Asymmetric Levy flight in financial ratios

作者:Podobnik Boris*; Valentincic Aljosa; Horvatic Davor; Stanley H Eugene
来源:Proceedings of the National Academy of Sciences of the United States of America, 2011, 108(44): 17883-17888.
DOI:10.1073/pnas.1113330108

摘要

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 Levy probability distribution PDF) to describe the stochastic properties of commodity changes and price changes. We find that an asymmetric Levy 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, Delta X-i. We thus find that Levy PDFs describe both the static and dynamics of credit ratings. We find that for the majority of ratios, Delta X-i scales with the Levy parameter alpha approximate to 1, even though only a few of the individual ratios are characterized by a PDF with power-law tails X-i(-1-alpha) with infinite variance. We also find that alpha 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(Delta Z) follows a Levy PDF with power-law exponent alpha approximate to 1, consistent with changes of individual financial ratios. Estimating the conditional P(Delta Z|Z) versus Z, we demonstrate how this continuous credit rating approach and its dynamics can be used to evaluate credit risk.

  • 出版日期2011-11-1