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Short-time asymptotics for marginal distributions of semimartingales

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  • Amel Bentata
  • Rama Cont
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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 \textit{out-of-the-money} options is found to be linear in time, the short time asymptotics of \textit{at-the-money} options is shown to depend on the fine structure of the semimartingale.

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    File URL: http://arxiv.org/pdf/1202.1302
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    Paper provided by arXiv.org in its series Papers with number 1202.1302.

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    Date of creation: Feb 2012
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    Handle: RePEc:arx:papers:1202.1302

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    1. Johannes Muhle-Karbe & Marcel Nutz, 2010. "Small-Time Asymptotics of Option Prices and First Absolute Moments," Papers 1006.2294, arXiv.org, revised Jun 2011.
    2. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(1), pages 61-69.
    3. Amel Bentata & Rama Cont, 2009. "Forward equations for option prices in semimartingale models," Working Papers hal-00445641, HAL.
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