Q1. This question uses the spot rates in the following table, expressed as APR with s.a. compounding (i.e., BEY). Date t 6m ly Rate r(0, t) 0.0320 0.0350 18m 2y 30m 3y 0.0385 0.0430 0.0480 0.0520 a) What is the swap rate in a 2-year plain-vanilla swap? b) Given this rate, what is the net payment to the fixed payer at date t = 6m, per $1M of notional? c) Consider now an amortizing 2-year swap, on which the principal falls by 25% of the original after every 6 months. What is the swap rate? d) Consider now a forward-start 2-year swap starting in 1 year. (Thus, all payment dates are 1 year later than they would be on a plain-vanilla swap.) What is the swap rate on this swap? e) Finally, what is the swap rate on an amortizing forward-start 2-year swap starting in 1 year, on which the principal falls by 25% of the original after every 6 months? Q2. Consider the rates in the table above (Q1.). Suppose further that now, at time 0, you are in the middle of a swap contract that started 6 years ago; the latest payment has just been made (at time 0). a) If you are a fixed receiver on a plain-vanilla swap that has 3 years left until maturity, the swap rate is c = 3.55%, and the notional is $12M, what is the value of your swap? b) What is the dollar duration of your position (expressed with respect to BEY)? c) According to this duration, how would your value react to an increase of 30bp in all spot rates? d) What would be the actual change in your value if all spot rates increased by 30bp?