Scale-free tails in colombian financial indexes: a primer

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Autores

Carlos León

Resumen

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 (iv) suggest that local financial markets are self-organizing systems.

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Referencias

Allen, F., Gale, D. (2000). Financial contagion. Journal of Political Economy, 108, (1).

Andriani, P., McKelvey, B. (2009). From Gaussian to Paretian thinking: causes and implications of power laws in organizations. Organization Science, 6 (20).

Bak, P. (1996). How Nature Works. Copernicus.

Barabási, A.-L. (2003). Linked. Plume.

Barabási, A.-L., Albert, R. (1999). Emergence of scaling in random networks. Science, 286, October.

Carmona, R. (2014). Statistical Analysis of Financial Data in R. Springer.

Christoffersen, P. F. (2003). Elements of Financial Risk Management. Academic Press.

Clauset, A., Shalizi, C. R., Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review, 51 (4).

Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, 11.

Derman, E. (2000). Laughter in the dark: an introduction to the volatility smile - lecture notes. Recover from: http://www.ederman.com/new/docs/laughter.html.

Dowd, K. (2005). Measuring Market Risk. John Wiley & Sons.

Eryigit, M., Cukur, S., Eryigit, R. (2009). Tail distribution of index fluctuations in Worldmarkets. Physica A, 388.

Fama, E. F. (1963). Mandelbrot and the stable Paretian hypothesis. The Journal of Business, 36 (4).

Fama, E. F. (1965). The behavior of stock-market prices. The Journal of Business, 38 (1).

Fiaschi, D., Kondor, I., Marisli, M. (2013). The interrupted power law and the size of shadow banking (mimeo).

Freixas, X., Parigi, B. M., Rochet J-C. (2000). Systemic risk, interbank relations, and liquidity provision by the central bank. Journal of Money, Credit and Banking, 32 (3).

Gabaix, X., Gopikrishnan, P., Plerou, V., Stanley, H. E. (2003a). A theory of power-lawdistributions in financial market fluctuations. Nature, 423.

Gabaix, X., Gopikrishnan, P., Plerou, V., Stanley, H. E. (2003b). Understanding the cubic and half-cubic laws of financial fluctuations. Physica, 324.

Geman, H. (2005). Commodities and commodity derivatives. John Wiley & Sons.

Gopikrishnan, P., Meyer, M., Nunes, L.A., Stanley. E. (1998). Inverse Cubic Law for the Distribution of Stock Price Variations. European Physics Journal B, (3).

Gupta, H. M., Campanha, J. R. (1999). The gradually truncated Lévy flight for systems with power-law distributions. Physica A, (268).

Hull, J (2003). Options futures and other derivatives. Prentice Hall.

Krugman, P. (1996). Self-Organizing Economy. Blackwell.

Lanaspa, L., Perdiguero, A. M., Sanz, F. (2004). La distribución del tamaño de las ciudades en España, 1900-1999. Revista de Economía Aplicada, 12 (34).

León, C., Berndsen, R. (2013). Modular scale-free architecture of Colombian financial networks: Evidence and challenges with financial stability in view. Borradores de Economía, 799, Banco de la República.

Mandelbrot, B. (1963). The variation of certain speculative prices. The Journal of Business, (4).

Mandelbrot, B., Hudson, R. (2000). The (Mis)Behavior of Markets. Basic Books.

Mantegna, R. N., Stanley, H. E. (1994). Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight. Physical Review Letters, 73 (22).

Marsili, M. (2003). Scale invariance and criticality in financial markets. Physica A, (324).

Mitchell, W. C. (1915). The making and using of index numbers. Introduction to index numbers and wholesale prices in the United States and foreign countries. Bulletin (173), U.S. Bureau of Labor Statistics.

Rebonato, R. (1999). Volatility and correlation: In the pricing of equity, FX and interest rate options. John Wiley & Sons.

Reveiz, A., León, C (2010). Índice Representativo del Mercado de Deuda Pública Interna: IDXTES. En Laserna, J. M. y Gómez, M. C. (eds.). Pensiones y portafolio: la construcción de una política pública. Bogotá: Banco de la República y Universidad Externado de Colombia.

Sánchez, F., España, I. (2012). Urbanización, desarrollo económico y pobreza en el sistema de ciudades colombianas 1951-2005. Documentos CEDE, Universidad de los Andes, 13.

Simon, H. A. (1955). On a class of skew distribution functions. Biometrika, 42, (3/4).

Sinha, S., Charrerjee, A., Chakraborti, A., Chakrabarti, B. K. (2011). Econophysics: an Introduction. Wiley-VCH.

Stanley, H. E., Amaral, L. A. N., Buldyrev, S. V., Gopikrishnan, Plerou, V., Salinger, M.A. (2002). Self-organized complexity in economics and finance. Proceedings of the National Academy of Sciences of the United States of America (PNAS), 99 (Suppl.1).

Strogatz, S. (2003). SYNC: How Order Emerges from Chaos in the Universe, Nature and Daily Life. Hyperion Books.

Stumpf, M. P. H., Porter, M. A. (2012). Critical truths about power laws. Science, 335.

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