In this paper,we derive two general parameterized boundaries of finite difference scheme for Vee’s PDE which is used to price both fixed and floating strike Asian options.Using these two boundaries,we can deal with all kinds of situations,especially,some extreme cases,like overhigh volatility,very small volatility,etc,under which the Asian option is usually mispriced in many existing numerical methods.Numerical results show that our boundaries are pretty efficient. In this paper, we derive two general parameterized boundaries of finite difference scheme for Ve   Ve ’s PDE which is used to price both fixed and floating strike Asian options. Use these two boundaries, we can deal with all kinds of situations, especially , some extreme cases, like overhigh volatility, very small volatility, etc, under which the the option is usually mispriced in many existing numerical methods. Numerical results show that our boundaries are pretty efficient.