1. Suppose you know the current price of a European call option. How should the American call option with the same strike and the same maturity be priced? Explain.

   1. The American call should be priced as European call if there are no additional payments from the stock, dividends, etc.

   2. We assume that the stock pays no dividend from any possible option exercise time to maturity.

   3. Suppose we sell the American call at time t=T S-K for any T < T. Indeed, if C S-K, there is an arbitrage opportunity:

      1. At time t=T: Shortsell the stock for S, buy an American call for C, invest $ (S-C).

      2. At time t=T: If S K, buy stock for $S with gain. If S >K, buy stock for $K - $S + (S - C)e > 0