Uniform Bounds for Black--Scholes Implied Volatility
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Authors
Tehranchi, Michael
Publication Date
2016-11-29Journal Title
SIAM Journal on Financial Mathematics
ISSN
1945-497X
Publisher
Society for Industrial and Applied Mathematics
Volume
7
Pages
893-916
Language
English
Type
Article
This Version
AM
Metadata
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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
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.
Identifiers
External DOI: https://doi.org/10.1137/14095248X
This record's URL: https://www.repository.cam.ac.uk/handle/1810/260929
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