For problem 1 to 7, we assume the effective 1 year interest rate is 4% and the S&R 6-month forward price $1020, and the use the following premiums, if necessary, for S&R options with 6 months to expiration:

C(950) = 120.405, C(1000) = 93.809, C(1020) = 84.470, C(1050) = 71.802 P (950) = 51.777, P (1000) = 74.201, P (1020) = 84.470, P (1050) = 101.214

where C(K) denotes by the call option premium with strike price K dollars and P(K) denotes by the put option premium with strike price K dollars.

1. Suppose that you buy the S&R index for $1000, buy a 1000-strike put, and borrow $980.39. Graph the result payoff and profit diagrams for the combined position.

2. Suppose you buy the S&R index for $1000 and buy a 950-strike put. Construct payoff and profit diagrams for this position. Verify the you obtain the same payoff and profit diagram by investing $931.37 in zero-coupon bonds and buying a 950-strike call.

3. Suppose you short the S&R index for $1000 and buy 1050-strike call. Construct payoff and profit diagrams for this position. Verify that you obtain the same payoff and profit diagram by borrowing $1029.41 and buying a 1050-strike put.

4. Suppose the premium on a 6-month S&R call is $110.40 and the premium on a put with the same strike price is 61.38. What is the strike price?

5. Suppose you purchase a 950-strike S&R call and sell a 1000-strike S&R call. Construct payoff and profit diagram for this position. Verify you obtain exactly the same profit diagram for the purchase of 950-strike S&R Put and sale of a 1000-strike S&R put. What is the difference in the payoff diagrams for the call and the put spreads? Why is there a difference?

6. Suppose you invest in the S&R index for $1000, buy a 950-strike put, and sell a 1050-strike call. Draw a profit diagram for this position. What is the net option premium? If you wanted to construct a zero- cost collar keeping the put strike equal to $950, in what direction would you have to change the call strike?

7. Draw profit diagram for the following positions:

a. 1050-strike S&R straddle.

b. Written 950-strike S&R straddle.

c. Simultaneous purchase of a 1050-strike straddle and sale of a 950- strike S&R straddle.

8. Compute profit diagrams for the following ratio spreads:

a. Buy 950-strike call, sell two 1050-strike calls.

b. Buy two 950-strike calls, sell three 1050-strike calls.

c. consider buying n 950-strike calls and selling m 1050-strike calls so that the premium of the position is zero. Considering your analysis in (a) and (b), what can you say about n/m? What exact ratio gives you a zero premium?