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American strangle options with arbitrary strikes

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  • Tsvetelin S. Zaevski

Abstract

The so‐called American strangle options are examined in this paper. Their main characteristic is the combined put and call feature. The holder has the right to exercise prematurely choosing the option's style—put or call. We abandon the traditional assumption that the put strike is below the call one considering arbitrary values. We also assume that the put and call weights are different. The equations for the early exercise boundaries are derived in the perpetual case. After that we approximate numerically these boundaries for the finite maturity options maximizing the option holder's utility. On the basis of them we apply a Crank–Nicolson finite difference method to the corresponding Black–Scholes‐style partial differential equation to obtain the fair option price.

Suggested Citation

  • Tsvetelin S. Zaevski, 2023. "American strangle options with arbitrary strikes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 880-903, July.
    • Handle: RePEc:wly:jfutmk:v:43:y:2023:i:7:p:880-903
    DOI: 10.1002/fut.22419
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    References listed on IDEAS

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    1. Laminou Abdou, Souleymane & Moraux, Franck, 2016. "Pricing and hedging American and hybrid strangles with finite maturity," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 112-125.
    2. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    3. Junkee Jeon & Geonwoo Kim, 2022. "Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    4. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game put options," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. G. Alobaidi & R. Mallier, 2002. "Laplace transforms and the American straddle," Journal of Applied Mathematics, Hindawi, vol. 2, pages 1-9, January.
    7. Shi Qiu, 2020. "American Strangle Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(3), pages 228-263, May.
    8. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
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    Cited by:

    1. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo, 2024. "Pricing first-touch digitals with a multi-step double boundary and American barrier options," Finance Research Letters, Elsevier, vol. 59(C).
    2. Tsvetelin S. Zaevski, 2024. "Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems," Mathematics, MDPI, vol. 12(10), pages 1-27, May.

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