publication . Article . Preprint . Other literature type . 2016

Uniform bounds for Black--Scholes implied volatility

Tehranchi, Michael;
Open Access
  • Published: 27 Oct 2016 Journal: SIAM Journal on Financial Mathematics, volume 7, pages 893-916 (eissn: 1945-497X, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
  • Country: United Kingdom
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. the Society for Industrial and Applied Mathematics 10.1137/14095248X
free text keywords: Financial economics, Upper and lower bounds, Mathematical optimization, No-arbitrage bounds, BlackÔÇôScholes model, Moneyness, Implied volatility, Mathematical economics, Economics, Homogeneous space, Quantitative Finance - Mathematical Finance, 91G20, 91B25, 41A60
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