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Short-time asymptotics for marginal distributions of semimartingales

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  • Amel Bentata
  • Rama Cont

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.

Suggested Citation

  • Amel Bentata & Rama Cont, 2012. "Short-time asymptotics for marginal distributions of semimartingales," Papers 1202.1302, arXiv.org.
  • Handle: RePEc:arx:papers:1202.1302
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    File URL: http://arxiv.org/pdf/1202.1302
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    References listed on IDEAS

    as
    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, 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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    Cited by:

    1. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 1501. "Short-Term Market Risks Implied by Weekly Options," CREATES Research Papers 2018-08, Department of Economics and Business Economics, Aarhus University.
    2. repec:wsi:ijtafx:v:16:y:2013:i:01:n:s0219024913500015 is not listed on IDEAS

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