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Theoretical and empirical analysis of trading activity

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...

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Detalles Bibliográficos
Autores principales: Pohl, Mathias, Ristig, Alexander, Schachermayer, Walter, Tangpi, Ludovic
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7319296/
https://www.ncbi.nlm.nih.gov/pubmed/32624621
http://dx.doi.org/10.1007/s10107-018-1341-x
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author Pohl, Mathias
Ristig, Alexander
Schachermayer, Walter
Tangpi, Ludovic
author_facet Pohl, Mathias
Ristig, Alexander
Schachermayer, Walter
Tangpi, Ludovic
author_sort Pohl, Mathias
collection PubMed
description 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 [Formula: see text] , 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., [Formula: see text] . More sophisticated relations are the so called 3/2-law [Formula: see text] and the intriguing scaling [Formula: see text] . 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 [Formula: see text] , which turns out to be more subtle than one might naively expect.
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spelling pubmed-73192962020-07-01 Theoretical and empirical analysis of trading activity Pohl, Mathias Ristig, Alexander Schachermayer, Walter Tangpi, Ludovic Math Program Full Length Paper 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 [Formula: see text] , 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., [Formula: see text] . More sophisticated relations are the so called 3/2-law [Formula: see text] and the intriguing scaling [Formula: see text] . 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 [Formula: see text] , which turns out to be more subtle than one might naively expect. Springer Berlin Heidelberg 2018-10-26 2020 /pmc/articles/PMC7319296/ /pubmed/32624621 http://dx.doi.org/10.1007/s10107-018-1341-x Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Full Length Paper
Pohl, Mathias
Ristig, Alexander
Schachermayer, Walter
Tangpi, Ludovic
Theoretical and empirical analysis of trading activity
title Theoretical and empirical analysis of trading activity
title_full Theoretical and empirical analysis of trading activity
title_fullStr Theoretical and empirical analysis of trading activity
title_full_unstemmed Theoretical and empirical analysis of trading activity
title_short Theoretical and empirical analysis of trading activity
title_sort theoretical and empirical analysis of trading activity
topic Full Length Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7319296/
https://www.ncbi.nlm.nih.gov/pubmed/32624621
http://dx.doi.org/10.1007/s10107-018-1341-x
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