Liquidity-free implied volatilities: An approach using conic finance

Matteo Michielon, Asma Khedher () and Peter Spreij
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Matteo Michielon: Quantitative Analysis and Quantitative Development, ABN AMRO Bank N.V., Gustav Mahlerlaan 10, 1082 PP Amsterdam, The Netherlands†Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, The Netherlands
Asma Khedher: ��Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, The Netherlands
Peter Spreij: ��Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, The Netherlands‡Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Huygens Building, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands

International Journal of Financial Engineering (IJFE), 2021, vol. 08, issue 04, 1-27

Abstract: In this paper, we consider the problem of calculating risk-neutral implied volatilities of European options without relying on option mid prices but solely on bid and ask prices. We provide an approach, based on the conic finance paradigm, that allows to uniquely strip risk-neutral implied volatilities from bid and ask quotes, and that does not require restrictive assumptions. Our methodology also allows to jointly calculate the implied liquidity of the market. The idea outlined in this paper can be applied to calculate other implied parameters from bid and ask security prices as soon as their theoretical risk-neutral counterparts are strictly increasing with respect to the former.

Keywords: Bid–ask spread; conic finance; distorted expectation; implied volatility; liquidity (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S2424786321500419

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