Short-time asymptotics for marginal distributions of semimartingales

Amel Bentata () and Rama Cont ()
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Amel Bentata: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Rama Cont: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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.

Keywords: semimartingale; short-time asymptotics; marginal distribution; short maturity asymptotics; Levy process; option pricing (search for similar items in EconPapers)
Date: 2012
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: View the original document on HAL open archive server: https://hal.science/hal-00667112v2
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Citations: View citations in EconPapers (5)

Published in 2012

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