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An Improved Approach to Computing Implied Volatility

Author

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  • Chambers, Donald R
  • Nawalkha, Sanjay K

Abstract

A well-known problem in finance is the absence of a closed form solution for volatility in common option pricing models. Several approaches have been developed to provide closed form approximations to volatility. This paper examines Chance's (1993, 1996) model, Corrado and Miller's (1996) model and Bharadia, Christofides and Salkin's (1996) model for approximating implied volatility. We develop a simplified extension of Chance's model that has greater accuracy than previous models. Our tests indicate dramatically improved results. Copyright 2001 by MIT Press.

Suggested Citation

  • Chambers, Donald R & Nawalkha, Sanjay K, 2001. "An Improved Approach to Computing Implied Volatility," The Financial Review, Eastern Finance Association, vol. 36(3), pages 89-99, August.
    • Handle: RePEc:bla:finrev:v:36:y:2001:i:3:p:89-99
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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. Yixiao Lu & Yihong Wang & Tinggan Yang, 2021. "Adaptive Gradient Descent Methods for Computing Implied Volatility," Papers 2108.07035, arXiv.org, revised Mar 2023.
    5. 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.
    6. 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.
    7. Kazuhiko NISHINA & Tatsuro Nabil MAGHREBI & Moo-Sung KIM, 2006. "Stock Market Volatility And The Forecasting Accuracy Of Implied Volatility Indices," Discussion Papers in Economics and Business 06-09, Osaka University, Graduate School of Economics.
    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. Adrienne Kearney & Raymond Lombra, 2004. "Stock market volatility, the news, and monetary policy," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 28(2), pages 252-259, June.
    15. 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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