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A Generalized Hyperbolic model for a risky asset with dependence

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  • Finlay, Richard
  • Seneta, Eugene

Abstract

We present a construction of the Generalized Hyperbolic (GH) subordinator model for a risky asset with dependence. The construction of the subordinator (activity time) process is implemented via superpositions of Ornstein–Uhlenbeck type processes driven by Lévy noise. It unifies, on the basis of self-decomposability of the Generalized Inverse Gaussian (GIG) distribution, the construction of the various special cases of the GH subordinator class, such as the Variance Gamma, normal inverse Gaussian, hyperbolic and, especially, t distributions. An option pricing formula for the proposed model is derived.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 82 (2012)
Issue (Month): 12 ()
Pages: 2164-2169

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Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2164-2169

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Related research

Keywords: Generalized Hyperbolic; Generalized Inverse Gaussian; Ornstein–Uhlenbeck process; Subordinator model; Long range dependence;

References

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  1. Tina Hviid Rydberg, 1999. "Generalized Hyperbolic Diffusion Processes with Applications in Finance," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(2), pages 183-201.
  2. Richard Finlay & Eugene Seneta, 2008. "Option Pricing With Vg–Like Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 943-955.
  3. Richard Finlay & Eugene Seneta, 2008. "Stationary-Increment Variance-Gamma and "t" Models: Simulation and Parameter Estimation," International Statistical Review, International Statistical Institute, International Statistical Institute, vol. 76(2), pages 167-186, 08.
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  5. Fung, Thomas & Seneta, Eugene, 2010. "Extending the multivariate generalised t and generalised VG distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 154-164, January.
  6. Leonenko, N.N. & Petherick, S. & Sikorskii, A., 2012. "A normal inverse Gaussian model for a risky asset with dependence," Statistics & Probability Letters, Elsevier, Elsevier, vol. 82(1), pages 109-115.
  7. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck type," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 13(4), pages 445-466.
  8. Yor, Marc & Madan, Dilip B. & Carr, Peter & Geman, Hélyette, 2007. "Self-decomposability and option pricing," Economics Papers from University Paris Dauphine 123456789/1380, Paris Dauphine University.
  9. Granger, Clive W.J., 2005. "The past and future of empirical finance: some personal comments," Journal of Econometrics, Elsevier, Elsevier, vol. 129(1-2), pages 35-40.
  10. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(1), pages 31-53.
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