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An Explicit Implied Volatility Formula

Author

Listed:
  • DAN STEFANICA

    (Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA)

  • RADOŠ RADOIČIĆ

    (Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA)

Abstract

We show that an explicit approximate implied volatility formula can be obtained from a Black–Scholes formula approximation that is 2% accurate. The relative error of the approximate implied volatility is uniformly bounded for options with any moneyness and with arbitrary large or small option maturities and volatilities, including for long dated options and options on highly volatile underlying assets. For options within a large trading range, such as options with maturity less than five years and implied volatility less than 150%, the error of the approximate implied volatility relative to the Black–Scholes implied volatility is less than 10% points.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:07:n:s0219024917500480
    DOI: 10.1142/S0219024917500480
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    References listed on IDEAS

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    9. 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.
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    Citations

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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. 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.
    3. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.
    4. 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.
    5. Geon Lee & Tae-Kyoung Kim & Hyun-Gyoon Kim & Jeonggyu Huh, 2022. "Newton Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities," Papers 2210.15969, arXiv.org.

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