Functional co-monotony of processes with applications to peacocks and barrier options
Résumé
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.
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Cite 10.1007/978-3-319-00321-4_15 Autre Pagès, G. (2013). Functional Co-monotony of Processes with Applications to Peacocks and Barrier Options. In Lecture Notes in Mathematics (pp. 365–400). Springer International Publishing. https://doi.org/10.1007/978-3-319-00321-4_15