Using Table 7.3 and linear interpolation in discount factors

(a) Calculate the spot and quarterly forward 3-month simple (add-on) rates, \(f\left(\left[T_{i}, T_{i+1}ight]ight)\) for \(T_{0}=0, T_{1}=3 m, \ldots, T_{12}=2 y 9 m\).

(b) Calculate the 2-year forward swap rate, 3 -month forward with semiannual payments on the fixed leg.

(c) Calculate the value to the fixed-rate receiver of a \(\$ 1 \mathrm{M} 3\)-month into 2 -year forward swap with semiannual fixed rate of \(3 \%\) per annum.

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

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%