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

Question

4. 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 (10 %) c) Suppose that put options on Luther Industries are not traded, but you want diagram. to have one. How could you achieve it? (Hint: design a strategy that uses a (8 %) d) Suppose that put options on Luther Industries stocks are traded. What no- combination of financial securities) arbitrage price should a 3-month European put option on Luther Industries (8 %) e) What is the minimum profit of your portfolio after you purchase this put (3% %) with an exercise price of £45 sell for? option?

Explanation / Answer

(a)

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

In this case,

47 - 45 = 2, but the call is selling at a premium 745. Since, you concerned the further decline of the stock price, should sell your stock as call option will be worth less if the stock price comes down to 45.

(b) Since, you feel the stock price will decline further, you can hedge this position with buying equal amount 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 comes down you can exercise the put option to hedge profit from the down side risk on call options.

(c) If put options are not traded then you can create a derivative using the given stock and create a contract to pay if the stock price decline beyond defined postion mentioned in the contract. In order to maintain the derivative you would need to pay the premium and when time comes you can exercise the contract.

(d) The put option is out of money since the Exercise/Strike Price > Stock Price. If you belive that stock price will decline the put and when the price goes down it will be in the money and you can exercise the option.

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