Jump-diffusion models of parametric volume-price distributions
This work provides insights into financial market microstructure by characterizing jump-diffusion dynamics in volume-price distributions, though it is incremental as it applies existing statistical methods to new data.
The authors tackled the problem of modeling the stochastic evolution of volume-price distributions from NYSE equities by fitting empirical data to parametric models and analyzing detrended parameters, showing that scale parameters exhibit jump-diffusion dynamics with rare discontinuities dominating volatility, while shape parameters are predominantly diffusive.
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, $θ$, 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) $Ï$ 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 $Ï$ 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.