On the ordering of option prices

The aim of this paper is to unify and extend some of the various results on the ordering of option prices in exponential semimartingale models. This is a problem of interest not only for financial applications but similar questions also arise in the ordering properties of Markovian networks or in the problem to develop consistency results for risk measures for portfolio vectors with respect to dependence orders. We consider these questions in the framework of multivariate semi-martingale models. The following comparison result for two homogeneous Markov processes was recently established. Let X, Y be Feller processes with values in a LCCB space E, typically E = R with transition operators S = (St)t≥0, T = (Tt)t≥0 on Co(E) and infinitesimal generators A, B with domains DA, DB. Assume that F ⊂ Co(E), F ⊂ DA ∩ DB. F generates a partial order ≤F on M(E, B) defining P ≤F Q if ∫ f dQ for all f ∈ F .