Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading”
In this paper a comparative, coarse grained, entropy data analysis of multi-scale log-returns distribution, produced by an ideal “optimal trader” and one thousand “noise traders” performing “bucket shop” trading, by following four different financial daily indices, is presented. A sole optimal trade...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/2/215 |
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| author | Alejandro Raúl Hernández-Montoya Carlos Manuel Rodríguez-Martínez Manuel Enríque Rodríguez-Achach David Hernández-Enríquez |
| author_facet | Alejandro Raúl Hernández-Montoya Carlos Manuel Rodríguez-Martínez Manuel Enríque Rodríguez-Achach David Hernández-Enríquez |
| author_sort | Alejandro Raúl Hernández-Montoya |
| collection | DOAJ |
| description | In this paper a comparative, coarse grained, entropy data analysis of multi-scale log-returns distribution, produced by an ideal “optimal trader” and one thousand “noise traders” performing “bucket shop” trading, by following four different financial daily indices, is presented. A sole optimal trader is assigned to each one of these four analyzed markets, DJIA, IPC, Nikkei and DAX. Distribution of differential entropies of the corresponding multi-scale log-returns of the optimal and noise traders are calculated. Kullback-Leiber distances between the different optimal traders returns distributions are also calculated and results discussed. We show that the entropy of returns distribution of optimal traders for each analyzed market indeed reaches minimum values with respect to entropy distribution of noise traders and we measure this distance in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula> units for each analyzed market. We also include a discussion on stationarity of the introduced multi-scale log-returns observable. Finally, a practical application of the obtained results related with ranking markets by their entropy measure as calculated here is presented. |
| first_indexed | 2024-03-10T01:01:28Z |
| format | Article |
| id | doaj.art-59e68e78eea94a5989af757a487fcf7d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:01:28Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-59e68e78eea94a5989af757a487fcf7d2023-11-23T14:34:06ZengMDPI AGMathematics2227-73902022-01-0110221510.3390/math10020215Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading”Alejandro Raúl Hernández-Montoya0Carlos Manuel Rodríguez-Martínez1Manuel Enríque Rodríguez-Achach2David Hernández-Enríquez3Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Xalapa Veracruz 91097, MexicoInstituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Xalapa Veracruz 91097, MexicoUnidad Experimental Marista (UNEXMAR), Universidad Marista de Mérida, Mérida Yucatán 97300, MexicoInstituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Xalapa Veracruz 91097, MexicoIn this paper a comparative, coarse grained, entropy data analysis of multi-scale log-returns distribution, produced by an ideal “optimal trader” and one thousand “noise traders” performing “bucket shop” trading, by following four different financial daily indices, is presented. A sole optimal trader is assigned to each one of these four analyzed markets, DJIA, IPC, Nikkei and DAX. Distribution of differential entropies of the corresponding multi-scale log-returns of the optimal and noise traders are calculated. Kullback-Leiber distances between the different optimal traders returns distributions are also calculated and results discussed. We show that the entropy of returns distribution of optimal traders for each analyzed market indeed reaches minimum values with respect to entropy distribution of noise traders and we measure this distance in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula> units for each analyzed market. We also include a discussion on stationarity of the introduced multi-scale log-returns observable. Finally, a practical application of the obtained results related with ranking markets by their entropy measure as calculated here is presented.https://www.mdpi.com/2227-7390/10/2/215financial marketsentropyprice trendsmulti-scale returnsoptimal tradernoise trader |
| spellingShingle | Alejandro Raúl Hernández-Montoya Carlos Manuel Rodríguez-Martínez Manuel Enríque Rodríguez-Achach David Hernández-Enríquez Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading” Mathematics financial markets entropy price trends multi-scale returns optimal trader noise trader |
| title | Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading” |
| title_full | Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading” |
| title_fullStr | Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading” |
| title_full_unstemmed | Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading” |
| title_short | Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading” |
| title_sort | entropy variations of multi scale returns of optimal and noise traders engaged in bucket shop trading |
| topic | financial markets entropy price trends multi-scale returns optimal trader noise trader |
| url | https://www.mdpi.com/2227-7390/10/2/215 |
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