Functional co-monotony of processes with an application to peacocks

Gilles Pagès (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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).

Mots clés: Co-monotony; antithetic simulation method; diffusion processes; processes with independent increments; Liouville processes; fractional Brownian motion; Asian options; sensitivity

Domaines: Probabilités [math.PR]

Gilles Pagès. Functional co-monotony of processes with an application to peacocks. 2012. ⟨hal-00733827v2⟩