  Risk-neutral default probabilities can be implied from credit default swap
(CDS) market quotes. In practice, mid CDS quotes are used as inputs, as their
risk-neutral counterparts are not observable. We show how to imply risk-neutral
default probabilities from bid and ask quotes directly by means of formulating
the CDS calibration problem to bid and ask market quotes within the conic
finance framework. Assuming the risk-neutral distribution of the default time
to be driven by a Poisson process we prove, under mild liquidity-related
assumptions, that the calibration problem admits a unique solution that also
allows to jointly calculate the implied liquidity of the market.
