Consistency of option prices under bid-ask spreads

TL;DR

This paper investigates the conditions under which observed European call option prices, including bid-ask spreads, can be explained by a consistent market model, providing a complete solution for single maturity and partial results for multiple maturities.

Contribution

It introduces a comprehensive analysis of market models with bid-ask spreads, extending previous work to include spreads and solving the problem for single maturity options.

Findings

Complete characterization for single maturity options

Partial results for multiple maturities

Bound on bid-ask spread for model consistency

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 result on approximation by peacocks [S. Gerhold, I.C. G\"ul\"uum, arXiv:1512.06640].