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Question 3 Value a 1.5-year swap, with swap rate 5.52%. The oating leg is referenced to the 6-month LIBOR, which is at 6% per annum. Notional is 100 million. Use the following discount factors: T Z(0,T) 0.25 0.9848 0.50 0.9745 0.75 0.9618 1.00 0.9490 1.25 0.9353 1.50 0.9215 You are told that this swap is at initiation. What is the payment frequency of the xed leg on the swap, quarterly or semiannually? Please show all assumptions and calculations. Question 4 Consider the same swap as in Question 3. What is the value of the swap three months after initiation, where the discount factors are now: T Z(0,T) 0.25 0.9840 0.50 0.9680 0.75 0.9520 1.00 0.9360 1.25 0.9190 1.50 0.9040 5. Consider a complete one-period model with 2 = {w1, W2, W3, w4} and let Vi, V2, V3, and V4 denote the Arrow-Debru securities with payment functions 1 w = wi vi (w ) = low * wit Assume that the initial prices of these securities are Vol = $0.38, V2 = $0.095, V3 = $0.19, VA = $0.285. (a) Find the arbitrage-free price Wo of the derivative security W with payment function W1 given by WI(W1) = 14, W1(W2) = 3, WI(w3) = 0, W1(WA ) = -6. (b) Determine the interest rate r. 6. Consider a one-period model with $ = {w1, W2, . . ., WN}. Let Vi, V2, ..., VN denote the Arrow-Debru securities which make payments Vi(w) = 1 w = Wi 10 w / Wi Assume that the prices Val, V2, ..., VON of the Arrow-Debru securities at time t = 0 are known. (a) Let Vi P ( wi ) = Vi + V2 + ... + V. N. gives a risk-neutral probability measure P. (b) Is this the only risk-neutral probability measure in this model, or could there be others