2016/02/09 by Benzaquen, Michael, Donier, Jonathan, Bouchaud, Jean-Philippe
#FOS: Economics and business #Trading and Market Microstructure (q-fin.TR)
paper · doi:10.48550/arxiv.1602.03011
We confirm and substantially extend the recent empirical result of Andersen et al. \citeAndersen2015, where it is shown that the amount of risk W exchanged in the E-mini S&P futures market (i.e. price times volume times volatility) scales like the 3/2 power of the number of trades N. We show that this 3/2-law holds very precisely across 12 futures contracts and 300 single US stocks, and across a wide range of time scales. However, we find that the "trading invariant" I=W/N3/2 proposed by Kyle and Obizhaeva is in fact quite different for different contracts, in particular between futures and single stocks. Our analysis suggests I/\cal C as a more natural candidate, where \cal C is the average spread cost of a trade, defined as the average of the trade size times the bid-ask spread. We also establish two more complex scaling laws for the volatility σ and the traded volume V as a function of N, that reveal the existence of a characteristic number of trades N0 above which the expected behaviour σ∼ √(N) and V ∼ N hold, but below which strong deviations appear, induced by the size of the~tick.