• The work of DGH was supported by an Advanced Fellowship from the EPSRC, held at the University of Bath. The paper was completed while both authors were at the Isaac Newton Institute for Mathematical Sciences, Cambridge. We thank the referee for drawing our attention to the paper by Laurent and Leisen (2000) and for helpful comments. DGH thanks Alex Cox for useful discussions. MHAD thanks Dilip Madan for provoking him into working on this problem.

  • Manuscript received October 2004; final revision received September 2005.

Address correspondence to Mark H. A. Davis, Department of Mathematics, Imperial College, London SW7 2AZ, UK; e-mail:


Suppose we are given a set of prices of European call options over a finite range of strike prices and exercise times, written on a financial asset with deterministic dividends which is traded in a frictionless market with no interest rate volatility. We ask: when is there an arbitrage opportunity? We give conditions for the prices to be consistent with an arbitrage-free model (in which case the model can be realized on a finite probability space). We also give conditions for there to exist an arbitrage opportunity which can be locked in at time zero. There is also a third boundary case in which prices are recognizably misspecified, but the ability to take advantage of an arbitrage opportunity depends upon knowledge of the null sets of the model.