Suppose that the yield curve is flat at $6\%$ with annual compounding. A swaption gives the holder the right to receive $5\%($with annual compounding$)$ in a four$-$year swap starting in four years. Payments are made annually. The volatility of the forward swap rate is $13\%$ per annum and the principal is $$15$ million. Use Black$$s model to price the swaption. Give d$1$ and d$2$ with four decimal places and interpolate using the tables for N$($x$).$

Given data:

S$0=5\%$

K$=5\%$

T$=4$ years

$\backslash$sigma $=13\%=0\mathrm{.}13$

N$=$$$15$ million

r$=6\%=0\mathrm{.}06$

Following the given.

$1.$Why are So $=$K $=5\%?($Because the holder has a right to receive $5\%($fixed rate$)$ and pay LIBOR$)$

$2.$ the risk free rate is annual compounding. Why dont you change to continuos compounding?

$3.$ the formula of put option of receive fixed rate $-$pay floating rate is incorrect.