IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v77y2008i1p64-71.html
   My bibliography  Save this article

Simulation of Brownian motion at first-passage times

Author

Listed:
  • Burq, Zaeem A.
  • Jones, Owen D.

Abstract

We show how to simulate Brownian motion not on a regular time grid, but on a regular spatial grid. That is, when it first hits points in δZ for some δ>0. Central to our method is an algorithm for the exact simulation of τ, the first time Brownian motion hits ±1. This work is motivated by boundary hitting problems for time-changed Brownian motion, such as appear in mathematical finance when pricing barrier-options.

Suggested Citation

  • Burq, Zaeem A. & Jones, Owen D., 2008. "Simulation of Brownian motion at first-passage times," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 64-71.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:1:p:64-71
    DOI: 10.1016/j.matcom.2007.01.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475407001267
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2007.01.038?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.

    Citations

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


    Cited by:

    1. Devroye, Luc, 2009. "On exact simulation algorithms for some distributions related to Jacobi theta functions," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2251-2259, November.
    2. Bender, Christian & Parczewski, Peter, 2018. "Discretizing Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2489-2537.
    3. Nan Chen & Zhengyu Huang, 2013. "Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 591-616, August.
    4. S'ergio C. Bezerra & Alberto Ohashi & Francesco Russo & Francys de Souza, 2017. "Discrete-type approximations for non-Markovian optimal stopping problems: Part II," Papers 1707.05250, arXiv.org, revised Dec 2019.
    5. Ledermann, Daniel & Alexander, Carol, 2012. "Further properties of random orthogonal matrix simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 56-79.
    6. Lee, Taeho, 2023. "Exact simulation for the first hitting time of Brownian motion and Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 193(C).
    7. Sérgio C. Bezerra & Alberto Ohashi & Francesco Russo & Francys Souza, 2020. "Discrete-type Approximations for Non-Markovian Optimal Stopping Problems: Part II," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1221-1255, September.
    8. Murray Pollock & Paul Fearnhead & Adam M. Johansen & Gareth O. Roberts, 2020. "Quasi‐stationary Monte Carlo and the ScaLE algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1167-1221, December.
    9. Vyacheslav M. Abramov, 2023. "Crossings States and Sets of States in Random Walks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-34, March.
    10. Kay Giesecke & Dmitry Smelov, 2013. "Exact Sampling of Jump Diffusions," Operations Research, INFORMS, vol. 61(4), pages 894-907, August.
    11. Dorival Le~ao & Alberto Ohashi & Francesco Russo, 2017. "Discrete-type approximations for non-Markovian optimal stopping problems: Part I," Papers 1707.05234, arXiv.org, revised Jun 2019.

    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:matcom:v:77:y:2008:i:1:p:64-71. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.