NDLI: Asymmetric Lévy flight in financial ratios

Content Provider	PubMed Central
Author	Podobnik, Boris Valentinčič, Aljoša Horvatić, Davor Stanley, H. Eugene
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, , 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, ΔX i . We thus find that Lévy PDFs describe both the static and dynamics of credit ratings. We find that for the majority of ratios, ΔX i scales with the Lévy parameter α ≈ 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 α 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 P(ΔZ) follows a Lévy PDF with power-law exponent α ≈ 1, consistent with changes of individual financial ratios. Estimating the conditional P(ΔZ\|Z) versus Z, we demonstrate how this continuous credit rating approach and its dynamics can be used to evaluate credit risk.
Related Links	http://dx.doi.org/10.1073/pnas.1113330108
Ending Page	17888
Page Count	6
Starting Page	17883
File Format	PDF
ISSN	00278424
e-ISSN	10916490
Journal	Proceedings of the National Academy of Sciences of the United States of America
Issue Number	44
Volume Number	108
Language	English
Publisher	National Academy of Sciences
Publisher Date	2011-11-01
Access Restriction	Open
Rights Holder	National Academy of Sciences
Subject Keyword	General Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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