Given a finite set of European call option prices on a single underlying, we want to know when there is a market model that 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.
Keywords: Strassen's theorem; Transaction costs; bid–ask spread; call option; martingale; peacock.
© 2019 The Authors. Mathematical Finance published by Wiley Periodicals, Inc.