IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i22p5193-5207.html
   My bibliography  Save this article

Pricing bounds for discrete arithmetic Asian options under Lévy models

Author

Listed:
  • Lemmens, D.
  • Liang, L.Z.J.
  • Tempere, J.
  • De Schepper, A.

Abstract

Analytical bounds for Asian options are almost exclusively available in the Black–Scholes framework. In this paper we derive bounds for the price of a discretely monitored arithmetic Asian option when the underlying asset follows an arbitrary Lévy process. Explicit formulas are given for Kou’s model, Merton’s model, the normal inverse Gaussian model, the CGMY model and the variance gamma model. The results are compared with the comonotonic upper bound, existing numerical results, Monte carlo simulations and in the case of the variance gamma model with an existing lower bound. The method outlined here provides lower and upper bounds that are quick to evaluate, and more accurate than existing bounds.

Suggested Citation

  • Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
  • Handle: RePEc:eee:phsmap:v:389:y:2010:i:22:p:5193-5207
    DOI: 10.1016/j.physa.2010.07.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110006539
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    2. Matsushita, Raul & Rathie, Pushpa & Da Silva, Sergio, 2003. "Exponentially damped Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 326(3), pages 544-555.
    3. Mantegna, Rosario N & Palágyi, Zoltán & Stanley, H.Eugene, 1999. "Applications of statistical mechanics to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 216-221.
    4. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    5. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
    6. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    7. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    8. Mariani, M.C. & Liu, Y., 2007. "Normalized truncated Levy walks applied to the study of financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 590-598.
    9. Linetsky, Vadim, 1998. "The Path Integral Approach to Financial Modeling and Options Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 129-163, April.
    10. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    11. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
    12. Vanduffel, Steven & Shang, Zhaoning & Henrard, Luc & Dhaene, Jan & Valdez, Emiliano A., 2008. "Analytic bounds and approximations for annuities and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1109-1117, June.
    13. Raberto, Marco & Scalas, Enrico & Cuniberti, Gianaurelio & Riani, Massimo, 1999. "Volatility in the Italian stock market: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 148-155.
    14. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    15. Yanhui Liu & Parameswaran Gopikrishnan & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1999. "The statistical properties of the volatility of price fluctuations," Papers cond-mat/9903369, arXiv.org, revised Mar 1999.
    16. D. Lemmens & M. Wouters & J. Tempere & S. Foulon, 2008. "A path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models," Papers 0806.0932, arXiv.org.
    17. Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
    18. H. Albrecher & P. A. Mayer & W. Schoutens, 2008. "General Lower Bounds for Arithmetic Asian Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 123-149.
    19. Miccichè, Salvatore & Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N, 2002. "Volatility in financial markets: stochastic models and empirical results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 756-761.
    20. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
    21. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    22. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 449-473, June.
    23. Friedrich Hubalek & Carlo Sgarra, 2006. "Esscher transforms and the minimal entropy martingale measure for exponential Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 125-145.
    24. Erik Van der Straeten & Christian Beck, 2009. "Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence," Papers 0901.2271, arXiv.org, revised Sep 2009.
    25. 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.
    26. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alexander Novikov & Nino Kordzakhia, 2013. "On lower and upper bounds for Asian-type options: a unified approach," Papers 1309.2383, arXiv.org.
    2. repec:eee:apmaco:v:258:y:2015:i:c:p:372-387 is not listed on IDEAS
    3. Alexander Novikov & Scott Alexander & Nino Kordzakhia & Timothy Ling, 2016. "Pricing of Asian-type and Basket Options via Upper and Lower Bounds," Papers 1612.08767, arXiv.org.

    More about this item

    Keywords

    Asian options; Analytical bounds; Lévy models;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:389:y:2010:i:22:p:5193-5207. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.