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Exponentially Damped Levy Flights, Multiscaling, and Exchange Rates

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  • Sergio Da Silva

    (Federal University of Rio Grande Do Sul, Brazil)

Abstract

We employ our previously suggested exponentially damped Lévy flight (Physica A 326 (2003) 544) to study the multiscaling properties of 30 daily exchange rates against the US dollar together with a fictitious euro-dollar rate (Physica A 286 (2000) 353). Though multiscaling is not theoretically seen in either stable Lévy processes or abruptly truncated Lévy flights, it is even characteristic of smoothly truncated Lévy flights (Phys. Lett. A 266 (2000) 282; Eur. Phys. J. B 4 (1998) 143). We have already defined a class of “quasi-stable” processes in connection with the finding that single scaling is pervasive among the dollar price of foreign currencies (Physica A 323 (2003) 601). Here we show that the same goes as far as multiscaling is concerned. Our novel findings incidentally reinforce the case for real-world relevance of the Lévy flights for modeling financial prices.
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Suggested Citation

  • Sergio Da Silva, 2004. "Exponentially Damped Levy Flights, Multiscaling, and Exchange Rates," Finance 0405027, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0405027
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    References listed on IDEAS

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    1. Matsushita, Raul & Rathie, Pushpa & Da Silva, Sergio, 2003. "Exponentially damped Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 326(3), pages 544-555.
    2. 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.
    3. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    4. Gupta, Hari M. & Campanha, José R., 2000. "The gradually truncated Lévy flight: stochastic process for complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 275(3), pages 531-543.
    5. Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon, 2001. "Scaling properties of foreign exchange volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 249-266.
    6. Xu, Zhaoxia & Gençay, Ramazan, 2003. "Scaling, self-similarity and multifractality in FX markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 578-590.
    7. Ausloos, M & Ivanova, K, 2000. "Introducing False EUR and False EUR exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(1), pages 353-366.
    8. repec:ebl:ecbull:v:7:y:2003:i:2:p:1-13 is not listed on IDEAS
    9. repec:ebl:ecbull:v:7:y:2002:i:3:p:1-12 is not listed on IDEAS
    10. 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.
    11. Bershadskii, A., 2003. "Self-averaging phenomenon and multiscaling in Hong Kong stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(3), pages 591-596.
    12. Skjeltorp, Johannes A, 2000. "Scaling in the Norwegian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 486-528.
    13. Sergio Da Silva & Annibal Figueiredo & Iram Gleria & Raul Matsushita, 2003. "Fractal structure in the Chinese yuan/US dollar rate," Economics Bulletin, AccessEcon, vol. 7(2), pages 1-13.
    14. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    15. Gupta, Hari M. & Campanha, José R., 1999. "The gradually truncated Lévy flight for systems with power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 231-239.
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    Cited by:

    1. Apergis, Nicholas & Christou, Christina & Miller, Stephen M., 2014. "Country and industry convergence of equity markets: International evidence from club convergence and clustering," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 36-58.
    2. 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.
    3. Sergio Da Silva, 2004. "International Finance, Levy Distributions, and the Econophysics of Exchange Rates," International Finance 0405018, University Library of Munich, Germany.

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