Uniform bounds for Black--Scholes implied volatility
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Tehranchi, MR
Abstract
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.
Description
Keywords
implied volatility, put-call symmetry, asymptotic formulas
Journal Title
SIAM Journal on Financial Mathematics
Conference Name
Journal ISSN
1945-497X
1945-497X
1945-497X
Volume Title
7
Publisher
Society for Industrial and Applied Mathematics