IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v14y2017i3d10.1007_s10287-017-0278-5.html
   My bibliography  Save this article

Fast binomial procedures for pricing Parisian/ParAsian options

Author

Listed:
  • Marcellino Gaudenzi

    (Universitá di Udine)

  • Antonino Zanette

    (Universitá di Udine)

Abstract

The discrete procedures for pricing Parisian/ParAsian options depend, in general, on three dimensions: time, space, time spent over the barrier. Here we present some combinatorial and lattice procedures which reduce the computational complexity to second order. In the European case the reduction was already given by Lyuu and Wu (Decisions Econ Finance 33(1):49–61, 2010) and Li and Zhao (J Deriv 16(4):72–81, 2009), in this paper we present a more efficient procedure in the Parisian case and a different approach (again of order 2) in the ParAsian case. In the American case we present new procedures which decrease the complexity of the pricing problem for the Parisian/ParAsian knock-in options. The reduction of complexity for Parisian/ParAsian knock-out options is still an open problem.

Suggested Citation

  • Marcellino Gaudenzi & Antonino Zanette, 2017. "Fast binomial procedures for pricing Parisian/ParAsian options," Computational Management Science, Springer, vol. 14(3), pages 313-331, July.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:3:d:10.1007_s10287-017-0278-5
    DOI: 10.1007/s10287-017-0278-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-017-0278-5
    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/s10287-017-0278-5?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. Figlewski, Stephen & Gao, Bin, 1999. "The adaptive mesh model: a new approach to efficient option pricing," Journal of Financial Economics, Elsevier, vol. 53(3), pages 313-351, September.
    2. Marcellino Gaudenzi & Antonino Zanette, 2009. "Pricing American barrier options with discrete dividends by binomial trees," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(2), pages 129-148, November.
    3. Marco Avellaneda & Lixin Wu, 1999. "Pricing Parisian-Style Options With A Lattice Method," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-16.
    4. Yuh-Dauh Lyuu & Cheng-Wei Wu, 2010. "An improved combinatorial approach for pricing Parisian options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 49-61, May.
    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. Anna Battauz & Francesco Rotondi, 2022. "American options and stochastic interest rates," Computational Management Science, Springer, vol. 19(4), pages 567-604, October.

    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. Tian-Shyr Dai & Chun-Yuan Chiu, 2013. "Pricing barrier stock options with discrete dividends by approximating analytical formulae," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1367-1382, October.
    2. Lihua Zhang & Weiguo Zhang & Weijun Xu & Xiang Shi, 2014. "A Modified Least-Squares Simulation Approach to Value American Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 489-506, December.
    3. San-Lin Chung & Pai-Ta Shih, 2007. "Generalized Cox-Ross-Rubinstein Binomial Models," Management Science, INFORMS, vol. 53(3), pages 508-520, March.
    4. Dassios, Angelos & Lim, Jia Wei, 2013. "Parisian option pricing: a recursive solution for the density of the Parisian stopping time," LSE Research Online Documents on Economics 58985, London School of Economics and Political Science, LSE Library.
    5. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    6. Pressacco, Flavio & Gaudenzi, Marcellino & Zanette, Antonino & Ziani, Laura, 2008. "New insights on testing the efficiency of methods of pricing and hedging American options," European Journal of Operational Research, Elsevier, vol. 185(1), pages 235-254, February.
    7. Kim, Young Shin & Stoyanov, Stoyan & Rachev, Svetlozar & Fabozzi, Frank J., 2019. "Enhancing binomial and trinomial equity option pricing models," Finance Research Letters, Elsevier, vol. 28(C), pages 185-190.
    8. Yuh-Dauh Lyuu & Cheng-Wei Wu, 2010. "An improved combinatorial approach for pricing Parisian options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 49-61, May.
    9. Jin-Yu Zhang & Wen-Bo Wu & Yong Li & Zhu-Sheng Lou, 2021. "Pricing Exotic Option Under Jump-Diffusion Models by the Quadrature Method," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 867-884, October.
    10. Qianru Shang & Brian Byrne, 2021. "American option pricing: Optimal Lattice models and multidimensional efficiency tests," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 514-535, April.
    11. Erwinna Chendra & Kuntjoro A. Sidarto, 2020. "An improved of Hull–White model for valuing Employee Stock Options (ESOs)," Review of Quantitative Finance and Accounting, Springer, vol. 54(2), pages 651-669, February.
    12. Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, vol. 102(2), pages 390-415.
    13. Dassios, Angelos & Zhang, You You, 2016. "The joint distribution of Parisian and hitting times of the Brownian motion with application to Parisian option pricing," LSE Research Online Documents on Economics 64959, London School of Economics and Political Science, LSE Library.
    14. Nicholas Sharp & Paul Johnson & David Newton & Peter Duck, 2009. "A New Prepayment Model (with Default): An Occupation-time Derivative Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 39(2), pages 118-145, August.
    15. Benjamin Jourdain & Antonino Zanette, 2008. "A moments and strike matching binomial algorithm for pricing American Put options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(1), pages 33-49, May.
    16. Liu, Liang-Chih & Dai, Tian-Shyr & Wang, Chuan-Ju, 2016. "Evaluating corporate bonds and analyzing claim holders’ decisions with complex debt structure," Journal of Banking & Finance, Elsevier, vol. 72(C), pages 151-174.
    17. Pingjin Deng & Xiufang Li, 2017. "Barrier Options Pricing With Joint Distribution Of Gaussian Process And Its Maximum," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-18, September.
    18. Pelsser, Antoon & Salahnejhad Ghalehjooghi, Ahmad, 2016. "Time-consistent actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 97-112.
    19. San‐Lin Chung & Yi‐Ta Huang & Pai‐Ta Shih & Jr‐Yan Wang, 2019. "Semistatic hedging and pricing American floating strike lookback options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 418-434, April.
    20. D. Andricopoulos, Ari & Widdicks, Martin & Newton, David P. & Duck, Peter W., 2007. "Extending quadrature methods to value multi-asset and complex path dependent options," Journal of Financial Economics, Elsevier, vol. 83(2), pages 471-499, February.

    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:comgts:v:14:y:2017:i:3:d:10.1007_s10287-017-0278-5. 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.