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Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models

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  • Andreas Behr
  • Ulrich Pötter

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  • Andreas Behr & Ulrich Pötter, 2009. "Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models," Annals of Finance, Springer, vol. 5(1), pages 49-68, January.
    • Handle: RePEc:kap:annfin:v:5:y:2009:i:1:p:49-68
    DOI: 10.1007/s10436-007-0089-8
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    1. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 443-453.
    2. Vicente, Renato & de Toledo, Charles M. & Leite, Vitor B.P. & Caticha, Nestor, 2006. "Underlying dynamics of typical fluctuations of an emerging market price index: The Heston model from minutes to months," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 272-288.
    3. Ralf Remer & Reinhard Mahnke, 2004. "Application of the heston and hull-white models to german dax data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 685-693.
    4. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Hans Eijgenhuijsen & Adrian Buckley, 1999. "An overview of returns in Europe," The European Journal of Finance, Taylor & Francis Journals, vol. 5(3), pages 276-297.
    7. Bauer, Christian, 2000. "Value at risk using hyperbolic distributions," Journal of Economics and Business, Elsevier, vol. 52(5), pages 455-467.
    8. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
    9. Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-472, October.
    10. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
    11. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    12. Block, Henry W. & Li, Yulin & Savits, Thomas H., 2005. "Mixtures of normal distributions: Modality and failure rate," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 253-264, October.
    13. Silva, A. Christian & Prange, Richard E. & Yakovenko, Victor M., 2004. "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 227-235.
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    Cited by:

    1. Göncü, Ahmet & Karahan, Mehmet Oğuz & Kuzubaş, Tolga Umut, 2016. "A comparative goodness-of-fit analysis of distributions of some Lévy processes and Heston model to stock index returns," The North American Journal of Economics and Finance, Elsevier, vol. 36(C), pages 69-83.
    2. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    3. Bhat, Harish S. & Kumar, Nitesh, 2012. "Option pricing under a normal mixture distribution derived from the Markov tree model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 762-774.
    4. Jose E. Figueroa-Lopez & K. Lee, 2017. "Estimation of a noisy subordinated Brownian Motion via two-scales power variations," Papers 1702.01164, arXiv.org.
    5. Olivia Andreea Baciu, 2015. "Generalized Hyperbolic Distributions: Empirical Evidence on Bucharest Stock Exchange," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 7(1), pages 007-018, June.
    6. Nikola Gradojevic & Dragan Kukolj & Ramazan Gencay, 2011. "Clustering and Classification in Option Pricing," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 3(2), pages 109-128, October.
    7. Sak, Halis & Hörmann, Wolfgang & Leydold, Josef, 2010. "Efficient risk simulations for linear asset portfolios in the t-copula model," European Journal of Operational Research, Elsevier, vol. 202(3), pages 802-809, May.
    8. Göncü, Ahmet & Yang, Hao, 2016. "Variance-Gamma and Normal-Inverse Gaussian models: Goodness-of-fit to Chinese high-frequency index returns," The North American Journal of Economics and Finance, Elsevier, vol. 36(C), pages 279-292.

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    More about this item

    Keywords

    Stock returns; Non-normality; Gaussian mixtures; Generalised hyperbolic distribution; Generalised logF distribution; G12; C16;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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