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Scientific paper - Original scientific paper
Asymmetric Lévy flight in financial ratios
Proceedings of the National Academy of Sciences of the United States of America, 108 (2011), 44; 17883-17888. https://doi.org/10.1073/pnas.1113330108
Podobnik, Boris; Valentinčić, Aljoša; Horvatić, Davor; Stanley, H. Eugene

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Podobnik, B., Valentinčić, A., Horvatić, D. & Stanley, H. E. (2011). Asymmetric Lévy flight in financial ratios. Proceedings of the National Academy of Sciences of the United States of America, 108. (44), 17883-17888. doi: 10.1073/pnas.1113330108

Podobnik, Boris, et al. "Asymmetric Lévy flight in financial ratios." Proceedings of the National Academy of Sciences of the United States of America, vol. 108, no. 44, 2011, pp. 17883-17888. https://doi.org/10.1073/pnas.1113330108

Podobnik, Boris, Aljoša Valentinčić, Davor Horvatić and H. Eugene Stanley. "Asymmetric Lévy flight in financial ratios." Proceedings of the National Academy of Sciences of the United States of America 108, no. 44 (2011): 17883-17888. https://doi.org/10.1073/pnas.1113330108

Podobnik, B., et al. (2011) 'Asymmetric Lévy flight in financial ratios', Proceedings of the National Academy of Sciences of the United States of America, 108(44), pp. 17883-17888. doi: 10.1073/pnas.1113330108

Podobnik B, Valentinčić A, Horvatić D, Stanley HE. Asymmetric Lévy flight in financial ratios. Proceedings of the National Academy of Sciences of the United States of America [Internet]. 2011 [cited 2025 March 24];108(44):17883-17888. doi: 10.1073/pnas.1113330108

B. Podobnik, A. Valentinčić, D. Horvatić and H. E. Stanley, "Asymmetric Lévy flight in financial ratios", Proceedings of the National Academy of Sciences of the United States of America, vol. 108, no. 44, pp. 17883-17888, 2011. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:217:376358. [Accessed: 24 March 2025]

Metadata
Title (english)Asymmetric Lévy flight in financial ratios
AuthorBoris Podobnik
AuthorAljoša Valentinčić
AuthorDavor Horvatić
AuthorH. Eugene Stanley
Author's institutionUniversity of Zagreb
Faculty of Science
(Department of Physics)
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract (english)
Because financial crises are characterized by dangerous rare events that occur more frequently than those predicted by models with finite variances, we investigate the underlying stochastic process generating these events. In the 1960s Mandelbrot [Mandelbrot B (1963) J Bus 36:394–419] and Fama [Fama EF (1965) J Bus 38:34– 105] proposed a symmetric Lévy probability distribution function (PDF) to describe the stochastic properties of commodity changes and price changes. We find that an asymmetric... More Lévy PDF, L, characterized by infinite variance, models several multiple credit ratios used in financial accounting to quantify a firm’s financial health, such as the Altman [Altman EI (1968) J Financ 23:589–609] Z score and the Zmijewski [Zmijewski ME (1984) J Accounting Res 22:59–82] score, and models changes of individual financial ratios, ΔXi. We thus find that Lévy PDFs describe both the static and dynamics of credit ratings. We find that for the majority of ratios, ΔXi scales with the Lévy parameter ! ! 1, even though only a few of the individual ratios are characterized by a PDF with power-law tails with infinite variance. We also find that " exhibits a striking stability over time. A key element in estimating credit losses is the distribution of credit rating changes, the functional form of which is unknown for alphabetical ratings. For continuous credit ratings, the Altman Z score, we find that pdf follows a Lévy PDF with power-law exponent ! ! 1, consistent with changes of individual financial ratios. Estimating the conditional pdf versus Z, we demonstrate how this continuous credit rating approach and its dynamics can be used to evaluate credit risk. Less
Keywords (english)
Languageenglish
Publication typeScientific paper - Original scientific paper
Publication statusPublished
Peer reviewPeer review - international
Publication versionPublished version
Journal titleProceedings of the National Academy of Sciences of the United States of America
Numberingvol. 108, no. 44, pp. 17883-17888
p-ISSN0027-8424
DOIhttps://doi.org/10.1073/pnas.1113330108
URN:NBNurn:nbn:hr:217:376358
Publication2011
Document URLhttps://www.pnas.org/content/108/44/17883
Type of resourceText
Access conditionsOpen access
Terms of useLicence In copyright icon
Public note© 2011 National Academy of Sciences. Freely available online through the PNAS open access option. Contributed by H. Eugene Stanley, August 30, 2011 (sent for review July 7, 2011). Published online before print on October 17, 2011.
Created on2019-11-15 16:18:34
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