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Exponentially Damped Levy Flights

  • Sergio Da Silva

    (Federal University of Rio Grande Do Sul, Brazil)

Since real processes seem to departure from standard Lévy distributions, modifications to the latter have been suggested in literature. These include (abruptly) truncated (Phys. Rev. Lett. 73 (1994) 2946), smoothly truncated (Phys. Rev. E 52 (1995) 1197; Phys. Lett. A 266 (2000) 282) and gradually truncated Lévy flights (Physica A 268 (1999) 231; Physica A 275 (2000) 531). We put forward what we call an exponentially damped Lévy flight which encompasses the previous cases. In the presence of increasing and positive feedbacks, our distribution is assumed to deviate from the Lévy in both a smooth and gradual fashion. We estimate the truncation parameters by nonlinear least squares to optimally fit the distribution tails. That is a novel approach for estimating parameters α and γ of the Lévy. The method is illustrated with daily data on exchange rates for 15 countries against the US dollar. Our results show that the exponentially damped Lévy flight fits the data well when increasing and positive deviations are present.

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File URL: http://128.118.178.162/eps/fin/papers/0406/0406002.pdf
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Paper provided by EconWPA in its series Finance with number 0406002.

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Date of creation: 07 Jun 2004
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Handle: RePEc:wpa:wuwpfi:0406002
Note: Type of Document - pdf
Contact details of provider: Web page: http://128.118.178.162

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  1. Sergio Da Silva, 2004. "Autocorrelation as a Source of Truncated Levy Flights in Foreign Exchange Rates," Finance 0405018, EconWPA.
  2. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  3. 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.
  4. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
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