Stochastic flows approach to Dupire's formula

Benjamin Jourdain (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

The probabilistic equivalent formulation of Dupire's PDE is the Put-Call duality equality. In local volatility models including exponential Lévy jumps, we give a direct probabilistic proof for this result based on stochastic flows arguments. This approach also enables us to check the probabilistic equivalent formulation of various generalizations of Dupire's PDE recently obtained by Pironneau by the adjoint equation technique in the case of complex options.

Domaines: Probabilités [math.PR]

Benjamin Jourdain. Stochastic flows approach to Dupire's formula. 2006. ⟨hal-00110196⟩