Let (B, S) a multi period binomial model that is arbitrage free. Prove that the unique time for an American call is the maturity T.
I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My idea is to prove this result by contradiction. I want to find an exercise time t<T, such that there exists an arbitrage opportunity, so that the value of the portfolio at time t is greater than zero, starting with an initial value equal to zero. Is this a good idea, and how can I find such strategy explicitely?