Suppose C_a is the call price of an arithmetic average Asian option with a payoff function like max((S_T+S_(T-1))/2 - K, 0). Let C_e_T be the European call price of similar term and payoff function max(S_T - K, 0)I know that C_e_T = exp(-rT)*E[max(S_T - K, 0)] and C_e_(T-1) = exp(-r(T-1))*E[max(S_(T-1) - K, 0)]Since C_a = exp(-rT)*E[max((S_T+S_(T-1))/2 - K, 0)], does that meanC_a = exp(-rT)*(exp(rT)*C_e_T + exp(r(T-1))*C_e_(T-1))/2 = (C_e_T + exp(-r)*C_e(T-1))/2???Is there something wrong here? If it is true, does that mean I can express any discrete arithmetic average Asian option in terms of European options?

The maximum of a sum is not the sum of the maximums: max{(S+S')/2 - K; 0} is not equal to 0.5*[max{S - K; 0} + max{S' - K; 0}]

Oops I think you are right. I am trying to use an SV model to price Asian options. I have an analytic approximation to price European ones. I guess now I have to resort to Monte Carlo.

There is as yet no closed formed solution for Arithmetic average Asian options.TJ.

But there are good approximations, see the paper of Lord.