Functional co-monotony of processes with applications to peacocks and barrier options

We show that several general classes of stochastic processes satisfy a functional co-monotony principle, including processes with independent increments, Brownian diffusions, Liouville processes. As a first application, we recover some recent results about peacock processes obtained by Hirsch et al. which were themselves motivated by a former work of Carr et al. about the sensitivity of Asian Call options with respect to their volatility and residual maturity (seniority). We also derive semi-universal bounds for various barrier options.