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Theoretical and empirical analysis of trading activity.


ABSTRACT: 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 ?2 , 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??2 . More sophisticated relations are the so called 3/2-law N3/2??PV/C and the intriguing scaling N?(?P/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 ? , which turns out to be more subtle than one might naively expect.

SUBMITTER: Pohl M 

PROVIDER: S-EPMC7319296 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Theoretical and empirical analysis of trading activity.

Pohl Mathias M   Ristig Alexander A   Schachermayer Walter W   Tangpi Ludovic L  

Mathematical programming 20181026 2


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 <i>N</i>, the traded volume <i>V</i>, the asset price <i>P</i>, the squared volatility σ2 , the bid-ask spread <i>S</i> and the cost of trading <i>C</i>. Different reasonings result in simple proportionality relations ("scaling laws") between these variables. A basi  ...[more]

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