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Tighter Bounds For Implied Volatility

Author

Listed:
  • JIM GATHERAL

    (Department of Mathematics, Baruch College, City University of New York, One Bernard Baruch Way, New York 10010, USA)

  • IVAN MATIĆ

    (Department of Mathematics, Baruch College, City University of New York, One Bernard Baruch Way, New York 10010, USA)

  • RADOŠ RADOIČIĆ

    (Department of Mathematics, Baruch College, City University of New York, One Bernard Baruch Way, New York 10010, USA)

  • DAN STEFANICA

    (Department of Mathematics, Baruch College, City University of New York, One Bernard Baruch Way, New York 10010, USA)

Abstract

We establish bounds on Black–Scholes implied volatility that improve on the uniform bounds previously derived by Tehranchi. Our upper bound is uniform, while the lower bound holds for most options likely to be encountered in practical applications. We further demonstrate the practical effectiveness of our new bounds by showing how the efficiency of the bisection algorithm is improved for a snapshot of SPX option quotes.

Suggested Citation

  • Jim Gatheral & Ivan Matić & Radoš Radoičić & Dan Stefanica, 2017. "Tighter Bounds For Implied Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-14, August.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:05:n:s0219024917500352
    DOI: 10.1142/S0219024917500352
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    References listed on IDEAS

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    1. Corrado, Charles J. & Miller, Thomas Jr., 1996. "A note on a simple, accurate formula to compute implied standard deviations," Journal of Banking & Finance, Elsevier, vol. 20(3), pages 595-603, April.
    2. Hallerbach, W.G.P.M., 2004. "An Improved Estimator For Black-Scholes-Merton Implied Volatility," ERIM Report Series Research in Management ERS-2004-054-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Dan Stefanica & Radoš Radoičić, 2017. "An Explicit Implied Volatility Formula," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-32, November.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Michael R. Tehranchi, 2015. "Uniform bounds for Black--Scholes implied volatility," Papers 1512.06812, arXiv.org, revised Aug 2016.
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    Cited by:

    1. Yuxuan Xia & Zhenyu Cui, 2018. "An exact and explicit implied volatility inversion formula," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-29, September.
    2. Ivan Matić & Radoš Radoičić & Dan Stefanica, 2017. "Pólya-based approximation for the ATM-forward implied volatility," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-15, June.
    3. Olesya Grishchenko & Xiao Han & Victor Nistor, 2018. "A volatility-of-volatility expansion of the option prices in the SABR stochastic volatility model," Papers 1812.09904, arXiv.org.
    4. Dan Stefanica & Radoš Radoičić, 2017. "An Explicit Implied Volatility Formula," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-32, November.

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