Are the Trading Volume and the Number of Trades Distributions Universal?

Abstract

Analysis of dynamical phenomena in financial markets have revealed the existence of several features that appear to be invariant with respect to details of the specific markets being considered. While some of these “stylized facts”, such as the inverse cubic law distribution of price returns indeed seem to be universal, there is less consensus about other phenomena. In particular, there has been a long-running debate in the literature about whether the distributions of trading volume V _Δt and the number of trades N _Δt occurring in a given time interval Δt, are universal, and whether the volume distribution is Levy-stable. In this article, we analyse data from the National Stock Exchange of India, both daily and high frequency tick-by-tick, to answer the above questions. We observe that it is difficult to fit the V _Δt and N _Δt distributions for all stocks using the same theoretical curve, e.g., one having a power-law form. Instead, we use the concept of the stability of a distribution under temporal aggregation of data to show that both these distributions converge towards a Gaussian when considered at a time-scale of Δt = 10 days. This appears to rule out the possibility that either of these distributions could be Levy-stable and at least for the Indian market, the claim for universality of the volume distribution does not hold.