4. Assume you own 1,000 shares of XYZ company that has S₀ = 50. The following are the prices of put and call options on XYZ company with t=1 year, =.20 and r=.01:

Put Options Price Call Options Price

K=50 $3.72 K=50 4.22

K=48 $2.69 K=52 3.34

K=46 $1.98 K=54 2.69

(a) If you want to buy 1,000 put options so that the value of your investment in XYZ stays at $47,500 or higher no matter what happens to the stock price, which option should you pick (K=50, K=48 or K=46)? Explain.

(b) If you sell 1,000 call options at K=54 and buy 1,000 put options at K=48, draw a diagram showing the value of (i) the 1000 shares of stock you own, (ii) the 1000 call options at K=54, (iii) the 1000 put options at K=48 and (iv) the net position. Clearly label your diagram

(c) If you think the stock will stay at $50, what is a zero cost strategy using more than one option to profit from the price staying at $50 at time T?