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Monotonicity of implied volatility for perpetual put options

Part of: Stochastic processes Mathematical finance

Published online by Cambridge University Press:  19 June 2023

Erik Ekström Open the ORCID record for Erik Ekström [Opens in a new window]  and
Ebba Mellquist
Erik Ekström*
Affiliation:
Uppsala University
Ebba Mellquist*
Affiliation:
Uppsala University
*
*Postal address: Department of Mathematics, Box 256, 75105 Uppsala, Sweden.
*Postal address: Department of Mathematics, Box 256, 75105 Uppsala, Sweden.
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Abstract

We define and study properties of implied volatility for American perpetual put options. In particular, we show that if the market prices are derived from a local volatility model with a monotone volatility function, then the corresponding implied volatility is also monotone as a function of the strike price.

Keywords

Implied volatilityAmerican optionsvolatility skew

MSC classification

Primary: 91G20: Derivative securities
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 1 , March 2024 , pp. 301 - 310
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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