2. Exchange optionsSuppose that:

The stock of Exxon Mobile Corp. (XOM) is currently trading at 76.38.

It is expected to pay an 80 cent dividend at the end of each of the next four quarters.

It has also just payed a dividend. The NYSE ARCA Oil & Gas Index (XOI) is currently trading at 1,301.57. It pays a continuously compounded dividend yield of 3%.

Bonds with one, two, three, and four quarters to maturity are priced at B0,1/4 = 0.995 B0,1/2 = 0.985 B0,3/4 = 0.97 B0,1 = 0.95.

B0,1/4 = 0.995

B0,1/2 = 0.985

B0,3/4 = 0.97

B0,1 = 0.95

(a) What are the one-year forward prices of XOM and XOI?

(b) Suppose that the volatilities of XOM and XOI are 60% and 30%, respectively, and the returns to the two are 55.5% correlated. What is the price of the exchange option that gives the owner the right, but not the obligation, to deliver 58 shares of XOI in exactly one year in return for 1,000 shares of XOM?