The SPX index is currently trading at a value of $1265, and the FESX index (the Dow Jones EuroSTOXX Index of 50 stocks, subsequently referred to as “STOXX”) is trading at €3671. The dollar interest rate is 3% per year, and the Euro interest rate is 5% per year. The exchange rate is $1.28/euro. The six-month futures on the STOXX is quoted at €3782. All interest rates are continuously compounded. There are no borrowing costs for securities. For simplicity, assume there are no dividends on either index. 

(a) Compute the correct six-month futures prices of the SPX, STOXX, and the currency exchange rate between the dollar and the euro. 

(b) Is the futures on the STOXX correctly priced? If not, show how to undertake an arbitrage strategy assuming you are not allowed to undertake borrowing or lending transactions in either currency. (Assume that the futures on SPX is correctly priced.)