Small-time asymptotics for fast mean-reverting stochastic volatility models
AbstractIn this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB-type equations where the "fast variable" lives in a noncompact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle, and we deduce asymptotic prices for out-of-the-money call and put options, and their corresponding implied volatilities. The results of this paper generalize the ones obtained in Feng, Forde and Fouque [SIAM J. Financial Math. 1 (2010) 126-141] by a moment generating function computation in the particular case of the Heston model.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1009.2782.
Date of creation: Sep 2010
Date of revision: Aug 2012
Publication status: Published in Annals of Applied Probability 2012, Vol. 22, No. 4, 1541-1575
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- Jos\'e E. Figueroa-L\'opez & Ruoting Gong & Christian Houdr\'e, 2013. "A note on high-order short-time expansions for ATM option prices under the CGMY model," Papers 1305.4719, arXiv.org, revised Jun 2013.
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