IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v82y2011i4p691-704.html
   My bibliography  Save this article

Using the continuous price as control variate for discretely monitored options

Author

Listed:
  • Dingeç, Kemal Dinçer
  • Hörmann, Wolfgang

Abstract

Variance reduction is of highest importance in financial simulation. In this study, we present a new and simple variance reduction technique for pricing discretely monitored lookback and barrier options. It is based on using the corresponding continuously monitored option as external control variate. To obtain the value of the continuously monitored price both, conditional simulation and conditional expectation can be utilized. From numerical experiments we can conclude that the efficiency gains obtained by our new method are significant.

Suggested Citation

  • Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2011. "Using the continuous price as control variate for discretely monitored options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 691-704.
  • Handle: RePEc:eee:matcom:v:82:y:2011:i:4:p:691-704
    DOI: 10.1016/j.matcom.2011.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475411002606
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2011.09.007?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. Paul Glasserman & Jeremy Staum, 2001. "Conditioning on One-Step Survival for Barrier Option Simulations," Operations Research, INFORMS, vol. 49(6), pages 923-937, December.
    2. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, 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. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2012. "A general control variate method for option pricing under Lévy processes," European Journal of Operational Research, Elsevier, vol. 221(2), pages 368-377.

    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. Xie, Fei & He, Zhijian & Wang, Xiaoqun, 2019. "An importance sampling-based smoothing approach for quasi-Monte Carlo simulation of discrete barrier options," European Journal of Operational Research, Elsevier, vol. 274(2), pages 759-772.
    2. 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.
    3. 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.
    4. Jorge Ignacio Gonz'alez C'azares & Aleksandar Mijatovi'c & Ger'onimo Uribe Bravo, 2018. "Geometrically Convergent Simulation of the Extrema of L\'{e}vy Processes," Papers 1810.11039, arXiv.org, revised Jun 2021.
    5. Lokeshwar, Vikranth & Bharadwaj, Vikram & Jain, Shashi, 2022. "Explainable neural network for pricing and universal static hedging of contingent claims," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    6. C. E. Phelan & D. Marazzina & G. Germano, 2020. "Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 899-918, June.
    7. Tian-Shyr Dai & Yuh-Yuan Fang & Yuh-Dauh Lyuu, 2005. "Analytics for geometric average trigger reset options," Applied Economics Letters, Taylor & Francis Journals, vol. 12(13), pages 835-840.
    8. Ernst, Philip A. & Rogers, L.C.G. & Zhou, Quan, 2017. "The value of foresight," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3913-3927.
    9. Kenichiro Shiraya & Cong Wang & Akira Yamazaki, 2021. "A general control variate method for time-changed Lévy processes: An application to options pricing," CARF F-Series CARF-F-499, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Holger Fink & Stefan Mittnik, 2021. "Quanto Pricing beyond Black–Scholes," JRFM, MDPI, vol. 14(3), pages 1-27, March.
    11. L. C. G. Rogers & Fanyin Zhou, 2008. "Estimating correlation from high, low, opening and closing prices," Papers 0804.0162, arXiv.org.
    12. Engelen, Peter-Jan & Kool, Clemens & Li, Ye, 2016. "A barrier options approach to modeling project failure: The case of hydrogen fuel infrastructure," Resource and Energy Economics, Elsevier, vol. 43(C), pages 33-56.
    13. Mike Giles & Lukasz Szpruch, 2012. "Multilevel Monte Carlo methods for applications in finance," Papers 1212.1377, arXiv.org.
    14. Carole Bernard & Phelim Boyle, 2011. "Monte Carlo methods for pricing discrete Parisian options," The European Journal of Finance, Taylor & Francis Journals, vol. 17(3), pages 169-196.
    15. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2023. "Partial quanto lookback options," The North American Journal of Economics and Finance, Elsevier, vol. 64(C).
    16. Pavel V. Shevchenko & Pierre Del Moral, 2014. "Valuation of Barrier Options using Sequential Monte Carlo," Papers 1405.5294, arXiv.org, revised Jul 2015.
    17. A. Golbabai & L. Ballestra & D. Ahmadian, 2014. "A Highly Accurate Finite Element Method to Price Discrete Double Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 44(2), pages 153-173, August.
    18. Phelan, Carolyn E. & Marazzina, Daniele & Fusai, Gianluca & Germano, Guido, 2018. "Fluctuation identities with continuous monitoring and their application to the pricing of barrier options," European Journal of Operational Research, Elsevier, vol. 271(1), pages 210-223.
    19. Lindset, Snorre & Persson, Svein-Arne, 2008. "Continuous Monitoring: Look before You Leap," Discussion Papers 2008/8, Norwegian School of Economics, Department of Business and Management Science.
    20. Yan Dolinsky & Yuri Kifer, 2009. "Binomial Approximations for Barrier Options of Israeli Style," Papers 0907.4136, arXiv.org.

    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:82:y:2011:i:4:p:691-704. 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.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.