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Generalized Hyperbolic Distributions and Brazilian Data

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  • José Fajardo
  • Aquiles Farias

Abstract

The aim of this paper is to discuss the use of the Generalized Hyperbolic Distributions to fit Brazilian assets returns. Selected subclasses are compared regarding goodness of fit statistics and distances. Empirical results show that these distributions fit data well. Then we show how to use these distributions in value at risk estimation and derivative price computation.

Suggested Citation

  • José Fajardo & Aquiles Farias, 2002. "Generalized Hyperbolic Distributions and Brazilian Data," Working Papers Series 52, Central Bank of Brazil, Research Department.
    • Handle: RePEc:bcb:wpaper:52
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    1. 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.
    2. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    3. Issler, João Victor, 1999. "Estimating and Forecasting the Volatility of Brazilian Finance Series Using ARCH Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 19(1), May.
    4. Mendes, Beatriz Vaz de Melo & Júnior, Antonio Marcos Duarte, 1999. "Robust Estimation for ARCH Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 19(1), May.
    5. Migon, Helio S. & Mazucheli, Josmar, 1999. "Modelos GARCH Bayesianos: Métodos Aproximados e Aplicações," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 19(1), May.
    6. 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, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    7. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    8. Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-10.
    9. 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..
    10. 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.
    11. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
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