The Dupire derivatives and Fréchet derivatives on continuous pathes

Abstract

In this paper, we study the relation between Fréchet derivatives and Dupire derivatives, in which the latter are recently introduced by Dupire [4]. After introducing the definition of Fréchet derivatives for non-anticipative functionals, we prove that the Dupire derivatives and the extended Fréchet derivatives are coherent on continuous pathes.

arXiv admin note: text overlap with arXiv:1108.4317 by other authors