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Asymmetric Lévy flight in financial ratios
Boris Podobnik1, Aljoša Valentinčič, Davor Horvatić
1Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA. bp@phy.hr
Summary
Financial crises involve rare, extreme events. This study shows asymmetric Lévy probability distribution functions (PDFs) model credit ratios and rating changes, revealing stable dynamics crucial for credit risk evaluation.
Area of Science:
- Quantitative Finance
- Financial Modeling
- Stochastic Processes
Background:
- Financial crises exhibit rare, extreme events exceeding standard models.
- Lévy probability distribution functions (PDFs) were previously proposed for commodity and price changes.
Purpose of the Study:
- To investigate the stochastic process behind rare financial crisis events.
- To model credit ratios and financial rating changes using Lévy PDFs.
- To evaluate the dynamics of credit ratings for risk assessment.
Main Methods:
- Applied asymmetric Lévy PDFs to multiple credit ratios (e.g., Altman Z score, Zmijewski score).
- Analyzed changes in individual financial ratios (ΔX(i)) and credit ratings (ΔZ).
- Investigated the scaling behavior with the Lévy parameter α and its temporal stability.
Main Results:
- Asymmetric Lévy PDFs accurately model static and dynamic aspects of credit ratings.
- Changes in financial ratios (ΔX(i)) and Altman Z scores (ΔZ) follow Lévy PDFs with α ≈ 1.
- The Lévy parameter α demonstrates remarkable stability over time.
Conclusions:
- Lévy PDFs provide a robust framework for understanding credit rating dynamics.
- The findings support using continuous credit ratings and their dynamics for credit risk evaluation.
- The study highlights the importance of infinite variance models for financial crisis events.
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