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Value at risk for a mixture of normal distributions: the use of quasi- Bayesian estimation techniques

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  • Subu Venkataraman

Abstract

This article proposes a methodology for measuring value at risk for fat-tailed asset return distributions. Simulation-based results indicate that this approach provides better estimates of risk than one based on the assumption that asset returns are normally distributed.

Suggested Citation

  • Subu Venkataraman, 1997. "Value at risk for a mixture of normal distributions: the use of quasi- Bayesian estimation techniques," Economic Perspectives, Federal Reserve Bank of Chicago, issue Mar, pages 2-13.
  • Handle: RePEc:fip:fedhep:y:1997:i:mar:p:2-13:n:v.21no.2
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    References listed on IDEAS

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    1. Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-528, June.
    2. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
    3. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    4. Kim, Dongcheol & Kon, Stanley J, 1994. "Alternative Models for the Conditional Heteroscedasticity of Stock Returns," The Journal of Business, University of Chicago Press, vol. 67(4), pages 563-598, October.
    5. Hamilton, James D, 1991. "A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 27-39, January.
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    Cited by:

    1. Jean-Francois Richard, 2016. "Finite Gaussian Mixture Approximations to Analytically Intractable Density Kerkels," Working Paper 5980, Department of Economics, University of Pittsburgh.
    2. Ender Su & Thomas W. Knowles, 2006. "Asian Pacific Stock Market Volatility Modeling and Value at Risk Analysis," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 42(2), pages 18-62, April.
    3. Cotter, John, 2001. "Margin exceedences for European stock index futures using extreme value theory," Journal of Banking & Finance, Elsevier, vol. 25(8), pages 1475-1502, August.
    4. Huang, Alex YiHou, 2010. "An optimization process in Value-at-Risk estimation," Review of Financial Economics, Elsevier, vol. 19(3), pages 109-116, August.
    5. Meade, Nigel, 2010. "Oil prices -- Brownian motion or mean reversion? A study using a one year ahead density forecast criterion," Energy Economics, Elsevier, vol. 32(6), pages 1485-1498, November.
    6. Mark R. Manfredo & Raymond M. Leuthold, 1998. "Agricultural Applications of Value-at-Risk Analysis: A Perspective," Finance 9805002, EconWPA.
    7. de Araújo, André da Silva & Garcia, Maria Teresa Medeiros, 2013. "Risk contagion in the north-western and southern European stock markets," Journal of Economics and Business, Elsevier, vol. 69(C), pages 1-34.
    8. Buckley, Ian & Saunders, David & Seco, Luis, 2008. "Portfolio optimization when asset returns have the Gaussian mixture distribution," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1434-1461, March.
    9. Ender Su & Thomas W. Knowles, 2006. "Asian Pacific Stock Market Volatility Modeling and Value at Risk Analysis," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 42(2), pages 18-62, April.
    10. Ning, Cathy & Xu, Dinghai & Wirjanto, Tony S., 2015. "Is volatility clustering of asset returns asymmetric?," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 62-76.
    11. John Cotter, 2004. "Downside risk for European equity markets," Applied Financial Economics, Taylor & Francis Journals, vol. 14(10), pages 707-716.
    12. Marco Bee, 2007. "The asymptotic loss distribution in a fat-tailed factor model of portfolio credit risk," Department of Economics Working Papers 0701, Department of Economics, University of Trento, Italia.
    13. Tae-Hwy Lee & Yong Bao & Burak Saltoğlu, 2007. "Comparing density forecast models Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003;," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 203-225.
    14. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    15. José Carlos Ramirez Sánchez, 2004. "Usos y limitaciones de los procesos estocásticos en el tratamiento de distribuciones de rendimientos con colas gordas," Revista de Analisis Economico – Economic Analysis Review, Ilades-Georgetown University, Universidad Alberto Hurtado/School of Economics and Bussines, vol. 19(1), pages 51-76, June.

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    Keywords

    Econometric models ; Risk;

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