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

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). We also derive semi-universal bounds for various barrier options.

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 applications to peacocks and barrier options. Séminaire de Probabilités XLV, SEMPROBAB,volume 2078 (2078 (XLV)), pp.365-400, 2013, Lecture Notes in Mathematics book series, 978-3-319-00321-4. ⟨hal-00733827v3⟩