16 Pages Posted: 24 Feb 2017 Last revised: 23 Aug 2017
Date Written: June 26, 2017
We establish bounds on Black-Scholes implied volatility that improve on the uniform bounds previously derived by Tehranchi. Our upper bound is uniform, while the lower bound holds for most options likely to be encountered in practical applications. We further demonstrate the practical effectiveness of our new bounds by showing how the efficiency of the bisection algorithm is improved for a snapshot of SPX options quotes.
Keywords: Implied Volatility, Polya Approximation, Bisection Method
Suggested Citation: Suggested Citation
Gatheral, Jim and Matic, Ivan and Radoicic, Rados and Stefanica, Dan, Tighter Bounds for Implied Volatility (June 26, 2017). International Journal of Theoretical and Applied Finance, Vol. 20, No. 5, 1750035, 2017. Available at SSRN: https://ssrn.com/abstract=2922742 or http://dx.doi.org/10.2139/ssrn.2922742