Abstract:

The main purpose of this paper is to estimate and forecast stochastic volatility from the Euler discretization and ARCH discretization . We are interested in stochastic volatility model where volatility is governed by logarithmic Ornstein-Uhlenbeck process. The Kalman filter procedure is compared to an EGARCH estimation approach. Our empirical study is based on historical daily data of TUNINDEX on the period between 1 January 1998 and 31 December 2009. The empirical results show that movements in Tunindex returns and movements in volatility are correlated. Indeed, an unanticipated increase in Tunindex return leads to increased uncertainty that is greater than that induced by an unanticipated drop in return. In addition, estimates obtained from the two discretization schemes (Euler and ARCH) are quite similar. We also find that the stochastic volatility model provides an increase in volatility like the EGARCH (1,1) model. Thus, the two volatilities tend to be closer to their equilibrium value in the long term.