Asymmetric Lévy Flight in Financial Ratios
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, Graphic, 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 α ≈ 1, even though only a few of the individual ratios are characterized by a PDF with power-law tails Graphic 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
Year of publication: |
2013
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Authors: | Podobnik, Boris |
Other Persons: | Valentincic, Aljosa (contributor) ; Stanley, H. Eugene (contributor) |
Publisher: |
[2013]: [S.l.] : SSRN |
Description of contents: | Abstract [papers.ssrn.com] |
Saved in:
Extent: | 1 Online-Ressource |
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Type of publication: | Book / Working Paper |
Language: | English |
Notes: | In: Proceedings of the National Academy of Sciences, Vol. 108, No. 44, pp.17883-17888, 2011, DOI:10.1073/pnas.1113330108 Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments August 30, 2011 erstellt Volltext nicht verfügbar |
Source: | ECONIS - Online Catalogue of the ZBW |
Persistent link: https://www.econbiz.de/10013071491
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