knowing that the payoff of a ECC at maturity T is given by $C_T = max(S_T-K,0)$ can we deduce by the law of one price that $C_t = max(S_t-K,0)$ given that K is the strike price? In particular, why do make the effort and find pricing strategies for the ECC that give us arbitrage free prices if the first remark already holds?
I have the feeling that I confuse different topics, but I do not see how these are connected.
Appreciate any help!