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Closed Form Valuation Of American Barrier Options

Author

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  • ESPEN GAARDER HAUG

    (Amaranth Advisors, Two American Lane, Greenwich, CT 06836, USA)

Abstract

Closed form formulae for European barrier options are well known from the literature. This is not the case for American barrier options, for which no closed form formulae have been published. One has therefore had to resort to numerical methods. Lattice models like a binomial or a trinomial tree, for valuation of barrier options are known to converge extremely slowly, compared to plain vanilla options. Methods for improving the algorithms have been described by several authors. However, these are still numerical methods that are quite computer intensive. In this paper we show how some American barrier options can be valued analytically in a very simple way. This speeds up the valuation dramatically as well as give new insight into barrier option valuation.

Suggested Citation

  • Espen Gaarder Haug, 2001. "Closed Form Valuation Of American Barrier Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 355-359.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:02:n:s0219024901001012
    DOI: 10.1142/S0219024901001012
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    Citations

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    Cited by:

    1. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2015. "Pricing and static hedging of American-style knock-in options on defaultable stocks," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 343-360.
    2. Daniel Wei-Chung Miao & Yung-Hsin Lee & Jr-Yan Wang, 2018. "Using forward Monte-Carlo simulation for the valuation of American barrier options," Annals of Operations Research, Springer, vol. 264(1), pages 339-366, May.
    3. J. C. Ndogmo, 2008. "Classification of barrier options," Papers 0806.4676, arXiv.org.
    4. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    5. Chung, San-Lin & Shih, Pai-Ta & Tsai, Wei-Che, 2013. "Static hedging and pricing American knock-in put options," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 191-205.
    6. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.

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