Jump-diffusion models of parametric volume-price distributions

A team of researchers has published a significant paper on arXiv titled 'Jump-diffusion models of parametric volume-price distributions,' introducing a sophisticated, data-driven framework to decode the complex stochastic behavior of stock market dynamics. The study analyzes high-frequency data from New York Stock Exchange (NYSE) equities, sampling empirical volume-price distributions every 10 minutes across 976 trading days. The core methodology involves fitting this massive dataset to four parametric statistical models—Gamma, Inverse Gamma, Weibull, and Log-Normal—each described by a shape (φ) and scale (θ) parameter. The researchers then detrend these parameters from their daily averages and apply advanced techniques like adaptive binning and regression-based extraction of Kramers-Moyal (KM) coefficients to classify the intrinsic dynamics.

The analysis yields a crucial insight into what drives market volatility. For the Gamma, Inverse Gamma, and Weibull models, the scale parameter (θ) shows dominant 'jump-diffusion' dynamics, characterized by elevated contributions from fourth- and sixth-order moments. This means its evolution is not a smooth process but is punctuated by significant, discontinuous jumps. Global moment inversion confirms that these rare jumps account for a large share of the total variance in θ. In contrast, the shape parameter (φ) for these models behaves more predictably as a pure diffusion. Interestingly, the Log-Normal model flips this script, with θ being predominantly diffusive and φ showing weak jump signatures. This research provides a new mathematical lens, moving beyond traditional models, to show that abrupt, rare events are a primary engine of observable market volatility.