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A note on high-order short-time expansions for close-to-the-money option prices under the CGMY model

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  • Jos\'e E. Figueroa-L\'opez
  • Ruoting Gong
  • Christian Houdr\'e
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    Abstract

    The short-time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In the present work, a novel third-order approximation for close-to-the-money European option prices under the CGMY L\'{e}vy model is derived, and extended to a model with an additional independent Brownian component. The asymptotic regime considered, in which the strike is made to converge to the spot stock price as the maturity approaches $0$, is more relevant in applications since the most liquid options have strikes that close to the spot price. Our results shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of option prices near expiration when the strike is close to the spot price. In particular, a new type of transition phenomenon is uncovered in which the third order term exhibits two district asymptotic regimes depending on whether $1

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    File URL: http://arxiv.org/pdf/1305.4719
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    Paper provided by arXiv.org in its series Papers with number 1305.4719.

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    Date of creation: May 2013
    Date of revision: Aug 2014
    Handle: RePEc:arx:papers:1305.4719

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    1. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 75(2), pages 305-332, April.
    2. Jin Feng & Jean-Pierre Fouque & Rohini Kumar, 2010. "Small-time asymptotics for fast mean-reverting stochastic volatility models," Papers 1009.2782, arXiv.org, revised Aug 2012.
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