Forward equations for option prices in semimartingale models

Amel Bentata (1) , Rama Cont (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We derive a forward partial integro-differential equation for prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by a -possibly discontinuous- semimartingale. This result generalizes Dupire's forward equation to a large class of non-Markovian models with jumps and allows to retrieve various forward equations previously obtained for option prices in a unified framework.

Domaines: Pricing [q-fin.PR]; Equations aux dérivées partielles [math.AP]

Amel Bentata, Rama Cont. Forward equations for option prices in semimartingale models. 2009. ⟨hal-00445641v3⟩