Uniform bounds for Black--Scholes implied volatility

Michael R. Tehranchi

Papers from arXiv.org

Abstract: In this note, Black--Scholes implied volatility is expressed in terms of various optimisation 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 formulae for implied volatility at extreme strikes and/or maturities.

Date: 2015-12, Revised 2016-08
New Economics Papers: this item is included in nep-rmg
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Published in SIAM Journal on Financial Mathematics 7(1): 893-916 (2016)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1512.06812

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