Problem 1.3. Let Cebe the value of a European call option, Pg be the value of European put option, CA denote the value of American call option and P, denote the value of American put option. All options are written on same stock, which is currently trading at So. Options mature at time T and strike price is K. The continuously compounded risk free rate is r 1. Explain why American call options on non dividend paying stock should never be exer- cised before maturity. You should justify any claim you made in you explanation 2. Suppose stock pays continuous dividend at a rate of 8. Prove following relationship: Ce-Pe=Soe-7-ke- 3. Suppose stock pays no dividend. Prove following relationship So 2C 2C 2 max(Su Ke", 0) 4. Suppose stock pays no dividend. Prove following relationship K2 PA2 max(K - S.,0) and Ke-2 P: max(Ke - 50,0) 5. Prove the following relationship (put-call parity for American options) So - Ke CA-PAS-K