Short-time asymptotics for marginal distributions of semimartingales

Amel Bentata (1) , Rama Cont (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior of call options with short maturity in a semimartingale model: whereas the behavior of out-of-the-money options is found to be linear in time, the short time asymptotics of at-the-money options is shown to depend on the fine structure of the semimartingale.

Mots clés: semimartingale; short-time asymptotics; marginal distribution; short maturity asymptotics; Levy process; option pricing

Domaines: Probabilités [math.PR]; Pricing [q-fin.PR]

Amel Bentata, Rama Cont. Short-time asymptotics for marginal distributions of semimartingales. 2012. ⟨hal-00667112v1⟩