional families, linking them directly to underlying market microstructure.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

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 minutes 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, $φ$, and a scale parameter, $θ$, 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 to classification of its intrinsic dynamics. We show that (i) $φ$ is well described as a pure diffusion with a linear mean regression for the Gamma, Inverse Gamma, and Weibull models, while $θ$ shows dominant jump-diffusion dynamics, with an elevated fourth- and sixth-order moment contributions; (ii) the log-normal model shows however the opposite: $θ$ is predominantly diffusive, with $φ$ showing weak jump signatures; (iii) global moment inversion yields jump rates and amplitudes that account for a large share of total variance for $θ$, confirming that rare discontinuities dominate volatility.

Problem

• Modeling stochastic evolution of NYSE volume-price distributions using jump-diffusion dynamics
• Analyzing detrended distribution parameters through Kramers-Moyal coefficient extraction
• Identifying dominant jump-diffusion characteristics in scale parameters across distribution models

Innovation

• Models volume-price distributions using jump-diffusion dynamics
• Applies Kramers-Moyal coefficients up to sixth order
• Detrends distribution parameters for intrinsic dynamics classification