IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i18p1983-1993.html
   My bibliography  Save this article

Asian options with jumps

Author

Listed:
  • Chou, Ching-Sung
  • Lin, Hsien-Jen

Abstract

The paper is concerned with the computation of Asian options when the underlying asset has a jump. In the Black and Scholes model, Geman and Yor give a closed-form of formula for the price of an Asian option at a random exponential distributed maturity (it then "suffices" to invert the Laplace transform to have the price at a fixed time). The aim of this paper is to obtain such a formula in a model (which seems more realistic) of Black and Scholes with a jump at a random time, which extends the well-known case of the continuous Black and Scholes model. Furthermore, we treat the multi-jump case. Here we also develop a formula for pricing such an option.

Suggested Citation

  • Chou, Ching-Sung & Lin, Hsien-Jen, 2006. "Asian options with jumps," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1983-1993, December.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:18:p:1983-1993
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(06)00182-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Protter, Philip, 2001. "A partial introduction to financial asset pricing theory," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 169-203, February.
    2. Aase, Knut K., 1988. "Contingent claims valuation when the security price is a combination of an Ito process and a random point process," Stochastic Processes and their Applications, Elsevier, vol. 28(2), pages 185-220, June.
    3. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    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. Chou, Ching-Sung & Lin, Hsien-Jen, 2007. "Pricing model for zero coupon bonds driven by Bessel-squared interest processes with a jump," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 475-482, March.

    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. Jean-Yves Datey & Genevieve Gauthier & Jean-Guy Simonato, 2003. "The Performance of Analytical Approximations for the Computation of Asian Quanto-Basket Option Prices," Multinational Finance Journal, Multinational Finance Journal, vol. 7(1-2), pages 55-82, March-Jun.
    2. Goovaerts, M. J. & Dhaene, J., 1999. "Supermodular ordering and stochastic annuities," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 281-290, May.
    3. 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.
    4. Geman, Helyette, 2002. "Pure jump Levy processes for asset price modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1297-1316, July.
    5. 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.
    6. Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
    7. Bossaerts, P. & Ghysels, E. & Gourieroux, C., 1996. "Arbitrage-Based Pricing when Volatility is Stochastic," Cahiers de recherche 9615, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Eric Ghysels & Christian Gouriéroux & Joann Jasiak, 1995. "Market Time and Asset Price Movements Theory and Estimation," CIRANO Working Papers 95s-32, CIRANO.
    9. 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.
    10. Matsumoto, Hiroyuki & Wesolowski, Jacek & Witkowski, Piotr, 2009. "Tree structured independence for exponential Brownian functionals," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3798-3815, October.
    11. Chenxu Li, 2016. "Bessel Processes, Stochastic Volatility, And Timer Options," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 122-148, January.
    12. Anselm Hudde & Ludger Rüschendorf, 2023. "European and Asian Greeks for Exponential Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.
    13. Ma, Jingtang & Deng, Dongya & Lai, Yongzeng, 2015. "Explicit approximate analytic formulas for timer option pricing with stochastic interest rates," The North American Journal of Economics and Finance, Elsevier, vol. 34(C), pages 1-21.
    14. Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
    15. Cen, Zhongdi & Xu, Aimin & Le, Anbo, 2015. "A hybrid finite difference scheme for pricing Asian options," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 229-239.
    16. 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.
    17. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    18. Xueping Wu & Jin Zhang, 1999. "Options on the minimum or the maximum of two average prices," Review of Derivatives Research, Springer, vol. 3(2), pages 183-204, May.
    19. Shih-Hsien Tseng & Tien Son Nguyen & Ruei-Ci Wang, 2021. "The Lie Algebraic Approach for Determining Pricing for Trade Account Options," Mathematics, MDPI, vol. 9(3), pages 1-9, January.
    20. 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.

    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:stapro:v:76:y:2006:i:18:p:1983-1993. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.