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Faster Implied Volatilities via the Implicit Function Theorem

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  • Michael A. Kelly

Abstract

We present a faster, more accurate technique for estimating implied volatility using the standard partial derivatives of the Black‐Scholes option‐pricing formula. Beside Newton‐Raphson and slower approximation methods, this technique is the first to provide an error tolerance, which is essential for practical application. All existing noniterative approximation methods do not provide error tolerances and have the potential for large errors.

Suggested Citation

  • Michael A. Kelly, 2006. "Faster Implied Volatilities via the Implicit Function Theorem," The Financial Review, Eastern Finance Association, vol. 41(4), pages 589-597, November.
    • Handle: RePEc:bla:finrev:v:41:y:2006:i:4:p:589-597
    DOI: 10.1111/j.1540-6288.2006.00158.x
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    Cited by:

    1. Minqiang Li & Kyuseok Lee, 2011. "An adaptive successive over-relaxation method for computing the Black-Scholes implied volatility," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1245-1269.
    2. Don M. Chance & Thomas A. Hanson & Weiping Li & Jayaram Muthuswamy, 2017. "A bias in the volatility smile," Review of Derivatives Research, Springer, vol. 20(1), pages 47-90, April.
    3. Sukhomlin, Nikolay & Santana Jiménez, Lisette Josefina, 2010. "Problema de calibración de mercado y estructura implícita del modelo de bonos de Black-Cox = Market Calibration Problem and the Implied Structure of the Black-Cox Bond Model," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 10(1), pages 73-98, December.
    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.
    5. Noshaba Zulfiqar & Saqib Gulzar, 2021. "Implied volatility estimation of bitcoin options and the stylized facts of option pricing," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-30, December.

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