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Pólya-based approximation for the ATM-forward implied volatility

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  • Ivan Matić

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

  • Radoš Radoičić

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

  • Dan Stefanica

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

Abstract

We introduce a closed form approximation for the implied volatility of ATM-forward options. The relative error of this approximation is uniformly bounded for all option maturities and implied volatilities. The approximation is extremely precise, having relative error less than 10−6 for all options with integrated volatility less than 1.9, such as options with maturity less than three years and implied volatility less than 100%. Moreover, the approximate implied volatilities fall within the implied volatility bid–ask spread for all the liquid options, such as options with volatility less than 200% and maturity less than nine years.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:02n03:n:s2424786317500323
    DOI: 10.1142/S2424786317500323
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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. Dan Stefanica & Radoš Radoičić, 2016. "A sharp approximation for ATM-forward option prices and implied volatilites," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-24, March.
    3. 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.
    4. Li, Minqiang, 2008. "Approximate inversion of the Black-Scholes formula using rational functions," European Journal of Operational Research, Elsevier, vol. 185(2), pages 743-759, March.
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    Cited by:

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    2. 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.
    3. Michele Mininni & Giuseppe Orlando & Giovanni Taglialatela, 2021. "Challenges in approximating the Black and Scholes call formula with hyperbolic tangents," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 73-100, June.

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