Consistency of option prices under bid–ask spreads. (11th November 2019)

• Record Type: Journal Article
• Authors: Gerhold, Stefan; Gülüm, Ismail Cetin
• Is Part Of: Mathematical finance. Volume 30:Number 2(2020)
• Page Start: 377
• Page End: 402
• Publication Date: 2019-11-11
• Subjects: bid–ask spread -- call option -- martingale -- peacock -- Strassen's theorem -- Transaction costs; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12230
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: 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.