2. Consider a one-period binomial model with the riskless rate of interest equal to r > 0. Let UND0 be the initial market value of an underlying asset. One period later, the value of this asset will be either UND0(1 + u) in the up state with probability p, or UND0(1 + d) in the down state with probability 1 p, where d < r < u. There is a security (called the Red) that pays one dollar at the end of the period if, and only if, the up state occurs. Likewise, there is a security (called the Blue) that pays one dollar at the end of the period if, and only if, the down state occurs.

(a) What are the initial market prices of the Red and the Blue? What are their required rates of return that take risk and time value of money into account?

(b) Consider another underlying asset whose initial market value is UND0 0. One period later, the value of this asset will be either UND0 0(1 + u0) in the up state with probability p, or UND0 0(1 + d0) in the down state with probability 1 p, where d0 < r < u0. What are the initial market prices of the Red and the Blue?

(c) If there are no arbitrage opportunities, show that the markets prices of the Red and the Blue derived in parts (a) and (b) are perfectly consistent.