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A Comparative Goodness-of-fit Analysis of Distributions of Some Levy Processes and Heston Model to Stock Index Returns


  • Ahmet Göncü
  • Mehmet Oguz Karahan
  • Tolga Umut Kuzubas


In this paper, we investigate the goodness-of-fit of three Lévy processes, namely Variance-Gamma (VG), Normal-Inverse Gaussian (NIG) and Generalized Hyperbolic (GH) distributions, and probability distribution of the Heston model to index returns of twenty developed and emerging stock markets. Furthermore, we extend our analysis by applying a Markov regime switching model to identify normal and turbulent periods. Our findings indicate that the probability distribution of the Heston model performs well for emerging markets under full sample estimation and retains goodness of fit for high volatility periods, as it explicitly accounts for the volatility process. On the other hand, the distributions of the Lévy processes, especially the VG and NIG distributions, generally improves upon the fit of the Heston model, particularly for developed markets and low volatility periods. Furthermore, some distributions yield to significantly large test statistics for some countries, even though they fit well to other markets, which suggest that properties of the stock markets are crucial in identifying the best distribution representing empirical returns.
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  • Ahmet Göncü & Mehmet Oguz Karahan & Tolga Umut Kuzubas, 2014. "A Comparative Goodness-of-fit Analysis of Distributions of Some Levy Processes and Heston Model to Stock Index Returns," Working Papers 2014/07, Bogazici University, Department of Economics.
  • Handle: RePEc:bou:wpaper:2014/07

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    Cited by:

    1. Till Massing, 2019. "What is the best Lévy model for stock indices? A comparative study with a view to time consistency," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 33(3), pages 277-344, September.
    2. Ricardo Crisóstomo, 2017. "Speed and biases of Fourier-based pricing choices: Analysis of the Bates and Asymmetric Variance Gamma models," CNMV Working Papers CNMV Working Papers no. 6, CNMV- Spanish Securities Markets Commission - Research and Statistics Department.
    3. Endres, Sylvia & Stübinger, Johannes, 2018. "A flexible regime switching model with pairs trading application to the S&P 500 high-frequency stock returns," FAU Discussion Papers in Economics 07/2018, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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