Asymmetric Lévy flight in financial ratios

Podobnik, Boris and Valentinčić, Aljoša and Horvatić, Davor and Stanley, H. Eugene (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. ISSN 0027-8424

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Abstract

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.

Item Type: Article
Keywords: financial ratios, complex systems, econophysics, rating migrations
Date: 17 October 2011
Subjects: NATURAL SCIENCES > Physics
NATURAL SCIENCES > Physics > Econophysics
Additional Information: © 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.
Divisions: Faculty of Science > Department of Physics
Project code: 119-0982930-1016, 114-0352827-1370
Publisher: National Academy of Sciences
Depositing User: Davor Horvatić
Date Deposited: 04 May 2016 12:20
Last Modified: 04 May 2016 12:29
URI: http://digre.pmf.unizg.hr/id/eprint/4804

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