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 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