Jump-diffusion models of parametric volume-price distributions

TL;DR

This paper models the stochastic evolution of NYSE volume-price distributions using jump-diffusion models, analyzing parameters with Kramers-Moyal coefficients to classify their intrinsic dynamics.

Contribution

It introduces a data-driven framework applying jump-diffusion models and Kramers-Moyal analysis to characterize volume-price distribution dynamics.

Findings

Gamma, Inverse Gamma, Weibull parameters show diffusive and jump behaviors.

Log-normal model exhibits predominantly diffusive scale parameter with weak jump signatures.

Jump rates and amplitudes explain a large share of variance, indicating rare discontinuities dominate volatility.

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