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Closed form valuation of American chained knock-in options

Author

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  • Han, Heejae
  • Jeon, Junkee
  • Kang, Myungjoo

Abstract

In this paper, we study pricing of American chained knock-in option. Chained barrier option is a new type of barrier option with two barrier levels. A knock-in American chained barrier option under a trigger clause is an option contract in which the option holder receives an American knock-in option conditional on the underlying asset price breaching a specified barrier level. We derive analytic valuation formulas for knock-in American chained options under the Black–Scholes pricing framework by using reflection principle and formulas for knock-in American options. Furthermore, we present some numerical solutions and plots of the value of knock-in American chained options.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:finlet:v:17:y:2016:i:c:p:176-185
    DOI: 10.1016/j.frl.2016.03.003
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    References listed on IDEAS

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    1. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    4. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double‐Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378, October.
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    Cited by:

    1. Liu, Yanchu & Cui, Zhenyu & Zhang, Ning, 2016. "Integral representation of vega for American put options," Finance Research Letters, Elsevier, vol. 19(C), pages 204-208.
    2. Zhang, Jiayi & Zhou, Ke, 2024. "Analytical valuation of vulnerable chained options," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).

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    More about this item

    Keywords

    Chained options; Knock-in options; American barrier options; Reflection principle;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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