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Hedging Barrier Options: Current Methods and Alternatives

Author

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  • Dupont, Dominique Y.

    (EURANDOM - TUE, The Netherlands)

Abstract

This paper applies to the static hedge of barrier options a technique, mean-square hedging, designed to minimize the size of the hedging error when perfect replication is not possible. It introduces an extension of this technique which preserves the computational efficiency of mean-square hedging while being consistent with any prior pricing model or with any linear constraint on the hedging residual. This improves on current static hedging methods, which aim at exactly replicating barrier options and rely on strong assumptions on the availability of traded options with certain strikes or maturities, or on the distribution of the underlying asset.

Suggested Citation

  • Dupont, Dominique Y., 2001. "Hedging Barrier Options: Current Methods and Alternatives," Economics Series 103, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:103
    as

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    File URL: https://irihs.ihs.ac.at/id/eprint/1366
    File Function: First version, 2001
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    References listed on IDEAS

    as
    1. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    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. 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.
    4. Peter G. Zhang, 1998. "Hedging Exotic Options," World Scientific Book Chapters, in: Exotic Options A Guide to Second Generation Options, chapter 35, pages 639-643, World Scientific Publishing Co. Pte. Ltd..
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    7. David S. Bates, "undated". "The Cash Premium: Option Pricing Under Asymmetric Processes, with Applications to Options on Deutschemark Futures," Rodney L. White Center for Financial Research Working Papers 36-88, Wharton School Rodney L. White Center for Financial Research.
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    Citations

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    Cited by:

    1. Sbuelz, A., 2000. "Hedging Double Barriers with Singles," Discussion Paper 2000-112, Tilburg University, Center for Economic Research.
    2. J. Maruhn & E. Sachs, 2009. "Robust static hedging of barrier options in stochastic volatility models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 405-433, December.
    3. Alessandro Sbuelz, 2005. "Hedging Double Barriers With Singles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 393-407.
    4. Sbuelz, A., 2000. "Hedging Double Barriers with Singles," Other publications TiSEM e810e3ab-1936-457e-a3ae-7, Tilburg University, School of Economics and Management.
    5. Stephane Crepey, 2004. "Delta-hedging vega risk?," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 559-579.
    6. Alev{s} v{C}ern'y, 2016. "Discrete-Time Quadratic Hedging of Barrier Options in Exponential L\'{e}vy Model," Papers 1603.03747, arXiv.org.

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    More about this item

    Keywords

    Barrier options; Static hedging; Mean-square hedging;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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