# Asian option, portfolio of calls control variate

One possible control variate for the Asian option with strike $$K$$ and discrete time average at the times $$t_i$$ for $$i\in {1,\dots, m}$$ is the portfolio of $$1/m$$ European call options at times $$t_i$$, all with strike $$K$$.

The value of this portfolio is usually an upper bound for the value of the Asian call option. My intuition is that this is because with an Asian option we are protected against the variation in the mean whereas for the portfolio of calls we are protected for each date. Are there other explanations/proofs for why that is the case?