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. 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..
    2. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    3. 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.
    4. Michael Schmutz, 2011. "Semi-static hedging for certain Margrabe-type options with barriers," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 979-986.
    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. Ilya Molchanov & Michael Schmutz, 2008. "Geometric extension of put-call symmetry in the multiasset setting," Papers 0806.4506, arXiv.org, revised Mar 2009.
    3. 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.
    4. Petra Andrlikova, 2014. "Is Barrier version of Merton model more realistic? Evidence from Europe," Proceedings of International Academic Conferences 0801868, International Institute of Social and Economic Sciences.
    5. José Fajardo, 2014. "Symmetry and Bates’ rule in Ornstein–Uhlenbeck stochastic volatility models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 319-327, October.
    6. 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..
    7. Kau, James B. & Keenan, Donald C., 1999. "Patterns of rational default," Regional Science and Urban Economics, Elsevier, vol. 29(6), pages 765-785, November.
    8. Gady Jacoby & Chuan Liao & Jonathan A. Batten, 2007. "A Pure Test for the Elasticity of Yield Spreads," The Institute for International Integration Studies Discussion Paper Series iiisdp195, IIIS.
    9. 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.
    10. Dankenbring, Henning, 1998. "Volatility estimates of the short term interest rate with an application to German data," SFB 373 Discussion Papers 1998,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Norden, Lars, 2003. "Asymmetric option price distribution and bid-ask quotes: consequences for implied volatility smiles," Journal of Multinational Financial Management, Elsevier, vol. 13(4-5), pages 423-441, December.
    12. Leluc, Rémi & Portier, François & Zhuman, Aigerim & Segers, Johan, 2023. "Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence," LIDAM Discussion Papers ISBA 2023019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    14. Loncarski, I. & Ter Horst, J.R. & Veld, C.H., 2006. "Why do Companies issue Convertible Bond Loans? An Empirical Analysis for the Canadian Market," Discussion Paper 2006-65, Tilburg University, Center for Economic Research.
    15. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    16. Boyle, Glenn & Clyne, Stefan & Roberts, Helen, 2005. "Valuing Employee Stock Options: Implications for the Implementation of NZ IFRS 2," Working Paper Series 18949, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    17. Miller, M. & Weller, P., 1988. "Solving Stochastic Saddlepoint Systems: A Qualitative Treatment With Economic Applications," The Warwick Economics Research Paper Series (TWERPS) 309, University of Warwick, Department of Economics.
    18. Vorst, A. C. F., 1988. "Option Pricing And Stochastic Processes," Econometric Institute Archives 272366, Erasmus University Rotterdam.
    19. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    20. Lei Fan & Justin Sirignano, 2024. "Machine Learning Methods for Pricing Financial Derivatives," Papers 2406.00459, 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: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.