TY - JOUR

T1 - Theoretical and empirical analysis of trading activity

AU - Pohl, Mathias

AU - Ristig, Alexander

AU - Schachermayer, Walter

AU - Tangpi, Ludovic

N1 - Funding Information:
Open access funding provided by Austrian Science Fund (FWF). We thank Jean-Philippe Bouchaud, Rama Cont, Friedrich Hubalek and particularly Mathieu Rosenbaum for helpful comments as well as interesting discussions.
Publisher Copyright:
© 2018, The Author(s).

PY - 2020/6/1

Y1 - 2020/6/1

N2 - Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades N, the traded volume V, the asset price P, the squared volatility σ2, the bid-ask spread S and the cost of trading C. Different reasonings result in simple proportionality relations (“scaling laws”) between these variables. A basic proportionality is established between the trading activity and the squared volatility, i.e., N∼ σ2. More sophisticated relations are the so called 3/2-law N3 / 2∼ σPV/ C and the intriguing scaling N∼ (σP/ S) 2. We prove that these “scaling laws” are the only possible relations for considered sets of variables by means of a well-known argument from physics: dimensional analysis. Moreover, we provide empirical evidence based on data from the NASDAQ stock exchange showing that the sophisticated relations hold with a certain degree of universality. Finally, we discuss the time scaling of the volatility σ, which turns out to be more subtle than one might naively expect.

AB - Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades N, the traded volume V, the asset price P, the squared volatility σ2, the bid-ask spread S and the cost of trading C. Different reasonings result in simple proportionality relations (“scaling laws”) between these variables. A basic proportionality is established between the trading activity and the squared volatility, i.e., N∼ σ2. More sophisticated relations are the so called 3/2-law N3 / 2∼ σPV/ C and the intriguing scaling N∼ (σP/ S) 2. We prove that these “scaling laws” are the only possible relations for considered sets of variables by means of a well-known argument from physics: dimensional analysis. Moreover, we provide empirical evidence based on data from the NASDAQ stock exchange showing that the sophisticated relations hold with a certain degree of universality. Finally, we discuss the time scaling of the volatility σ, which turns out to be more subtle than one might naively expect.

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U2 - 10.1007/s10107-018-1341-x

DO - 10.1007/s10107-018-1341-x

M3 - Article

C2 - 32624621

AN - SCOPUS:85055933622

SN - 0025-5610

VL - 181

SP - 405

EP - 434

JO - Mathematical Programming

JF - Mathematical Programming

IS - 2

ER -