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Dependence Calibration and Portfolio Fit with FactorBased Time Changes

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  • Elisa Luciano
  • Marina Marena
  • Patrizia Semeraro

Abstract

The paper explores the fit properties of a class of multivariate Lévy processes, which are characterized as time-changed correlated Brownian motions. The time-change has a common and an idiosyncratic component, to re ect the properties of trade, which it represents. The resulting process may provide Variance-Gamma, Normal-Inverse- Gaussian or Generalized-Hyperbolic margins. A non-pairwise calibration to a portfolio of ten US daily stock returns over the period 2009-2013 shows that fit of the Hyperbolic specification is very good, in terms of marginal distributions and overall correlation matrix. It succeeds in explaining the return distribution of both long-only and long- short random portfolios better than competing models do. Their tail behavior is very well captured also by the Variance-Gamma specification.

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Bibliographic Info

Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 307.

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Length: 35 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:cca:wpaper:307

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Related research

Keywords: Lévy processes; multivariate subordinators; dependence; correlation; multi- variate asset modelling; multivariate time-changed processes; factor-based time changes.;

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References

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  1. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
  2. Roberto Marf�, 2012. "A generalized variance gamma process for financial applications," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 75-87, June.
  3. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
  4. 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.
  5. Martin Wallmeier & Martin Diethelm, 2012. "Multivariate downside risk: Normal versus Variance Gamma," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(5), pages 431-458, 05.
  6. Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
  7. Harris, Lawrence, 1986. "Cross-Security Tests of the Mixture of Distributions Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(01), pages 39-46, March.
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