IDEAS home Printed from https://ideas.repec.org/a/kap/apfinm/v20y2013i1p71-81.html
   My bibliography  Save this article

Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion

Author

Listed:
  • Yuri Imamura
  • Katsuya Takagi

Abstract

On a multi-assets Black-Scholes economy, we introduce a class of barrier options, where the knock-out boundary is a cone. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula and the semi-static hedge. The result is a multi-dimensional generalization of the put-call symmetry by Bowie and Carr (Risk (7):45–49, 1994 ), Carr and Chou (Risk 10(9):139–145, 1997 ), etc. The important implication of our result is that with a given volatility matrix structure of the multi-assets, one can design a multi-barrier option and a system of plain options, with the latter the former is statically hedged. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Yuri Imamura & Katsuya Takagi, 2013. "Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(1), pages 71-81, March.
    • Handle: RePEc:kap:apfinm:v:20:y:2013:i:1:p:71-81
    DOI: 10.1007/s10690-012-9159-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10690-012-9159-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10690-012-9159-7?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. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
    2. Yuri Imamura, 2011. "A remark on static hedging of options written on the last exit time," Review of Derivatives Research, Springer, vol. 14(3), pages 333-347, October.
    3. Michael Schmutz, 2011. "Semi-static hedging for certain Margrabe-type options with barriers," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 979-986.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Rolf Poulsen, 2006. "Barrier options and their static hedges: simple derivations and extensions," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 327-335.
    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. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2017. "The Value of Timing Risk," Papers 1701.05695, arXiv.org.
    2. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2018. "Asymptotic Static Hedge via Symmetrization," Papers 1801.04045, arXiv.org.

    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. Jun, Doobae & Ku, Hyejin, 2015. "Static hedging of chained-type barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 317-327.
    2. Hansjörg Albrecher & Philipp Mayer, 2010. "Semi-Static Hedging Strategies For Exotic Options," World Scientific Book Chapters, in: Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), Alternative Investments And Strategies, chapter 14, pages 345-373, World Scientific Publishing Co. Pte. Ltd..
    3. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    4. Bas Peeters & Cees L. Dert & André Lucas, 2003. "Black Scholes for Portfolios of Options in Discrete Time: the Price is Right, the Hedge is wrong," Tinbergen Institute Discussion Papers 03-090/2, Tinbergen Institute.
    5. Sbuelz, A., 2000. "Hedging Double Barriers with Singles," Discussion Paper 2000-112, Tilburg University, Center for Economic Research.
    6. Johannes Siven & Rolf Poulsen, 2009. "Auto-static for the people: risk-minimizing hedges of barrier options," Review of Derivatives Research, Springer, vol. 12(3), pages 193-211, October.
    7. Kraft, Holger, 2007. "Pitfalls in static superhedging of barrier options," Finance Research Letters, Elsevier, vol. 4(1), pages 2-9, March.
    8. Peter Carr & Roger Lee & Matthew Lorig, 2015. "Robust replication of barrier-style claims on price and volatility," Papers 1508.00632, arXiv.org, revised Jan 2022.
    9. Jia‐Hau Guo & Lung‐Fu Chang, 2020. "Repeated Richardson extrapolation and static hedging of barrier options under the CEV model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 974-988, June.
    10. Carol Alexander & Leonardo Nogueira, 2007. "Model-free price hedge ratios for homogeneous claims on tradable assets," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 473-479.
    11. Lee, Hangsuck & Ko, Bangwon & Lee, Minha, 2023. "The pricing and static hedging of multi-step double barrier options," Finance Research Letters, Elsevier, vol. 55(PA).
    12. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    13. Sbuelz, A., 2000. "Hedging Double Barriers with Singles," Other publications TiSEM e810e3ab-1936-457e-a3ae-7, Tilburg University, School of Economics and Management.
    14. Gabriel Drimus, 2010. "A forward started jump-diffusion model and pricing of cliquet style exotics," Review of Derivatives Research, Springer, vol. 13(2), pages 125-140, July.
    15. Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.
    16. Claude Bardos & Raphaël Douady & Andrei Fursikov, 2002. "Static Hedging Of Barrier Options With A Smile: An Inverse Problem," Post-Print hal-01477102, HAL.
    17. Rolf Poulsen, 2006. "Barrier options and their static hedges: simple derivations and extensions," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 327-335.
    18. Zura Kakushadze, 2015. "Coping with Negative Short-Rates," Papers 1502.06074, arXiv.org, revised Aug 2015.
    19. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    20. Imamura Yuri & Ishigaki Yuta & Okumura Toshiki, 2014. "A numerical scheme based on semi-static hedging strategy," Monte Carlo Methods and Applications, De Gruyter, vol. 20(4), pages 223-235, December.

    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:kap:apfinm:v:20:y:2013:i:1:p:71-81. 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.