Preferred numbers and the distribution of trade sizes and trading volumes in the Chinese stock market

TL;DR

This paper analyzes the distribution of trade sizes and volumes in the Chinese stock market, revealing jump patterns due to trader preferences and fitting these distributions with the $q$-Gamma function, showing power-law tails with exponents exceeding 2.

Contribution

It demonstrates the applicability of the $q$-Gamma distribution to model trade size and volume distributions in a Chinese stock market context, highlighting the impact of trader preferences.

Findings

Trade size distribution exhibits jumps caused by trader preferences.

$q$-Gamma function fits trading volume distributions well for certain transaction counts.

Trade volume distributions have power-law tails with exponents greater than 2.

Abstract

The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the "$q$-Gamma" function for fitting the distribution by the Cram\'{e}r-von Mises criterion. The empirical PDFs of trading volumes at different timescales $\Delta{t}$ ranging from 1 min to 240 min can be well modeled. The applicability of the $q$-Gamma functions for multiple trades is restricted to the transaction numbers $\Delta{n}\leqslant8$. We find that all the PDFs have power-law tails for large volumes. Using careful estimation of the average tail exponents $\alpha$ of the distribution of trade sizes and trading volumes, we get $\alpha>2$, well outside the L{\'e}vy regime.