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SMALL-TIME ASYMPTOTICS FOR FAST MEAN-REVERTING STOCHASTIC VOLATILITY MODELS
Feng, Jin Pouque, Jean-Pierre Kuman, Rohini
Feng, Jin
Pouque, Jean-Pierre
Kuman, Rohini
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Abstract
In 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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This is the published version, also available here: http://dx.doi.org/10.1214/11-AAP801.
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2012-01-01
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Institute of Mathematical Statistics
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Feng, Jin., Fouque, Jean-Pierre., Kuman, Rohini. "SMALL-TIME ASYMPTOTICS FOR FAST MEAN-REVERTING
STOCHASTIC VOLATILITY MODELS." Annals of Applied Probability. (2012) 22, 4. 1541-1575. http://dx.doi.org/10.1214/11-AAP801.