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Options with Extreme Strikes

Author

Listed:
  • Lingjiong Zhu

    (School of Mathematics, University of Minnesota-Twin Cities, 206 Church Street S.E., Minneapolis, MN 55455, USA)

Abstract

In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black–Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the tail asymptotics for these option types fall into four scenarios.

Suggested Citation

  • Lingjiong Zhu, 2015. "Options with Extreme Strikes," Risks, MDPI, vol. 3(3), pages 1-16, July.
    • Handle: RePEc:gam:jrisks:v:3:y:2015:i:3:p:234-249:d:52276
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    References listed on IDEAS

    as
    1. Victor Nistor & Wen Cheng & Nick Costanzino & John Liechty & Anna L. Mazzucato, 2011. "Closed-form asymptotics and numerical approximations of 1{D} parabolic equations with applications to option pricing," Post-Print hal-01284880, HAL.
    2. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 61-69.
    3. Jim Gatheral & Tai-Ho Wang, 2012. "The Heat-Kernel Most-Likely-Path Approximation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-18.
    4. Jim Gatheral & Tai-Ho Wang, 2012. "The Heat-Kernel Most-Likely-Path Approximation," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 17, pages 389-406, World Scientific Publishing Co. Pte. Ltd..
    5. Valdo Durrleman, 2010. "From implied to spot volatilities," Finance and Stochastics, Springer, vol. 14(2), pages 157-177, April.
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    Citations

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    Cited by:

    1. Pirjol, Dan & Zhu, Lingjiong, 2016. "Discrete sums of geometric Brownian motions, annuities and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 19-37.
    2. Giacomo Morelli & Lea Petrella, 2021. "Option Pricing, Zero Lower Bound, and COVID-19," Risks, MDPI, vol. 9(9), pages 1-13, September.
    3. Dan Pirjol & Lingjiong Zhu, 2016. "Discrete Sums of Geometric Brownian Motions, Annuities and Asian Options," Papers 1609.07558, arXiv.org.

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