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Liquidity-free implied volatilities: An approach using conic finance

Author

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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)

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.

Suggested Citation

  • Matteo Michielon & Asma Khedher & Peter Spreij, 2021. "Liquidity-free implied volatilities: An approach using conic finance," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 1-27, December.
    • Handle: RePEc:wsi:ijfexx:v:08:y:2021:i:04:n:s2424786321500419
    DOI: 10.1142/S2424786321500419
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