摘要

In this paper, we study the relation between Frechet derivatives, Dupire derivatives in Dupire (2009) and the derivatives modified by Levental et al. (2010). After introducing the definition of Frechet derivatives for non-anticipative functionals, we prove that the Dupire derivatives, the extended Frechet derivatives and the new setup in Levental et al. (2010) are coherent on continuous paths.