Using the data in Table 7.3

(a) Compute the semiannual forward swap rate for a 1-year swap, 2 -year forward, \(F_{2,1}\).

(b) Using Black's normal formula with \(\sigma_{N}=0.80 \%\), compute the value of a \$1M 2 year into a 1 -year ATMF payer swaption with semiannual fixed rate \(K=F_{2,1}\).

(c) Using Black's normal formula with \(\sigma_{N}=0.80 \%\), compute the value of a \$1M 2 year into 1-year ATMF receiver swaption with semiannual fixed rate \(K=F_{2,1}\).

(d) Solve for the implied volatility \(\sigma_{N}\) if the market value of a \(\$ 1 \mathrm{M}\) 2 -year into 1 -year semiannual payer swaption with \(K=5 \%\) p.a. is \(\$ 5,000\).

Table 7.3

Transcribed Image Text:

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%