Asymmetric Lévy flight in financial ratios

Scientific paper - Original scientific paper

• Author: Boris Podobnik
• Author: Aljoša Valentinčić
• Author: Davor Horvatić
• Author: H. Eugene Stanley
• Author's institution: University 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 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.

• Keywords (english): financial ratios; complex systems; econophysics; rating migrations
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Proceedings of the National Academy of Sciences of the United States of America
• Numbering: vol. 108, no. 44, pp. 17883-17888
• p-ISSN: 0027-8424
• DOI: https://doi.org/10.1073/pnas.1113330108
• URN:NBN: urn:nbn:hr:217:376358
• Publication: 2011
• Document URL: https://www.pnas.org/content/108/44/17883
• Type of resource: Text
• Access conditions: Open access
• 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 on: 2019-11-15 16:18:34