  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.
