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

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  • 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
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    References listed on IDEAS

    as
    1. 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.
    2. 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..
    3. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    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.
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    Cited by:

    1. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2018. "Asymptotic Static Hedge via Symmetrization," Papers 1801.04045, arXiv.org.
    2. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2017. "The Value of Timing Risk," Papers 1701.05695, arXiv.org.

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