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Dependence Calibration and Portfolio Fit with FactorBased Time Changes

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Listed:
  • 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 well captured also by the Variance-Gamma specification.

Suggested Citation

  • 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.
    • Handle: RePEc:cca:wpaper:307
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    References listed on IDEAS

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    1. Harris, Lawrence, 1986. "Cross-Security Tests of the Mixture of Distributions Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(1), pages 39-46, March.
    2. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    3. 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.
    4. 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, May.
    5. 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.
    6. Roberto Marfè, 2012. "A generalized variance gamma process for financial applications," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 75-87, June.
    7. Lo, Andrew W & Wang, Jiang, 2000. "Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 257-300.
    8. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    9. Laura Ballotta & Efrem Bonfiglioli, 2016. "Multivariate asset models using Lévy processes and applications," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1320-1350, October.
    10. 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.
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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. Roman V. Ivanov, 2018. "A Credit-Risk Valuation under the Variance-Gamma Asset Return," Risks, MDPI, vol. 6(2), pages 1-25, May.
    3. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
    4. Roman V. Ivanov, 2018. "Option Pricing In The Variance-Gamma Model Under The Drift Jump," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-19, June.
    5. Petar Jevtić & Marina Marena & Patrizia Semeraro, 2019. "Multivariate Marked Poisson Processes And Market Related Multidimensional Information Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-26, March.
    6. Marina Marena & Andrea Romeo & Patrizia Semeraro, 2018. "Multivariate Factor-Based Processes With Sato Margins," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-30, February.
    7. Marina Marena & Andrea Romeo & Patrizia Semeraro, 2015. "Pricing multivariate barrier reverse convertibles with factor-based subordinators," Carlo Alberto Notebooks 439, Collegio Carlo Alberto.

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    More about this item

    Keywords

    Lévy processes; multivariate subordinators; dependence; correlation; multi- variate asset modelling; multivariate time-changed processes; factor-based time changes.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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