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Lévy processes and the Brazilian market

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  • Barbachan, José Fajardo
  • Schuschny, Andrés Ricardo
  • Silva, André de Castro

Abstract

The present paper presents the Lévy processes used in the literature for the modeling of the returns of financial assets, which are generated by stable Paretian and hyperbolic distributions. Some properties of these distributions, especially the time-scale invariance, are analyzed. In the end, empirical evidence of the applicability of these processes is given for the modeling of Brazilian asset returns through Ibovespa, and the Telebrás and Petrobrás receipt. The data were collected between January 1st, 1995 and December 31st, 1998 (Gl) and January 1st, 1996 and December 31st, 1997 (G2).

Suggested Citation

  • Barbachan, José Fajardo & Schuschny, Andrés Ricardo & Silva, André de Castro, 2001. "Lévy processes and the Brazilian market," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 21(2), November.
  • Handle: RePEc:sbe:breart:v:21:y:2001:i:2:a:2752
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    References listed on IDEAS

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    1. Issler, João Victor, 1999. "Estimating and forecasting the volatility of Brazilian finance series using arch models (Preliminary Version)," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 347, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    2. Pereira, Pedro L. Valls & Hotta, Luiz K. & Souza, Luiz Alvares R. de & Almeida, Nuno Miguel C. G. de, 1999. "Alternative Models To Extract Asset Volatility: A Comparative Study," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 19(1), May.
    3. Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
    4. repec:sbe:breart:v:19:y:1999:i:1:a:2792 is not listed on IDEAS
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Fajardo, José & Farias, Aquiles, 2009. "Multivariate affine generalized hyperbolic distributions: An empirical investigation," International Review of Financial Analysis, Elsevier, vol. 18(4), pages 174-184, September.
    2. Fajardo, José & Farias, Aquiles, 2004. "Generalized Hyperbolic Distributions and Brazilian Data," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(2), November.
    3. Fajardo, J. & Cajueiro, D. O., 2003. "Volatility Estimation and Option Pricing with Fractional Brownian Motion," Finance Lab Working Papers flwp_53, Finance Lab, Insper Instituto de Ensino e Pesquisa.

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