Tighter Bounds for Implied Volatility

Abstract

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