SMALL-TIME ASYMPTOTICS FOR FAST MEAN-REVERTING STOCHASTIC VOLATILITY MODELS
By Jin Feng, Jean-Pierre Fouque 3, Rohini Kumar. 2010
72 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/553563fedf37045c4deee213c7a50ce802424c32
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Citations in the corpus
- Large Deviations and Importance Sampling for Systems of Slow-Fast Motion (2012, background): “Multiscale stochastic control problems and related large deviations problems have been studied elsewhere as well under various assumptions and dependencies of the coefficients of the system on the slow and fast motion, see [3, 7, 12, 18, 19, 24, 25, 28, 30, 33, 34].”