Question 4. We have assumed that the payment dates for the fixed and floating legs of a swap are the same. However, in practice, the payment frequencies may differ. For example, in the US swap market, the fixed leg usually has semi-annual payments ( = 0.5) and the floating leg has quarterly payments ( = 0.25).

1. a) Draw a diagram similar to Figure 4.1 on page 34 of Blyth (also in the 10/04 lecture notes) for a swap where the fixed payments are semi-annual and floating payments are quarterly.

2. b) Consider a swap from T0 to Tn with fixed rate K. Suppose the term length for the

   floating leg is (FL) and the term length for the fixed leg is (FXD). Write down a

   formula for the value of the swap V SW (t) (where t T0) in terms of ZCB prices. K

3. c) This continues (b). Does the value of the swap depend on (FL)? Does it depend on (FXD)?

4. d) This continues (b). As usual, the swap rate yt[T0,Tn] is the special fixed rate such that V SW (t) = 0. Is the swap rate larger if the fixed leg payments are quarterly or if they

yt[T0,Tn] are annually?