Short-time asymptotics for marginal distributions of semimartingales

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.
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Submitted on : Saturday, May 26, 2012 - 11:52:24 PM
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Amel Bentata, Rama Cont. Short-time asymptotics for marginal distributions of semimartingales. 2012. ⟨hal-00667112v2⟩

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