2015/12/31 by Michael R. Tehranchi · 1 citation
Economics, Econometrics and Finance · #msc:41A60 #msc:91B25 #msc:91G20 #q-fin.MF
paper · pdf · doi:10.1137/14095248x
published as SIAM Journal on Financial Mathematics 7(1): 893-916 (2016)
arxiv created 2016/08/31 · arxiv updated 2016/12/14
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.