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A non-Gaussian approach to risk measures

Author

Listed:
  • Bormetti, Giacomo
  • Cisana, Enrica
  • Montagna, Guido
  • Nicrosini, Oreste

Abstract

Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modelling the power-law tails of the returns distribution in terms of a Student-t distribution. Non-Gaussian closed-form solutions for value-at-risk and expected shortfall are obtained and standard formulae known in the literature under the normality assumption are recovered as a special case. The implications of the approach for risk management are demonstrated through an empirical analysis of financial time series from the Italian stock market and in comparison with the results of the most widely used procedures of quantitative finance. Particular attention is paid to quantify the size of the errors affecting the market risk measures obtained according to different methodologies, by employing a bootstrap technique.

Suggested Citation

  • Bormetti, Giacomo & Cisana, Enrica & Montagna, Guido & Nicrosini, Oreste, 2007. "A non-Gaussian approach to risk measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 532-542.
  • Handle: RePEc:eee:phsmap:v:376:y:2007:i:c:p:532-542
    DOI: 10.1016/j.physa.2006.10.008
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    Citations

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    Cited by:

    1. Giacomo Bormetti & Sofia Cazzaniga, 2011. "Multiplicative noise, fast convolution, and pricing," Papers 1107.1451, arXiv.org.
    2. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(1), pages 1-14, February.
    3. Jules Sadefo Kamdem, 2012. "VaR and ES for linear portfolios with mixture of generalized Laplace distributions risk factors," Annals of Finance, Springer, vol. 8(1), pages 123-150, February.
    4. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "Semi-nonparametric VaR forecasts for hedge funds during the recent crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 330-343.
    5. Giacomo Bormetti & Maria Elena De Giuli & Danilo Delpini & Claudia Tarantola, 2008. "Bayesian Analysis of Value-at-Risk with Product Partition Models," Papers 0809.0241, arXiv.org, revised May 2009.
    6. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    7. Kang, Sang Hoon & Yoon, Seong-Min, 2007. "Long memory properties in return and volatility: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 591-600.
    8. Giacomo Bormetti & Sofia Cazzaniga, 2014. "Multiplicative noise, fast convolution and pricing," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 481-494, March.

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