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Small-time asymptotics for fast mean-reverting stochastic volatility models (2010)
| Citations: | 5 - 0 self |
BibTeX
@MISC{Feng10small-timeasymptotics,
author = {Jin Feng and Jean-pierre Fouque and Rohini Kumar},
title = {Small-time asymptotics for fast mean-reverting stochastic volatility models },
year = {2010}
}
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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 non-compact 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 [11] (J. Feng, M. Forde and J.-P. Fouque, Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model, SIAM Journal on Financial Mathematics, Vol. 1, 2010) by a moment generating function computation in the particular case of the Heston model.
Keyphrases
heston model large deviation principle fast mean tothemean-reversion time stochastic volatility factor siam journal put option fast variable life homogenization problem asymptotic price out-of-the-money call non-compact space viscosity solution particular case short maturity asymptotic financial mathematics function computation heston stochastic volatility model nonlinear hjb type equation general argument stochastic volatility model thematurityis small butlarge
