Truncated Lévy walks and an emerging market economic index

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...

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Bibliographic Details
Published in:Physica A 2001-08, Vol.297 (3), p.509-520
Main Authors: Miranda, L.Couto, Riera, R.
Format: Article
Language:English
Subjects:
Econophysics
Lévy
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Summary: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 N c dependence on α and λ according to this model as well as the volatility dependence on α, λ and N c . We find an uncorrelated behaviour of the historical data and N c ≃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.
ISSN:0378-4371
1873-2119
DOI:10.1016/S0378-4371(01)00233-3