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A Generalized Normal Mean Variance Mixture for Return Processes in Finance


  • Elisa Luciano
  • Patrizia Semeraro


Time-changed Brownian motions are extensively applied as mathematical models for asset returns in Finance. Time change is interpreted as a switch to trade-related business time, different from calendar time. Time-changed Brownian motions can be generated by infinite divisible normal mixtures. The standard multivariate normal mean variance 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 mean-variance 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, 2008. "A Generalized Normal Mean Variance Mixture for Return Processes in Finance," Carlo Alberto Notebooks 97, Collegio Carlo Alberto, revised 2009.
  • Handle: RePEc:cca:wpaper:97

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    References listed on IDEAS

    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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    Cited by:

    1. 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,, revised Oct 2016.
    2. 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.
    3. Rüschendorf Ludger & Wolf Viktor, 2015. "Cost-efficiency in multivariate Lévy models," Dependence Modeling, De Gruyter Open, vol. 3(1), pages 1-16, April.
    4. Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216,, revised Jun 2014.

    More about this item


    multivariate normal mean variance mixtures; multivariate generalized hyperbolic distributions; Levy processes; multivariate subordinators;

    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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