Optimal models of extreme volume-prices are time-dependent

TL;DR

This paper demonstrates that the optimal model for volume-price distributions in stocks varies depending on the specific data region and time period, emphasizing the need for adaptable modeling approaches.

Contribution

It shows that the best-fitting distribution model for volume-price data is context-dependent, challenging the notion of a universal model in financial data analysis.

Findings

Model accuracy varies with volume-price spectrum region.

Different models perform better in different time periods.

Tail-specific distance measures improve tail modeling accuracy.

Abstract

We present evidence that the best model for empirical volume-price distributions is not always the same and it strongly depends in (i) the region of the volume-price spectrum that one wants to model and (ii) the period in time that is being modelled. To show these two features we analyze stocks of the New York stock market with four different models: Gamma, inverse-gamma, log-normal, and Weibull distributions. To evaluate the accuracy of each model we use standard relative deviations as well as the Kullback-Leibler distance and introduce an additional distance particularly suited to evaluate how accurate are the models for the distribution tails (large volume-price). Finally we put our findings in perspective and discuss how they can be extended to other situations in finance engineering.