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A Generalized Normal Mean-Variance Mixture For Return Processes In Finance

Author

Listed:
  • ELISA LUCIANO

    (Dipartimento di Statistica e Matematica Applicata D. De Castro, Università degli Studi di Torino, Italy;
    ICER and Collegio Carlo Alberto, Italy)

  • PATRIZIA SEMERARO

    (Dipartimento di Statistica e Matematica Applicata D. De Castro, Università degli Studi di Torino, Italy)

Abstract

Time-changed Brownian motions are extensively applied as mathematical models for asset returns in Finance. Time change is interpreted as a switch from calendar time to trade-related business time. Time-changed Brownian motions can be generated by infinitely divisible normal mixtures. The standard multivariate mixtures assume a common mixing variable. This corresponds to a multidimensional return process with a unique change of time for all assets under exam. The economic counterpart is uniqueness of trade or business time, which is not in line with empirical evidence. In this paper we propose a new multivariate definition of normal mixtures with a flexible dependence structure, based on the economic intuition of both a common and an idiosyncratic component of business time. We analyze both the distribution and the related process. We use the above construction to introduce a multivariate generalized hyperbolic process with generalized hyperbolic margins. We conclude with a stock market example to show the ease of calibration of the model.

Suggested Citation

  • Elisa Luciano & Patrizia Semeraro, 2010. "A Generalized Normal Mean-Variance Mixture For Return Processes In Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 415-440.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:03:n:s0219024910005838
    DOI: 10.1142/S0219024910005838
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    References listed on IDEAS

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    1. Elisa Luciano & Patrizia Semeraro, 2007. "Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators," Carlo Alberto Notebooks 42, Collegio Carlo Alberto.
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    Citations

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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. Boris Buchmann & Benjamin Kaehler & Ross Maller & Alexander Szimayer, 2015. "Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing," Papers 1502.03901, arXiv.org, revised Oct 2016.
    3. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    4. Rüschendorf Ludger & Wolf Viktor, 2015. "Cost-efficiency in multivariate Lévy models," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-16, April.
    5. Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    6. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    7. Elisa Luciano & Marina Marena & Patrizia Semeraro, 2013. "Dependence Calibration and Portfolio Fit with FactorBased Time Changes," Carlo Alberto Notebooks 307, Collegio Carlo Alberto, revised 2015.
    8. Patrizia Semeraro, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, June.
    9. Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216, arXiv.org, revised Jun 2014.

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    2. Elisa Luciano & Patrizia Semeraro, 2007. "Generalized Normal Mean Variance Mixture and Subordinated Brownian Motion," ICER Working Papers - Applied Mathematics Series 42-2007, ICER - International Centre for Economic Research.

    More about this item

    Keywords

    Multivariate normal mean-variance mixtures; multivariate generalized hyperbolic distributions; Lévy processes; multivariate subordinators;
    All these keywords.

    JEL classification:

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

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