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A Generalized Simple Formula to Compute the Implied Volatility

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  • Chance, Don M

Abstract

This paper provides a direct method of obtaining an accurate estimate of the implied volatility of a call option. It adds a quadratic adjustment term to an already-known formula for at-the-money calls, previously developed by Brenner and Subrahmanyam. The adjusted formula is quite accurate for options no more than 20 percent in- or out-of-the-money and is simple to program and compute. Copyright 1996 by MIT Press.

Suggested Citation

  • Chance, Don M, 1996. "A Generalized Simple Formula to Compute the Implied Volatility," The Financial Review, Eastern Finance Association, vol. 31(4), pages 859-867, November.
    • Handle: RePEc:bla:finrev:v:31:y:1996:i:4:p:859-67
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    Citations

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    Cited by:

    1. Steven Li, 2003. "The estimation of implied volatility from the Black-Scholes model: some new formulas and their applications," School of Economics and Finance Discussion Papers and Working Papers Series 141, School of Economics and Finance, Queensland University of Technology.
    2. Yibing Chen & Cheng-Few Lee & John Lee & Jow-Ran Chang, 2018. "Alternative Methods to Estimate Implied Variance: Review and Comparison," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-28, December.
    3. 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.
    4. 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.
    5. Yixiao Lu & Yihong Wang & Tinggan Yang, 2021. "Adaptive Gradient Descent Methods for Computing Implied Volatility," Papers 2108.07035, arXiv.org, revised Mar 2023.
    6. Jaehyuk Choi & Jeonggyu Huh & Nan Su, 2023. "Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding," Papers 2302.08758, arXiv.org, revised Oct 2024.
    7. 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.
    8. 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.
    9. Jaehyuk Choi & Kwangmoon Kim & Minsuk Kwak, 2009. "Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 261-268.
    10. 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.
    11. 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.
    12. Kathrin Glau & Paul Herold & Dilip B. Madan & Christian Potz, 2017. "The Chebyshev method for the implied volatility," Papers 1710.01797, arXiv.org.
    13. Shou-Lei Wang & Yu-Fei Yang & Yu-Hua Zeng, 2014. "The Adjoint Method for the Inverse Problem of Option Pricing," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, March.
    14. 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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