IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v9y1999i4p293-321.html
   My bibliography  Save this article

Pricing General Barrier Options: A Numerical Approach Using Sharp Large Deviations

Author

Listed:
  • Paolo Baldi
  • Lucia Caramellino
  • Maria Gabriella Iovino

Abstract

In this paper we develop simulation techniques in order to evaluate single and double barrier options with general features. Our method is based on Sharp Large Deviation estimates, which allow one to improve the usual Monte Carlo procedure. Numerical results are provided and show the validity of the proposed simulation algorithm.

Suggested Citation

  • Paolo Baldi & Lucia Caramellino & Maria Gabriella Iovino, 1999. "Pricing General Barrier Options: A Numerical Approach Using Sharp Large Deviations," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 293-321, October.
    • Handle: RePEc:bla:mathfi:v:9:y:1999:i:4:p:293-321
    DOI: 10.1111/1467-9965.t01-1-00071
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9965.t01-1-00071
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9965.t01-1-00071?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
    ---><---

    Citations

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


    Cited by:

    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. Keegan Mendonca & Vasileios E. Kontosakos & Athanasios A. Pantelous & Konstantin M. Zuev, 2018. "Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation," Papers 1803.03364, arXiv.org, revised Mar 2018.
    3. Suhan Altay & Stefan Gerhold & Karin Hirhager, 2012. "Digital double barrier options: Several barrier periods and structure floors," Papers 1207.4608, arXiv.org, revised Jul 2012.
    4. Amirhossein Sobhani & Mariyan Milev, 2017. "A Numerical Method for Pricing Discrete Double Barrier Option by Lagrange Interpolation on Jacobi Node," Papers 1712.01060, arXiv.org, revised Feb 2018.
    5. Angelos Dassios & Luting Li, 2018. "Explicit Asymptotics on First Passage Times of Diffusion Processes," Papers 1806.08161, arXiv.org.
    6. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.
    7. Choe, Geon Ho & Koo, Ki Hwan, 2014. "Probability of multiple crossings and pricing of double barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 156-184.
    8. Sabiwalsky, Ralf, 2010. "Nonlinear modelling of target leverage with latent determinant variables -- new evidence on the trade-off theory," Review of Financial Economics, Elsevier, vol. 19(4), pages 137-150, October.
    9. Peter Carr & Jian Sun, 2007. "A new approach for option pricing under stochastic volatility," Review of Derivatives Research, Springer, vol. 10(2), pages 87-150, May.
    10. Lucia Caramellino & Barbara Pacchiarotti & Simone Salvadei, 2015. "Large Deviation Approaches for the Numerical Computation of the Hitting Probability for Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 383-401, June.
    11. 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.
    12. Dassios, Angelos & Li, Luting, 2020. "Explicit asymptotic on first passage times of diffusion processes," LSE Research Online Documents on Economics 103087, London School of Economics and Political Science, LSE Library.
    13. Amirhossein Sobhani & Mariyan Milev, 2017. "A Numerical Method for Pricing Discrete Double Barrier Option by Legendre Multiwavelet," Papers 1703.09129, arXiv.org, revised Mar 2017.
    14. Baldi, Paolo & Caramellino, Lucia & Rossi, Maurizia, 2020. "Large deviations of conditioned diffusions and applications," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1289-1308.
    15. Paul Glasserman & Jeremy Staum, 2001. "Conditioning on One-Step Survival for Barrier Option Simulations," Operations Research, INFORMS, vol. 49(6), pages 923-937, December.
    16. Gobet, Emmanuel & Menozzi, Stéphane, 2004. "Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 201-223, August.
    17. Cetin, Umut, 2018. "Diffusion transformations, Black-Scholes equation and optimal stopping," LSE Research Online Documents on Economics 87261, London School of Economics and Political Science, LSE Library.
    18. Sun, David & Chow, Da-Ching, 2014. "Forgive, or Award, Your Debtor? - A Barrier Option Approach," MPRA Paper 44826, University Library of Munich, Germany, revised 06 Jan 2014.
    19. Martin Becker, 2010. "Exact simulation of final, minimal and maximal values of Brownian motion and jump-diffusions with applications to option pricing," Computational Management Science, Springer, vol. 7(1), pages 1-17, January.
    20. Hanbyeol Jang & Sangkwon Kim & Junhee Han & Seongjin Lee & Jungyup Ban & Hyunsoo Han & Chaeyoung Lee & Darae Jeong & Junseok Kim, 2020. "Fast Monte Carlo Simulation for Pricing Equity-Linked Securities," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 865-882, December.
    21. Huyen Pham, 2007. "Some applications and methods of large deviations in finance and insurance," Papers math/0702473, arXiv.org, revised Feb 2007.
    22. Ralf Sabiwalsky, 2010. "Nonlinear modelling of target leverage with latent determinant variables — new evidence on the trade‐off theory," Review of Financial Economics, John Wiley & Sons, vol. 19(4), pages 137-150, October.
    23. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.

    More about this item

    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:bla:mathfi:v:9:y:1999:i:4:p:293-321. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.