Assume that the common stock of Luther Industries is currently traded for 47 per

Question

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? (4 %)

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. (10 %)

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) (8 %)

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? (8 %)

e) What is the minimum profit of your portfolio after you purchase this put option? (3 %)

Explanation / Answer

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

Incase of call options-

1. For in-the-money call = Stock Price - Exercise/Strike Price > 0

2. For out-of-money call = Stock Price - Exercise/Strike Price < 0

In this Scenario, 47 - 45 = 2, but since the call is selling at a premium 7.45.

Since we are concerned about the decline of the stock price in the near future the stock should be sold as call option would be worth less if the stock price comes down to 45.

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.

Since, The common perception in the question is that the stock price will decline further, therefore one should hedge this position by buying equal number of put options.

For put option if the put is in-the-money then Exercise/Strike Price - Stock Price > 0 and for out-of-money Exercise/Strike Price - Stock Price < 0.

If the price of stock decreases one can simply exercise the put option to hedge profit from the down side risk on the call option.

c) Suppose that put options on Luther Industries are not traded, but you want to have one. How could you achieve it?

Incase of put options not being traded a derivative could be created with a contract to pay if the stock price decreases beyond the limit mentioned in the pay contract. To maintain the derivative premium would be needed to be paid and the contract can be exercised when the time comes.

d) Suppose that put options on Luther Industries stocks are traded. What no arbitrage price should a 3-month European put option on Luther Industries with an exercise price of £45 sell for?

The put option is out of money since the Exercise/Strike Price > Stock Price. If the price of stock decreases one can simply exercise the put option to hedge profit from the down side risk on the call option. The # month European put option should also sell for a price of atleast 7.45

Note- As per chegg answering guidelines we are only allowed to answer 4 subparts of a question. Thanks.

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