Using Table 7.3 and linear interpolation in discount factors, for a \(\$ 1 \mathrm{M}\) 1 -year swap with semiannual fixed rate of \(4 \%\) per annum and quarterly floating leg based on 3-month rates

(a) Compute the value of the semiannual fixed leg.

(b) Compute the value of the quarterly floating leg via discounting the forward 3-month rates.

(c) Compute the value of the floating leg via replication.

(d) What is the value of the swap to the fixed-rate receiver?

Table 7.3

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T (years) 0 0.5 1 1.5 2 2.5 3 D(T) 1 0.98 0.96 0.94 0.92 0.90 0.88 f([T, T + 6m]) 4.082% 4.167% 4.255% 4.348% 4.444% 4.545% S(T) 4.082% 4.124% 4.167% 4.211% 4.255% 4.301%