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Modelling and predicting market risk with Laplace-Gaussian mixture distributions

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  • Markus Haas
  • Stefan Mittnik
  • Marc Paolella

Abstract

While much of classical statistical analysis is based on Gaussian distributional assumptions, statistical modelling with the Laplace distribution has gained importance in many applied fields. This phenomenon is rooted in the fact that, like the Gaussian, the Laplace distribution has many attractive properties. This paper investigates two methods of combining them and their use in modelling and predicting financial risk. Based on 25 daily stock return series, the empirical results indicate that the new models offer a plausible description of the data. They are also shown to be competitive with, or superior to, use of the hyperbolic distribution, which has gained some popularity in asset-return modelling and, in fact, also nests the Gaussian and Laplace.

Suggested Citation

  • Markus Haas & Stefan Mittnik & Marc Paolella, 2006. "Modelling and predicting market risk with Laplace-Gaussian mixture distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 16(15), pages 1145-1162.
    • Handle: RePEc:taf:apfiec:v:16:y:2006:i:15:p:1145-1162
    DOI: 10.1080/09603100500438817
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    Cited by:

    1. Saissi Hassani, Samir & Dionne, Georges, 2021. "The new international regulation of market risk: Roles of VaR and CVaR in model validation," Working Papers 20-3, HEC Montreal, Canada Research Chair in Risk Management.
    2. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Fabozzi, Frank J., 2013. "CVaR sensitivity with respect to tail thickness," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 977-988.
    3. Rombouts Jeroen V. K. & Bouaddi Mohammed, 2009. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-32, May.
    4. Gel, Yulia R., 2010. "Test of fit for a Laplace distribution against heavier tailed alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 958-965, April.
    5. Mahmood Ul Hassan & Pär Stockhammar, 2016. "Fitting probability distributions to economic growth: a maximum likelihood approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(9), pages 1583-1603, July.
    6. John Douglas (J.D.) Opdyke, 2007. "Comparing Sharpe ratios: So where are the p-values?," Journal of Asset Management, Palgrave Macmillan, vol. 8(5), pages 308-336, December.
    7. Kaldasch, Joachim, 2014. "Evolutionary model of stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 449-462.
    8. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc S., 2006. "Accurate Value-at-Risk forecast with the (good old) normal-GARCH model," CFS Working Paper Series 2006/23, Center for Financial Studies (CFS).
    9. Yining Chen, 2015. "Semiparametric Time Series Models with Log-concave Innovations: Maximum Likelihood Estimation and its Consistency," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 1-31, March.
    10. Leopoldo Catania, 2016. "Dynamic Adaptive Mixture Models," Papers 1603.01308, arXiv.org, revised Jan 2023.
    11. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.

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    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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