Consistency among trading desks

We consider a bank having several trading desks, each of which trades a different class of contingent claims with each desk using a different model. We assume that the models are arbitrage-free. A practical question is whether a bank using several models can be arbitraged. Surprisingly it can happen that in some cases there must be an arbitrage. We discuss conditions under which the bank trades without offering arbitrage.The second-named author is grateful for support from NSERC Discovery grant 504316. An earlier version has been presented in the seminars at Fields Institute (2003), Cambridge University (2003) and IMA (2004); the authors thank for fruitful discussions. The authors also thank the referee for helpful comments.