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A Generalized Normal Mean Variance Mixture for Return Processes in Finance


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  • 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.

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Bibliographic Info

Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 97.

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Length: 30 pages
Date of creation: 2008
Date of revision: 2009
Handle: RePEc:cca:wpaper:97

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

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Cited by:
  1. Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216,, revised Jun 2014.
  2. Elisa Luciano & Marina Marena & Patrizia Semeraro, 2013. "Dependence Calibration and Portfolio Fit with FactorBased Time Changes," Carlo Alberto Notebooks 307, Collegio Carlo Alberto.


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