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A note on a simple, accurate formula to compute implied standard deviations

Citations

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  1. Butler, J. S. & Schachter, Barry, 1996. "The statistical properties of parameters inferred from the black-scholes formula," International Review of Financial Analysis, Elsevier, vol. 5(3), pages 223-235.
  2. Chargoy-Corona, Jesús & Ibarra-Valdez, Carlos, 2006. "A note on Black–Scholes implied volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 681-688.
  3. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, September.
  4. Matthias Fengler, 2010. "Option data and modeling BSM implied volatility," University of St. Gallen Department of Economics working paper series 2010 2010-32, Department of Economics, University of St. Gallen.
  5. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
  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. 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.
  8. 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.
  9. Ivan Damnjanovic & Xue Zhou, 2009. "Impact of crude oil market behaviour on unit bid prices: the evidence from the highway construction sector," Construction Management and Economics, Taylor & Francis Journals, vol. 27(9), pages 881-890.
  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. 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.
  14. Wolfgang Schadner, 2026. "An Explicit Solution to Black-Scholes Implied Volatility," Papers 2604.24480, arXiv.org, revised May 2026.
  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.
  16. Jingwei Liu & Xing Chen, 2012. "Implied volatility formula of European Power Option Pricing," Papers 1203.0599, arXiv.org.
  17. 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.
  18. Geon Lee & Tae-Kyoung Kim & Hyun-Gyoon Kim & Jeonggyu Huh, 2022. "Newton–Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities," JRFM, MDPI, vol. 15(12), pages 1-8, December.
  19. 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.
  20. 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.
  21. Hu, Duni & Wang, Hailong, 2026. "An equilibrium asset pricing model with heterogeneous beliefs about climate risks," International Review of Financial Analysis, Elsevier, vol. 109(C).
  22. Yixiao Lu & Yihong Wang & Tinggan Yang, 2021. "Adaptive Gradient Descent Methods for Computing Implied Volatility," Papers 2108.07035, arXiv.org, revised Mar 2023.
  23. 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.
  24. 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.
  25. 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.
  26. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
  27. Daniel Wei-Chung Miao & Xenos Chang-Shuo Lin & Chang-Yao Lin, 2021. "Using Householder’s method to improve the accuracy of the closed-form formulas for implied volatility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 493-528, December.
  28. Raeid Saqur, 2026. "Fast-Vollib: A Fast Implied Volatility Library for Pythonwith PyTorch, JAX, and CUDA Fused-Kernel Backends," Papers 2604.27210, arXiv.org, revised Jun 2026.
  29. Pareja Vasseur, Julián. DBA & Prada Sánchez, Marcela & Moreno Escobar, Martha, 2019. "Volatilidad en Opciones Reales: Revisión Literaria y un Caso de Aplicación en el Sector Petrolero Colombiano || Real Options Volatility: Literature Review and a Case of Application in the Colombian Oil Sector," 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. 27(1), pages 136-155, June.
  30. Michael R. Tehranchi, 2015. "Uniform bounds for Black--Scholes implied volatility," Papers 1512.06812, arXiv.org, revised Aug 2016.
  31. Hu, Duni & Wang, Hailong, 2024. "Heterogeneous beliefs with preference interdependence and asset pricing," International Review of Economics & Finance, Elsevier, vol. 93(PA), pages 1-37.
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