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Valuing stock options when prices are subject to a lower boundary

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  • Dirk Veestraeten

Abstract

This study examines the implications for stock option pricing when the domain of the stock price is constrained by a lower boundary. The valuation strategy starts from the familiar geometric Brownian motion framework of Black & Scholes (1973). However, an instantaneously reflecting lower boundary will be superimposed such that a reflected geometric Brownian motion arises. The particular nature of reflection in this approach precludes arbitrage opportunities such that risk‐neutral option valuation techniques can straightforwardly be applied. It will be shown that ignoring lower boundaries can lead to a substantial undervaluation of option prices. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:231–247, 2008

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  • Dirk Veestraeten, 2008. "Valuing stock options when prices are subject to a lower boundary," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(3), pages 231-247, March.
    • Handle: RePEc:wly:jfutmk:v:28:y:2008:i:3:p:231-247
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    Cited by:

    1. Dean Buckner & Kevin Dowd & Hardy Hulley, 2022. "Arbitrage Problems with Reflected Geometric Brownian Motion," Papers 2201.05312, arXiv.org, revised Sep 2022.
    2. Irena Mikolajun & Jean-Marie Viaene, 2015. "Trade, Factor Mobility and the Extent of Economic Integration: Theory and Evidence," CESifo Working Paper Series 5481, CESifo.
    3. Irena Mikolajun & Jean-Marie Viaene, 2015. "Trade, Factor Mobility and the Extent of Economic Integration: Theory and Evidence," Tinbergen Institute Discussion Papers 15-096/VI, Tinbergen Institute.
    4. Markus Hertrich & Heinz Zimmermann, 2017. "On the Credibility of the Euro/Swiss Franc Floor: A Financial Market Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(2-3), pages 567-578, March.
    5. Hertrich Markus, 2016. "The Costs of Implementing a Unilateral One-Sided Exchange Rate Target Zone," Review of Economics, De Gruyter, vol. 67(1), pages 91-120, May.
    6. Irena Mikolajun & Jean-Marie Viaene, 2019. "Is Hard Brexit Detrimental to EU Integration? Theory and Evidence," Open Economies Review, Springer, vol. 30(4), pages 621-654, September.
    7. Irena Mikolajun & Jean-Marie Viaene, 2018. "Is Hard Brexit Detrimental to EU Integration? Theory and Evidence," CESifo Working Paper Series 7199, CESifo.
    8. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    9. Ning Cai & Xuewei Yang, 2021. "A Computational Approach to First Passage Problems of Reflected Hyperexponential Jump Diffusion Processes," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 216-229, January.
    10. R. Guy Thomas, 2023. "Long-term option pricing with a lower reflecting barrier," Papers 2302.05808, arXiv.org.

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