Uniform Bounds for Black--Scholes Implied Volatility
SIAM Journal on Financial Mathematics
Society for Industrial and Applied Mathematics
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Tehranchi, M. (2016). Uniform Bounds for Black--Scholes Implied Volatility. SIAM Journal on Financial Mathematics, 7 893-916. https://doi.org/10.1137/14095248X
In this note, Black--Scholes implied volatility is expressed in terms of various optimization problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These bounds are used to reprove asymptotic formulas for implied volatility at extreme strikes and/or maturities.
External DOI: https://doi.org/10.1137/14095248X
This record's URL: https://www.repository.cam.ac.uk/handle/1810/260929