Universität zu Köln

Yarahmadi, Hediye ORCID: 0000-0002-7954-9885 and Saberi, Abbas Ali ORCID: 0000-0001-8864-4748 (2022). A 2D Levy-flight model for the complex dynamics of real-life financial markets. Chaos, 32 (3). MELVILLE: AIP Publishing. ISSN 1089-7682

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Abstract

We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S&P 500 index prices and its modeling based on the Levy flights in two dimensions (2D). The efficacy of our proposed model is verified and validated by using the extreme value statistics in the random matrix theory. We find that the random evolution of each pair of stocks in a 2D price space is a scale-invariant complex trajectory whose tortuosity is governed by a 2/3 geometric law between the gyration radius R-g (t) and the total length l(t) of the path, i.e., R-g (t) similar to l(t)(2/3). We construct a Wishart matrix containing all stocks up to a specific variable period and look at its spectral properties for over 30 years. In contrast to the standard random matrix theory, we find that the distribution of eigenvalues has a power-law tail with a decreasing exponent over time-a quantitative indicator of the temporal correlations. We find that the time evolution of the distance of 2D Levy flights with index alpha = 3/2 from origin generates the same empirical spectral properties. The statistics of the largest eigenvalues of the model and the observations are in perfect agreement.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Yarahmadi, Hediye UNSPECIFIED orcid.org/0000-0002-7954-9885 UNSPECIFIED Saberi, Abbas Ali UNSPECIFIED orcid.org/0000-0001-8864-4748 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-664130
DOI:	10.1063/5.0082926
Journal or Publication Title:	Chaos
Volume:	32
Number:	3
Date:	2022
Publisher:	AIP Publishing
Place of Publication:	MELVILLE
ISSN:	1089-7682
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language HIERARCHICAL STRUCTURE; CROSS-CORRELATIONS; SCALING BEHAVIOR; GROWTH DYNAMICS; RANDOM-WALKS; UNIVERSAL; DISTRIBUTIONS; FLUCTUATIONS; INFORMATION Multiple languages Mathematics, Applied; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66413