This is a question on options.

(a) Explain why it may be optimal to exercise before maturity a put option on a stock that does not pay dividend but it is never optimal to exercise before maturity a call option on a stock that does not pay dividend. [20%]

(b) The price of a stock is $40. The price of one-year European put option on the stock with a strike price of $30 is quoted at $7 and the price of a European call option on the stock with a strike price of $50 is quoted as $5. Suppose that an investor buys 10 shares, shorts 10 call options and buys 10 put options.

(i) Construct a table and draw a diagram illustrating how the investors profit or loss varies with the stock price over the next. What are the maximum gain, maximum loss, and break even point from this trade? [20%]

(ii) How does your answer change if the investor buys 10 shares, shorts 20 call options and buys 20 put options? Why would an investor want to enter into this trade? [20%] See Next Page - 6 - EC3011

(c) The domestic risk-free rate is 3% per annum, the foreign risk-free rate is 5% per annum, the exchange rate volatility is 12% and the time to maturity is 15 months. Interest rates are continuously compounded.

(i) Use a three-time-step tree to value an at-the-money American put option on a currency when the initial exchange rate is 1.2. [10%]

(ii) Calculate the option at t = 0 and after the first 5 months. [10%]

(iii) Suppose the exchange rate increases after 5 months. Explain how a financial institution would hedge a short position in the option in the first 5 months. How would you answer change if the exchange rate decreases after 5 months? [10%]

(iv) Will the value of the options increase or decrease if the exchange rate volatility rises? Explain your answer. [5%]

(v) Will the value of the option increase or decrease if the domestic interest rate decrease? Explain your answer