Shares of XYZ stock (which does not pay dividends) are trading at $460.

The prices of European options on XYZ with 1 year to expiry are as follows:

Strike 440 445 450 455 460 465 470 475 480

Call 83.99 81.67 79.40 77.18 75.02 72.92 70.86 68.86 66.90

Put 59.26 61.89 64.56 67.30 70.08 72.92 75.81 78.76 81.75

(a) What is the one-year forward price of XYZ?

(b) What is the riskless rate of interest?

(c) You become convinced that XYZ's price will end up between 450 and 470 in a year's time, and decide to put on a trade that pays you $100,000 if XYZ's share price is between 450 and 470, and nothing if XYZ's share price is less than 445 or more than 475. Draw the payoff diagram. (In the payoff diagram, join these payoffs by straight lines between 445 and 450, and between 470 and 475.) How much does it cost you to enter this position? If you wanted to do a zero-cost trade with the same profit diagram, how much would you stand to lose if you were wrong, and XYZ ended up above 475 or below 445?