Abstarct: Among stochastic volatality models, Hall-White model is one of the most important models. In this thesis, a zero coupon bonds pricing is considered under the mixed fractional Hull-White model. To this, the European option pricing under Black-scholes model, the Hall-White model and the fractional Hall-White model, the mixed fractional are presented. In the sequel the option pricing Under the Hall-White model is driven. Finally analytical solutions for option pricing is obtained via Lie symmetry group.