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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, Open Access Journal, vol. 3(3), pages 1-16, July.
  • Handle: RePEc:gam:jrisks:v:3:y:2015:i:3:p:234-249:d:52276
    as

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    File URL: http://www.mdpi.com/2227-9091/3/3/234/pdf
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    File URL: http://www.mdpi.com/2227-9091/3/3/234/
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    References listed on IDEAS

    as
    1. Valdo Durrleman, 2010. "From implied to spot volatilities," Finance and Stochastics, Springer, vol. 14(2), pages 157-177, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Dan Pirjol & Lingjiong Zhu, 2016. "Discrete Sums of Geometric Brownian Motions, Annuities and Asian Options," Papers 1609.07558, arXiv.org.
    2. 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.

    More about this item

    Keywords

    option pricing; extreme strikes; Black–Scholes models;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

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