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Positive Solutions of European Option Pricing with CGMY Process Models Using Double Discretization Difference Schemes

Author

Listed:
  • R. Company
  • L. Jódar
  • M. Fakharany

Abstract

This paper deals with the numerical analysis of PIDE option pricing models with CGMY process using double discretization schemes. This approach assumes weaker hypotheses of the solution on the numerical boundary domain than other relevant papers. Positivity, stability, and consistency are studied. An explicit scheme is proposed after a suitable change of variables. Advantages of the proposed schemes are illustrated with appropriate examples.

Suggested Citation

  • R. Company & L. Jódar & M. Fakharany, 2013. "Positive Solutions of European Option Pricing with CGMY Process Models Using Double Discretization Difference Schemes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:517480
    DOI: 10.1155/2013/517480
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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. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    3. M.-C. Casabán & R. Company & L. Jódar & J.-V. Romero, 2012. "Double Discretization Difference Schemes for Partial Integrodifferential Option Pricing Jump Diffusion Models," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. M.-C. Casabán & R. Company & L. Jódar & J.-V. Romero, 2012. "Double Discretization Difference Schemes for Partial Integrodifferential Option Pricing Jump Diffusion Models," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, December.
    5. 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.
    6. Svetlana I. Boyarchenko & Sergei Z. Levendorskiǐ, 2000. "Option Pricing For Truncated Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 549-552.
    7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    8. A. -M. Matache & P. -A. Nitsche & C. Schwab, 2005. "Wavelet Galerkin pricing of American options on Levy driven assets," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 403-424.
    9. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    10. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    11. Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 327-344, December.
    12. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    13. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
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    Cited by:

    1. M. Fakharany & R. Company & L. Jódar, 2015. "Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).

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