Assume that the common stock of Luther Industries is currently traded for 47 per share. The stock pays no dividends. A 3-month European call option on Luther with a strike price of 45 is currently traded for 7.45. The risk-free rate interest rate is 2% per year. Assume that you own common stock of Luther Industries, but you are concerned about a decline in its stock price in the near future.

a) Should you simply sell your holding? Why or why not?

b) Evaluate hedging the downside risk with options. What type of option should you use? Be specific, and show this strategy at maturity in a position diagram.

c) Suppose that put options on Luther Industries are not traded, but you want to have one. How could you achieve it? (Hint: design a strategy that uses a combination of financial securities)

d) Suppose that put options on Luther Industries stocks are traded. What noarbitrage price should a 3-month European put option on Luther Industries with an exercise price of 45 sell for?

e) What is the minimum profit of your portfolio after you purchase this put option?