  Given a finite set of European call option prices on a single underlying, we
want to know when there is a market model which is consistent with these
prices. In contrast to previous studies, we allow models where the underlying
trades at a bid-ask spread. The main question then is how large (in terms of a
deterministic bound) this spread must be to explain the given prices. We fully
solve this problem in the case of a single maturity, and give several partial
results for multiple maturities. For the latter, our main mathematical tool is
a recent result on approximation by peacocks [S. Gerhold, I.C. G\"ul\"uum,
arXiv:1512.06640].
