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Approximation of the variance gamma model with a finite mixture of normals

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  • Loregian, Angela
  • Mercuri, Lorenzo
  • Rroji, Edit

Abstract

We investigate the possibility of approximating the variance gamma distribution with a finite mixture of normals. Therefore, we apply this result to derive a simple historical estimation procedure by means of the Expectation Maximization algorithm.

Suggested Citation

  • Loregian, Angela & Mercuri, Lorenzo & Rroji, Edit, 2012. "Approximation of the variance gamma model with a finite mixture of normals," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 217-224.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:217-224
    DOI: 10.1016/j.spl.2011.10.004
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    4. Richard Finlay & Eugene Seneta, 2008. "Stationary‐Increment Variance‐Gamma and t Models: Simulation and Parameter Estimation," International Statistical Review, International Statistical Institute, vol. 76(2), pages 167-186, August.
    5. Lorenzo Mercuri & Fabio Bellini, 2014. "Option Pricing in a Dynamic Variance-Gamma Model," Papers 1405.7342, arXiv.org.
    6. Karlis, Dimitris, 2002. "An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 43-52, March.
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    Citations

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    Cited by:

    1. Lorenzo Mercuri & Edit Rroji, 2018. "Risk parity for Mixed Tempered Stable distributed sources of risk," Annals of Operations Research, Springer, vol. 260(1), pages 375-393, January.
    2. Iacus, Stefano M. & Mercuri, Lorenzo & Rroji, Edit, 2017. "COGARCH(p, q): Simulation and Inference with the yuima Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 80(i04).
    3. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2020. "Finite Mixture Approximation of CARMA(p,q) Models," Papers 2005.10130, arXiv.org, revised May 2020.
    4. Stefano Iacus & Lorenzo Mercuri, 2015. "Implementation of Lévy CARMA model in Yuima package," Computational Statistics, Springer, vol. 30(4), pages 1111-1141, December.
    5. Asmerilda Hitaj & Lorenzo Mercuri & Edit Rroji, 2019. "Lévy CARMA models for shocks in mortality," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 205-227, June.
    6. Asmerilda Hitaj & Lorenzo Mercuri, 2013. "Portfolio allocation using multivariate variance gamma models," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(1), pages 65-99, March.
    7. Edit Rroji & Lorenzo Mercuri, 2015. "Mixed tempered stable distribution," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1559-1569, September.
    8. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    9. Hiroki Masuda & Lorenzo Mercuri & Yuma Uehara, 2024. "Student t-L\'evy regression model in YUIMA," Papers 2403.12078, arXiv.org.
    10. Hitaj, Asmerilda & Mercuri, Lorenzo & Rroji, Edit, 2015. "Portfolio selection with independent component analysis," Finance Research Letters, Elsevier, vol. 15(C), pages 146-159.
    11. Lorenzo Mercuri & Edit Rroji, 2014. "Parametric Risk Parity," Papers 1409.7933, arXiv.org.

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