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

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