  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.
