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Consistency of option prices under bid-ask spreads

Stefan Gerhold and I. Cetin G\"ul\"um

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Abstract: 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 generalization of Strassen's theorem [S. Gerhold, I.C. G\"ul\"um, arXiv:1512.06640], which characterizes the existence of martingales in balls w.r.t. the infinity Wasserstein distance.

Date: 2016-08
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