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?

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?

Answer 1

a) 3-month european call with strike price 45 is trading at 7.45 and the underlying stock is trading at 47. Theoretically speaking, the call price is a function of intrinsic value and time value of money. In this case, the intrinsic value is 47-45 =2 and time value of money is 5.45. TV also indicates towards the market outlook and looking at the TV value, it seems that market is strongly anticipating the upside in the given stock. In addition to this, there is always a potential risk to stocks, instead of selling the holding, one may consider shorting a call option when the outlook is not a major downside risk

b) There are two ways of hedging the downside risk. first is long put with a strike price of 47. If such a put is not available in the market then one may consider hedging a small downside risk by writing a call option with strike price = 45. The position diagrams is as follows:

Strategy:
Long Stock, currently trading at 47
Short european call with strike price = 45; call price 7.45
Scenario 1 when stock price falls to 40; then call option is not exercised
Premium inflow = 7.47
Loss from Stock = 7	Net profit = 7.47-7 =0.47
Scenario 2: Stock price remains at 57; call option is exercised by call holder
Profit from long stock = 10
Cash inflow from call premium = 7.47
Cash outflow due to loss = 57-45= 12	Net Profit = 10+7.47-12 =5.47

c) Supposingly, put option is not being traded, however Put option can be synthesized using put-call parity.

Stock+Put = Bond+Call

Put = Bond (long) + Call (long) - Stock (short)

       = 45*e^(0.02*3/12) + 7.45 - 47

       = 45.23+7.45-47 = 5.68

d) 5.68 at solved in part c)

e) In the worst case scenario, if the price of stock fall to 0, then loss on stock -47, however long put option will yield profit of 45 and a cashoutflow of 5.68 for put premium. Hence, net outflow is -7.68. Which implies that max loss this strategy will have is 7.68.