Suppose that the Black-Scholes framework governs a currency exchange between the US and Martians (Martians only have one currency). One Martian dollar ($_M) costs $100. The risk free rate of the US dollar is r_u = 0.09, and the Martian risk free rate is r_M = 0.03. The volatility of the exchange is [sigma] = 0.3.

(a) Determine the price of a one year European call with strike 103 on one Martian dollar.

(b) Determine the price of a derivative that pays max{ X(1)² - 10000, 0 } in one year.