For Gamma-family fits to NYSE volume-price data the shape parameter follows diffusive mean-reverting dynamics while the scale parameter shows dominant jump-diffusion with elevated higher moments, and jumps explain a large share of variance; the log-normal model reverses the pattern.
Stochastic modelling of non-stationary financial assets
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abstract
We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely biology, medicine and geology.
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cs.NE 1years
2025 1verdicts
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Jump-diffusion models of parametric volume-price distributions
For Gamma-family fits to NYSE volume-price data the shape parameter follows diffusive mean-reverting dynamics while the scale parameter shows dominant jump-diffusion with elevated higher moments, and jumps explain a large share of variance; the log-normal model reverses the pattern.