Functional convex order for path-dependent American options using the Euler scheme of martingale jump diffusion process

Gilles Pagès (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We explore the functional convex order of martingale diffusions and stochastic integrals with respect to their diffusion coefficient in both a Brownian and a jump framework. We finally extend this result to the Snell envelope of functionals of these process i.e. to American options with pathwise payoffs.

Mots clés: American options

Mots clés: Convex order; local volatility models; Itô processes; Lévy-Itô processes; Laplace transform; completely monotonic functions; Lévy processes; pathwise European options; American options.

Domaines: Probabilités [math.PR]

Gilles Pagès. Functional convex order for path-dependent American options using the Euler scheme of martingale jump diffusion process. 2012. ⟨hal-00767885v1⟩