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We consider the problem of calculating risk-neutral implied volatilities ofEuropean options without relying on option mid prices but solely on bid and askprices. We provide an approach, based on the conic finance paradigm, thatallows to uniquely strip risk-neutral implied volatilities from bid and askquotes, and that does not require restrictive assumptions. Our methodology alsoallows to jointly calculate the implied liquidity of the market. The ideaoutlined in this paper can be applied to calculate other implied parametersfrom bid and ask security prices as soon as their theoretical risk-neutralcounterparts are strictly increasing with respect to the former.

Liquidity-free implied volatilities: an approach using conic finance