Under the premise that the market is not completely efficient, the BlackScholes model with constant volatility can no longer accurately describe the financial market in the real world. In view of this situation, this paper proposes a Heston stochastic volatility model with non-constant volatility to describe the motion process of asset returns, and then studies a kind of path-dependent derivatives, Asian options and look-back options. Under this model, the option prices of these two kinds of options in exotic options are simulated by Milstein discrete method and Multilevel Monte Carlo method. Finally, the results of numerical experiments are compared with those of ordinary Monte Carlo method. Numerical experiments verify the efficiency of Multilevel Monte Carlo method from the aspects of variance, expectation, sample number and calculation cost.