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Truncated Lévy walks and an emerging market economic index

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  • Miranda, L.Couto
  • Riera, R.

Abstract

In this paper, we perform a statistical analysis of the major stock index in Latin America, the São Paulo Stock Exchange Index in Brazil (IBOVESPA). Database contains daily records for the 15-year period 1986–2000. We find that the time evolution of the index of share prices is well described by an Exponentially Truncated Lévy Flight (ETLF) characterized by a Lévy exponent α≃1.6–1.7 and a cutoff exponent λ≃1.7. The ETLF statistics accounts for the observed short-term large fluctuations of the financial data time series and describes the long-term convergence to the Gaussian regime. We derive the characteristic crossover time scale Nc dependence on α and λ according to this model as well as the volatility dependence on α, λ and Nc. We find an uncorrelated behaviour of the historical data and Nc≃20 trading days which are in numerical agreement with the analytical results. This dynamic model provides a framework within which it is possible to develop an efficient risk management and option pricing practice for emerging economies.

Suggested Citation

  • Miranda, L.Couto & Riera, R., 2001. "Truncated Lévy walks and an emerging market economic index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 509-520.
    • Handle: RePEc:eee:phsmap:v:297:y:2001:i:3:p:509-520
    DOI: 10.1016/S0378-4371(01)00233-3
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    Cited by:

    1. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    2. Sergio Da Silva & Raul Matsushita & Iram Gleria, 2002. "Scaling power laws in the Sao Paulo Stock Exchange," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-12.
    3. Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2003. "Autocorrelation as a source of truncated Lévy flights in foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 601-625.
    4. Sosa-Correa, William O. & Ramos, Antônio M.T. & Vasconcelos, Giovani L., 2018. "Investigation of non-Gaussian effects in the Brazilian option market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 525-539.
    5. Gleria, Iram & Figueiredo, Annibal & Matsushita, Raul & Rathie, Pushpa & Da Silva, Sergio, 2004. "Exponentially damped Lévy flights, multiscaling and slow convergence in stockmarkets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 200-206.
    6. Pan, Raj Kumar & Sinha, Sitabhra, 2008. "Inverse-cubic law of index fluctuation distribution in Indian markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2055-2065.
    7. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    8. Gu, Gao-Feng & Zhou, Wei-Xing, 2007. "Statistical properties of daily ensemble variables in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 497-506.
    9. Ramos, Antônio M.T. & Carvalho, J.A. & Vasconcelos, G.L., 2016. "Exponential model for option prices: Application to the Brazilian market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 161-168.
    10. repec:ebl:ecbull:v:7:y:2002:i:3:p:1-12 is not listed on IDEAS

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    Keywords

    Lévy; Econophysics;

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