III (General no-arbitrage bounds) Consider European and American Call options, with the same maturity T = 1 and strike price K = 100, written on the same underlying asset. Denote by EC 0 and AC 0 the prices at time t = 0 of European and American Call options and assume that EC 0 = 5. We assume that the financial market does not admit arbitrage opportunities and that the underlying asset does not pay dividends. 1. Justify that AC 0 5. 2. Denote by P0(1) the price at time t = 0 of a zero-coupon bond with maturity T = 1 (and unit principal amount) and assume that P0(1) = 0.98. Prove that S0 103, where S0 denotes the price at t = 0 of the underlying asset. 3. By relying on the two previous questions, prove that AC 0 = 5.