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J. Gatheral, I. Matic, Ivan, R. Radoicic, D. Stefanica – “Tighter Bounds for Implied Volatility”

J. Gatheral, I. Matic, Ivan, R. Radoicic, D. Stefanica – “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.