IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i4d10.1007_s00362-018-1019-8.html
   My bibliography  Save this article

Analytic moment and Laplace transform formulae for the quasi-stationary distribution of the Shiryaev diffusion on an interval

Author

Listed:
  • Aleksey S. Polunchenko

    (Binghamton University, State University of New York)

  • Andrey Pepelyshev

    (Cardiff University
    St. Petersburg State University)

Abstract

We derive analytic closed-form moment and Laplace transform formulae for the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval [0, A] with absorption at a given $$A>0$$ A > 0 .

Suggested Citation

  • Aleksey S. Polunchenko & Andrey Pepelyshev, 2018. "Analytic moment and Laplace transform formulae for the quasi-stationary distribution of the Shiryaev diffusion on an interval," Statistical Papers, Springer, vol. 59(4), pages 1351-1377, December.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-018-1019-8
    DOI: 10.1007/s00362-018-1019-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-018-1019-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-018-1019-8?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. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    2. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    Full references (including those not matched with items on IDEAS)

    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. Runhuan Feng & Hans W. Volkmer, 2013. "An identity of hitting times and its application to the valuation of guaranteed minimum withdrawal benefit," Papers 1307.7070, arXiv.org.
    2. 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.
    3. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.
    4. Dan Pirjol & Lingjiong Zhu, 2023. "Sensitivities of Asian options in the Black-Scholes model," Papers 2301.06460, arXiv.org.
    5. 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.
    6. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659, arXiv.org.
    7. Cruz Báez, Domingo Israel & González Rodríguez, José Manuel, 2008. "Valoración de opciones. Un enfoque diferente," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 26, pages 341-362, Abril.
    8. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    9. William T. Shaw & Marcus Schofield, 2015. "A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 975-998, June.
    10. 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.
    11. Humayra Shoshi & Indranil SenGupta, 2023. "Some asymptotics for short maturity Asian options," Papers 2302.05421, arXiv.org, revised Oct 2023.
    12. Yuji Hishida & Kenji Yasutomi, 2009. "Asymptotic behavior of prices of path dependent options," Papers 0911.5579, arXiv.org.
    13. 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.
    14. Andrew Lyasoff, 2016. "Another look at the integral of exponential Brownian motion and the pricing of Asian options," Finance and Stochastics, Springer, vol. 20(4), pages 1061-1096, October.
    15. Jaehyuk Choi, 2018. "Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(6), pages 627-644, June.
    16. Jianqiang Sun & Langnan Chen & Shiyin Li, 2013. "A Quasi‐Analytical Pricing Model for Arithmetic Asian Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(12), pages 1143-1166, December.
    17. 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.
    18. Dai, Min & Li, Peifan & Zhang, Jin E., 2010. "A lattice algorithm for pricing moving average barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 542-554, March.
    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. Yanhong Zhong & Guohe Deng, 2019. "Geometric Asian Options Pricing under the Double Heston Stochastic Volatility Model with Stochastic Interest Rate," Complexity, Hindawi, vol. 2019, pages 1-13, January.

    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:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-018-1019-8. 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.