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Robust One-Period Option Hedging

Author

Listed:
  • Frank Lutgens

    (Department of Finance, Maastricht University, Tongerseweg 53, 6200 MD, Maastricht, The Netherlands)

  • Jos Sturm

    (Department of Econometrics, Tilburg University, Tilburg, The Netherlands)

  • Antoon Kolen

    (Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands)

Abstract

We consider robust optimization to cope with uncertainty about the stock return process in one-period option hedging problems. The robust approach relates portfolio choice to uncertainty, making more cautious hedges when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlying stocks and show that for this set the robust problem is a second-order cone program that can be solved efficiently. We apply the approach to find an optimal portfolio to hedge an index option.

Suggested Citation

  • Frank Lutgens & Jos Sturm & Antoon Kolen, 2006. "Robust One-Period Option Hedging," Operations Research, INFORMS, vol. 54(6), pages 1051-1062, December.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:6:p:1051-1062
    DOI: 10.1287/opre.1060.0352
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. António Alberto Santos & Ana Margarida Monteiro & Rui Pascoal, 2014. "Portfolio Choice under Parameter Uncertainty: Bayesian Analysis and Robust Optimization Comparison," GEMF Working Papers 2014-25, GEMF, Faculty of Economics, University of Coimbra.
    2. Panos Xidonas & Ralph Steuer & Christis Hassapis, 2020. "Robust portfolio optimization: a categorized bibliographic review," Annals of Operations Research, Springer, vol. 292(1), pages 533-552, September.
    3. Raquel J. Fonseca & Steve Zymler & Wolfram Wiesemann & Berc Rustem, 2009. "Robust Optimization of Currency Portfolios," Working Papers 012, COMISEF.
    4. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2018. "Recent advancements in robust optimization for investment management," Annals of Operations Research, Springer, vol. 266(1), pages 183-198, July.
    5. Maria Scutellà & Raffaella Recchia, 2013. "Robust portfolio asset allocation and risk measures," Annals of Operations Research, Springer, vol. 204(1), pages 145-169, April.
    6. Zymler, Steve & Rustem, Berç & Kuhn, Daniel, 2011. "Robust portfolio optimization with derivative insurance guarantees," European Journal of Operational Research, Elsevier, vol. 210(2), pages 410-424, April.
    7. Saeed Marzban & Masoud Mahootchi & Alireza Arshadi Khamseh, 2015. "Developing a multi-period robust optimization model considering American style options," Annals of Operations Research, Springer, vol. 233(1), pages 305-320, October.
    8. Ashrafi, Hedieh & Thiele, Aurélie C., 2021. "A study of robust portfolio optimization with European options using polyhedral uncertainty sets," Operations Research Perspectives, Elsevier, vol. 8(C).
    9. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    10. Balter, Anne G. & Pelsser, Antoon, 2020. "Pricing and hedging in incomplete markets with model uncertainty," European Journal of Operational Research, Elsevier, vol. 282(3), pages 911-925.

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