Suppose the annual compounding interest rate is r. The stock price is S0 at time 0 and ST at time T. Also, suppose all the following European call and put options have the same expiration date T, and their prices with different strikes are as follows:

Strike Call price Put price

K c0(K) p0(K)

2K c0(2K) p0(2K)

K/2 c0(K/2) p0(K/2)

Now you are constructing one portfolio with terminal cash flow CFT at time T. Use S0, T, r, K, c0(K), c0(2K), c0(K/2), p0(K), p0(2K), and p0(K/2) to answer the following questions.

8. What is the price of your portfolio today if CFT = min( 1 /2 ST ,K)?

9. What is the price of your portfolio today if CFT = max(2ST ,K)?

10. What is the price of your portfolio today if CFT = |2ST K|?

11. What is the price of your portfolio today if CFT = max(2ST ,2K)?