(a) You are a U.S. based investor with $10,000 to invest. The spot price of British Pounds (GBP) in the foreign exchange market is $1.26 per GBP. The annually compounded risk-free interest rate on 1-year zero coupon government bonds is 4.05% in the U.S. and 4.65% in the U.K. (1) Suppose you invest the $10,000 in a 1-year U.S. government zero coupon bond for one year. What will be your payoff (i.e., cash flow) at the end of the year from this strategy? (4 marks) (ii) Alternatively, you can exchange the $10,000 for British pounds today, invest in a 1-year U.K. government zero coupon bond for one year, and then convert the proceeds back into U.S. dollars at the end of the year at the prevailing exchange ralk What would the end-of-year exchange rate have to be so that your U.S. dollar payoff from this strategy is identical to the payoff from the strategy in part (i)? Express your answer as US dollars per GBP. (4 marks) (iii) Without doing any calculations, explain why the price you calculated in part () must be the no-arbitrage 1-year forward exchange rate. (4 marks) (iv) Suppose a dealer quotes you a 1-year forward price of $1.30 for the British pound. Show how you can take advantage of this offer to make an arbitrage profit. Clearly specify your trades, cash flows, and arbitrage profit. (5 marks) (b) Consider a European call and a European put on the same underlying non- dividend paying stock. Both options have one month to maturity, and a strike price of 100. The underlying stock can take one of two values at the maturity date, either 130 or 80. The price of the call is 16.36 and the price of the put is 7.27. (5 marks) (4 marks) (1) What is the implied one-month risk-free interest rate? (ii) What is the implied current price of the underlying stock? (c) Consider a two-period binomial model (t = 0, 1, 2), with a risky non-dividend paying stock, FML, which is currently trading for 3.50. In each period, the stock can go up by 30% or down by 10%. The risk-free interest rate is 4% in the first period and 2% in the second period. A European option in the market with underlying stock FML has the following payoff function at the maturity date t = 2 max (ST-Smin, 0) where S, is the price of FML at the maturity date t = 2 and Smin is the minimum stock price FML takes during the life of the option i.e., the minimum stock price FML realises on the path from t=0 to t=2. What is the value today of this option? (7 marks)