: In this thesis, we introduce stochastic volatility,, and long-memory Ornstein-Uhlenbeck model for volatility based on an article by Barndorff-Nielsen and Shephard (2001). In fact, this model of hould satisfy the following stochastic differential equation, This model was used by Roberts et. al. (2004), and fitted on financial data using Bayesian methods. Later Griffin and Steel (2006) follow their works and using Markov Chain Monte Carlo for special gamma marginal law for volatility, . It cause to using compound Poisson process for subordinator,, on above equation.
