In this study we deal with aspects of the modeling of the asset prices by means Ornstein-Uhlenbech process driven by Levy process. Barndorff-Nielsen and Shephard stochastic volatility model allows the volatility parameter to be a self-decomposable distribution. BNS models allow flexible modeling. For this reason we use as a model IG-Ornstein-Uhlenbeck process. We calibrate moments of Levy process and OU process. Finally we fit the model some real data series. We present a simulation study.