IDEAS home Printed from https://ideas.repec.org/a/sbe/breart/v26y2006i2a1581.html
   My bibliography  Save this article

Goodness-of-fit Tests Focus on Value-at-Risk Estimation

Author

Listed:
  • Barbachan, José Santiago Fajardo
  • Ornelas, José Renato Haas
  • de Farias, Aquiles Rocha

Abstract

A common statistical problem in finance is measuring the goodness-of-fit of a given distribution to real world data. This can be done using distances to measure how close an empirical distribution is from a theoretical distribution. The tails of the distribution should receive special importance if the focus is on Value-at-Risk (VaR) calculations. This paper analyzes the use of distances to test the goodness-of-fit of estimated distributions for VaR calculation purposes. The Crnkovic and Drachman (1996) distance and a new distance are used to perform goodness-of-fit tests. The critical values of the tests are obtained using Monte Carlo simulation, and goodness-of-fit tests are performed based on the distances. The power of the tests is assessed through Monte Carlo experiments, showing good results for sample sizes greater than 250. The US Dollar/Brazilian Real exchange rate and the Ibovespa index are used as examples of practical applications of how to test the hypothesis that an empirical distribution is equal to an estimated one. The estimated distributions considered are the Generalized Hyperbolic (GH), the NIG (Normal Inverse Gaussian) and Normal. The test results rejected the null hypothesis for the Normal distribution, but did not reject it for the Generalized Hyperbolic and NIG, both at a 1% significance level.

Suggested Citation

  • Barbachan, José Santiago Fajardo & Ornelas, José Renato Haas & de Farias, Aquiles Rocha, 2006. "Goodness-of-fit Tests Focus on Value-at-Risk Estimation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 26(2), November.
    • Handle: RePEc:sbe:breart:v:26:y:2006:i:2:a:1581
    as

    Download full text from publisher

    File URL: https://periodicos.fgv.br/bre/article/view/1581
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fajardo, José & Farias, Aquiles, 2004. "Generalized Hyperbolic Distributions and Brazilian Data," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(2), November.
    2. Kerkhof, Jeroen & Melenberg, Bertrand, 2004. "Backtesting for risk-based regulatory capital," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1845-1865, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. José Santiago Fajardo Barbachan & Aquiles Rocha de Farias & José Renato Haas Ornelas, 2008. "A Goodness-of-Fit Test with Focus on Conditional Value at Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 6(2), pages 139-155.
    2. Alfonso Novales & Laura Garcia-Jorcano, 2019. "Backtesting Extreme Value Theory models of expected shortfall," Documentos de Trabajo del ICAE 2019-24, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Tsukahara, Fábio Yasuhiro & Kimura, Herbert & Sobreiro, Vinicius Amorim & Zambrano, Juan Carlos Arismendi, 2016. "Validation of default probability models: A stress testing approach," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 70-85.
    4. Minella, Andre & de Freitas, Paulo Springer & Goldfajn, Ilan & Muinhos, Marcelo Kfoury, 2003. "Inflation targeting in Brazil: constructing credibility under exchange rate volatility," Journal of International Money and Finance, Elsevier, vol. 22(7), pages 1015-1040, December.
    5. Leonardo Soriano de Alencar & Márcio I. Nakane, 2004. "Bank Competition, Agency Costs and the Performance of the Monetary Policy," Working Papers Series 81, Central Bank of Brazil, Research Department.
    6. Lai, Yongzeng, 2009. "Generating inverse Gaussian random variates by approximation," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3553-3559, August.
    7. Wong, Woon K., 2008. "Backtesting trading risk of commercial banks using expected shortfall," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1404-1415, July.
    8. Kerkhof, F.L.J., 2003. "Model risk analysis for risk management and option pricing," Other publications TiSEM 01692df5-4c2d-4ed2-8108-4, Tilburg University, School of Economics and Management.
    9. Richard Gerlach & Declan Walpole & Chao Wang, 2017. "Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 199-215, February.
    10. Fajardo, Jose Santiago, 2006. "Equivalent Martingale Measures and Lévy Processes," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 60(4), February.
    11. Correa, Arnildo da Silva & Minella, André, 2010. "Nonlinear mechanisms of the exchange rate pass-through: A Phillips curve model with threshold for Brazil," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 64(3), September.
    12. Ricardo Schechtman, 2017. "Joint Validation of Credit Rating PDs under Default Correlation," International Journal of Central Banking, International Journal of Central Banking, vol. 13(2), pages 235-282, June.
    13. Benjamin M. Tabak, 2006. "The Dynamic Relationship Between Stock Prices And Exchange Rates: Evidence For Brazil," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(08), pages 1377-1396.
    14. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    15. Benjamin Miranda Tabak, 2003. "Monetary Policy Surprises and the Brazilian Term Structure of Interest Rates," Working Papers Series 70, Central Bank of Brazil, Research Department.
    16. Chen, Qian & Gerlach, Richard H., 2013. "The two-sided Weibull distribution and forecasting financial tail risk," International Journal of Forecasting, Elsevier, vol. 29(4), pages 527-540.
    17. Sander Barendse & Erik Kole & Dick van Dijk, 2023. "Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 528-568.
    18. Sebastian Bayer & Timo Dimitriadis, 2018. "Regression Based Expected Shortfall Backtesting," Papers 1801.04112, arXiv.org, revised Sep 2019.
    19. Gilneu F. A. Vivan & Benjamin M. Tabak, 2007. "A New Proposal for Collection and Generation of Information on Financial Institutions' Risk: the case of derivatives," Working Papers Series 133, Central Bank of Brazil, Research Department.
    20. José Fajardo, 2017. "A new factor to explain implied volatility smirk," Applied Economics, Taylor & Francis Journals, vol. 49(40), pages 4026-4034, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sbe:breart:v:26:y:2006:i:2:a:1581. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Núcleo de Computação da FGV EPGE (email available below). General contact details of provider: https://edirc.repec.org/data/sbeeeea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.