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Knock‐in American options

Author

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  • Min Dai
  • Yue Kuen Kwok

Abstract

A knock‐in American option under a trigger clause is an option contract in which the option holder receives an American option conditional on the underlying stock price breaching a certain trigger level (also called barrier level). We present analytic valuation formulas for knock‐in American options under the Black‐Scholes pricing framework. The price formulas possess different analytic representations, depending on the relation between the trigger stock price level and the critical stock price of the underlying American option. We also performed numerical valuation of several knock‐in American options to illustrate the efficacy of the price formulas. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:179–192, 2004

Suggested Citation

  • Min Dai & Yue Kuen Kwok, 2004. "Knock‐in American options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(2), pages 179-192, February.
    • Handle: RePEc:wly:jfutmk:v:24:y:2004:i:2:p:179-192
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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. Luluwah Al-Fagih, 2015. "The British Knock-Out Put Option," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-32.
    3. 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.
    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. Han, Heejae & Jeon, Junkee & Kang, Myungjoo, 2016. "Closed form valuation of American chained knock-in options," Finance Research Letters, Elsevier, vol. 17(C), pages 176-185.
    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.
    7. Le, Nhat-Tan & Dang, Duy-Minh, 2017. "Pricing American-style Parisian down-and-out call options," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 330-347.

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