IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v18y2014i4p825-844.html
   My bibliography  Save this article

Asian options and meromorphic Lévy processes

Author

Listed:
  • D. Hackmann
  • A. Kuznetsov

Abstract

One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on an exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper, we consider pricing Asian options in a model driven by a general meromorphic Lévy process. We prove that the exponential functional is equal in distribution to an infinite product of independent beta random variables, and its Mellin transform can be expressed as an infinite product of gamma functions. We show that these results lead to an efficient algorithm for computing the price of the Asian option via the inverse Mellin–Laplace transform, and we compare this method with some other techniques. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • D. Hackmann & A. Kuznetsov, 2014. "Asian options and meromorphic Lévy processes," Finance and Stochastics, Springer, vol. 18(4), pages 825-844, October.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:4:p:825-844
    DOI: 10.1007/s00780-014-0237-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-014-0237-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00780-014-0237-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Pierre Patie, 2009. "Law of the exponential functional of one-sided L\'evy processes and Asian options," Papers 0904.3000, arXiv.org.
    2. Kuznetsov, A., 2012. "On the distribution of exponential functionals for Lévy processes with jumps of rational transform," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 654-663.
    3. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    4. Ning Cai & Steven Kou, 2012. "Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model," Operations Research, INFORMS, vol. 60(1), pages 64-77, February.
    5. Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
    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. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility," Papers 2308.15672, arXiv.org, revised Feb 2024.
    2. Barker, A. & Savov, M., 2021. "Bivariate Bernstein–gamma functions and moments of exponential functionals of subordinators," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 454-497.
    3. Runhuan Feng & Alexey Kuznetsov & Fenghao Yang, 2016. "Exponential functionals of Levy processes and variable annuity guaranteed benefits," Papers 1610.00577, arXiv.org.
    4. Feng, Runhuan & Kuznetsov, Alexey & Yang, Fenghao, 2019. "Exponential functionals of Lévy processes and variable annuity guaranteed benefits," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 604-625.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    2. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    3. Ewald, Christian-Oliver & Menkens, Olaf & Hung Marten Ting, Sai, 2013. "Asian and Australian options: A common perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1001-1018.
    4. Chenxu Li, 2016. "Bessel Processes, Stochastic Volatility, And Timer Options," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 122-148, January.
    5. Alev{s} v{C}ern'y & Johannes Ruf, 2019. "Simplified stochastic calculus with applications in Economics and Finance," Papers 1912.03651, arXiv.org, revised Jan 2021.
    6. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.
    7. Chiu, Chun-Yuan & Dai, Tian-Shyr & Lyuu, Yuh-Dauh, 2015. "Pricing Asian option by the FFT with higher-order error convergence rate under Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 418-437.
    8. Lingjiong Zhu, 2015. "Short maturity options for Azéma–Yor martingales," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-32, December.
    9. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    10. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659, arXiv.org.
    11. Hideharu Funahashi & Masaaki Kijima, 2017. "A unified approach for the pricing of options relating to averages," Review of Derivatives Research, Springer, vol. 20(3), pages 203-229, October.
    12. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility," Papers 2308.15672, arXiv.org, revised Feb 2024.
    13. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-24.
    14. Serguei Pergamenchtchikov & Alena Shishkova, 2020. "Hedging problems for Asian options with transactions costs," Papers 2001.01443, arXiv.org.
    15. Nikita Ratanov, 2020. "Kac–Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 239-267, March.
    16. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2014. "Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps," Papers 1407.2514, arXiv.org.
    17. Ning Cai & Steven Kou, 2012. "Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model," Operations Research, INFORMS, vol. 60(1), pages 64-77, February.
    18. Yingda Song & Ning Cai & Steven Kou, 2018. "Computable Error Bounds of Laplace Inversion for Pricing Asian Options," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 634-645, January.
    19. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.
    20. Yulian Fan & Huadong Zhang, 2017. "The pricing of average options with jump diffusion processes in the uncertain volatility model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-31, March.

    More about this item

    Keywords

    Asian option; Meromorphic process; Hyper-exponential process; Exponential functional; Mellin transform; Gamma function; 60G51; 65C50; C63;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:spr:finsto:v:18:y:2014:i:4:p:825-844. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.