Consider a payer swaption giving its holder the right, but not the obligation, to enter into a 3-year annual pay swap in four years, where a fixed rate of \(5 \%\) will be paid and the LIBOR rate will be received. Assume that the yield curve is flat at \(5 \%\) with continuous annual compounding and the volatility of the swap rate is \(20 \%\). The notional principal is \(\$ 100,000\) per interest rate percentage point.

a) What are the key assumptions in order to apply Black's formula to value this swaption?

b) Compute the price of this swaption using Black's formula as an application of Proposition 19.17 .