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Multivariate affine generalized hyperbolic distributions: An empirical investigation

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  • Fajardo, José
  • Farias, Aquiles

Abstract

The aim of this paper is to estimate multivariate affine generalized distributions (MAGH) using market data. We use the Ibovespa, CAC, DAX, FTSE, NIKKEI and S&P500 indexes. We estimate the univariate distributions, bi-variate distributions and six-dimensional distribution. Then we assess their goodness of fit using Kolmogorov distances. As an application we study the efficient frontier.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:finana:v:18:y:2009:i:4:p:174-184
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    1. Fajardo, J. & Farias, A. R. & Ornelas, J. R. H., 2003. "Analyzing the Use of Generalized Hyperbolic Distributions to Value at Risk Calculations," Finance Lab Working Papers flwp_58, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    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. 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.
    4. Schmidt, Rafael & Hrycej, Tomas & Stutzle, Eric, 2006. "Multivariate distribution models with generalized hyperbolic margins," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2065-2096, April.
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    1. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    2. Aviv Alpern & Svetlozar Rachev, 2025. "Black-Litterman and ESG Portfolio Optimization," Papers 2511.21850, arXiv.org.
    3. Fajardo, José & Farias, Aquiles, 2010. "Derivative pricing using multivariate affine generalized hyperbolic distributions," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1607-1617, July.
    4. Wang, Chou-Wen & Liu, Kai & Li, Bin & Tan, Ken Seng, 2022. "Portfolio optimization under multivariate affine generalized hyperbolic distributions," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 49-66.
    5. Barros Fernandes, José Luiz & Haas Ornelas, José Renato & Martínez Cusicanqui, Oscar Augusto, 2012. "Combining equilibrium, resampling, and analyst’s views in portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1354-1361.
    6. Fajardo, José & Mordecki, Ernesto, 2010. "Market symmetry in time-changed Brownian models," Finance Research Letters, Elsevier, vol. 7(1), pages 53-59, March.

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