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Risk Measurement Performance of Alternative Distribution Functions

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  • Turan G. Bali
  • Panayiotis Theodossiou

Abstract

This paper evaluates the performance of three extreme value distributions, i.e., generalized Pareto distribution (GPD), generalized extreme value distribution (GEV), and Box-Cox-GEV, and four skewed fat-tailed distributions, i.e., skewed generalized error distribution (SGED), skewed generalized "t" (SGT), exponential generalized beta of the second kind (EGB2), and inverse hyperbolic sign (IHS) in estimating conditional and unconditional value at risk (VaR) thresholds. The results provide strong evidence that the SGT, EGB2, and IHS distributions perform as well as the more specialized extreme value distributions in modeling the tail behavior of portfolio returns. All three distributions produce similar VaR thresholds and perform better than the SGED and the normal distribution in approximating the extreme tails of the return distribution. The conditional coverage and the out-of-sample performance tests show that the actual VaR thresholds are time varying to a degree not captured by unconditional VaR measures. In light of the fact that VaR type measures are employed in many different types of financial and insurance applications including the determination of capital requirements, capital reserves, the setting of insurance deductibles, the setting of reinsurance cedance levels, as well as the estimation of expected claims and expected losses, these results are important to financial managers, actuaries, and insurance practitioners. Copyright (c) The Journal of Risk and Insurance, 2008.

Suggested Citation

  • Turan G. Bali & Panayiotis Theodossiou, 2008. "Risk Measurement Performance of Alternative Distribution Functions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 411-437.
  • Handle: RePEc:bla:jrinsu:v:75:y:2008:i:2:p:411-437
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    Cited by:

    1. Robert A. Jones & Christophe Pérignon, 2013. "Derivatives Clearing, Default Risk, and Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(2), pages 373-400, June.
    2. Karmakar, Madhusudan, 2013. "Estimation of tail-related risk measures in the Indian stock market: An extreme value approach," Review of Financial Economics, Elsevier, vol. 22(3), pages 79-85.
    3. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
    4. Chernobai, Anna & Yildirim, Yildiray, 2008. "The dynamics of operational loss clustering," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2655-2666, December.
    5. Stanislav Anatolyev & Dmitry Shakin, 2007. "Trade intensity in the Russian stock market: dynamics, distribution and determinants," Applied Financial Economics, Taylor & Francis Journals, vol. 17(2), pages 87-104.
    6. Martin Eling & Denis Toplek, 2009. "Modeling and Management of Nonlinear Dependencies-Copulas in Dynamic Financial Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 651-681.
    7. Lönnbark, Carl & Holmberg, Ulf & Brännäs, Kurt, 2011. "Value at Risk and Expected Shortfall for large portfolios," Finance Research Letters, Elsevier, vol. 8(2), pages 59-68, June.
    8. repec:eee:revfin:v:35:y:2017:i:c:p:1-10 is not listed on IDEAS
    9. Calluzzo, Paul & Dong, Gang Nathan, 2015. "Has the financial system become safer after the crisis? The changing nature of financial institution risk," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 233-248.
    10. Marie-Anne Cam & Vikash Ramiah, 2014. "The influence of systematic risk factors and econometric adjustments in catastrophic event studies," Review of Quantitative Finance and Accounting, Springer, vol. 42(2), pages 171-189, February.
    11. Li, Yunxian & Tang, Niansheng & Jiang, Xuejun, 2016. "Bayesian approaches for analyzing earthquake catastrophic risk," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 110-119.
    12. Wang, Zijun, 2012. "The causal structure of bond yields," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(1), pages 93-102.
    13. Shi, Peng & Frees, Edward W., 2010. "Long-tail longitudinal modeling of insurance company expenses," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 303-314, December.
    14. James Hansen & James McDonald & Panayiotis Theodossiou & Brad Larsen, 2010. "Partially Adaptive Econometric Methods For Regression and Classification," Computational Economics, Springer;Society for Computational Economics, vol. 36(2), pages 153-169, August.
    15. Holmberg, Ulf, 2012. "Essays on Credit Markets and Banking," Umeå Economic Studies 840, Umeå University, Department of Economics.
    16. 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.
    17. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "VaR performance during the subprime and sovereign debt crises: An application to emerging markets," Emerging Markets Review, Elsevier, vol. 20(C), pages 23-41.
    18. Pilar Abad Romero & Sonia Benito Muela & Miguel Angel Sánchez Granero & Carmen López, 2013. "Evaluating the performance of the skewed distributions to forecast Value at Risk in the Global Financial Crisis," Documentos de Trabajo del ICAE 2013-40, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    19. Carole Toque & Virginie Terraza, 2014. "Histogram-valued data on value at risk measures: a symbolic approach for risk attribution," Applied Economics Letters, Taylor & Francis Journals, vol. 21(17), pages 1243-1251, November.

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