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

TL;DR

This paper establishes a functional co-monotony principle for various stochastic processes and applies it to derive bounds for barrier options and analyze peacock processes, enhancing understanding of financial derivatives and process behaviors.

Contribution

It introduces a unifying co-monotony framework applicable to multiple stochastic processes and applies it to financial models and peacock processes, extending previous results.

Findings

Validated co-monotony for processes with independent increments, Brownian diffusions, and Liouville processes.

Reproduced recent results on peacock processes using the co-monotony principle.

Derived semi-universal bounds for barrier options.

Abstract

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.