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Scale-free tails in Colombian financial indexes: a primer

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  • Carlos León

    ()

Abstract

A maximum likelihood method for estimating the power-law exponent verifies that the positive and negative tails of the Colombian stock market index (IGBC) and the Colombian peso exchange rate (TRM) approximate a scale-free distribution, whereas none of the heavy tails of a local sovereign securities index (IDXTES) are a plausible case for such distribution. Results also (i) support critiques regarding the flaws of ordinary least squares estimation methods for scale-free distributions; (ii) question the validity of Zipf’s law; (iii) suggest that IGBC and TRM display the scale-free nature documented as a stylized fact of financial returns, and that they may be following a gradually truncated Lévy flight; and (v) suggest that local financial markets are self-organized systems.

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Paper provided by BANCO DE LA REPÚBLICA in its series BORRADORES DE ECONOMIA with number 011144.

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Length: 18
Date of creation: 07 Mar 2014
Handle: RePEc:col:000094:011144
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Keywords: Scale-free; power-law; Zipf’s law; financial returns.;

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Find related papers by JEL classification:
  • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
  • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
  • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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  1. Xavier Freixas & Bruno Parigi & Jean-Charles Rochet, 2000. "Systemic risk, interbank relations, and liquidity provision by the central bank," Proceedings, Federal Reserve Bank of Cleveland, pages 611-640.
  2. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, H.Eugene, 2003. "Understanding the cubic and half-cubic laws of financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 1-5.
  3. Carlos León & Ron J. Berndsen, 2013. "Modular scale-free architecture of Colombian financial networks: Evidence and challenges with financial stability in view," BORRADORES DE ECONOMIA 011104, BANCO DE LA REPÚBLICA.
  4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
  5. Davide Fiaschi & Imre Kondor & Matteo Marsili, 2013. "The Interrupted Power Law and The Size of Shadow Banking," Discussion Papers 2013/166, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
  6. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
  7. N. Lesca, 2011. "Introduction," Post-Print halshs-00640604, HAL.
  8. Christoffersen, Peter, 2003. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 1, number 9780121742324.
  9. C. Dominguez-Pery, 2011. "Introduction," Post-Print halshs-00740570, HAL.
  10. Marsili, Matteo, 2003. "Scale invariance and criticality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 17-24.
  11. Alejandro Reveiz & Carlos Eduardo León Rincón, 2008. "Índice representativo del mercado de deuda pública interna: IDXTES," Borradores de Economia 488, Banco de la Republica de Colombia.
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