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 \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% 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.
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 , %DIFDELCMD < {\it %%% 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.
A
,
R
HJB type
HJB-type
R
non-compact
noncompact
A
,
R
Out-of-The-Money
out-of-the-money
R
\mbox{%DIFAUXCMD FFF
Feng
D
Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model
R
, SIAM Journal on Financial Mathematics, Vol
Forde and Fouque
A
SIAM J. Financial Math
R
,
(
A
126-141