Show graphically and in a table the profit and LIBOR relationships at expiration for the following positions on interest rate options. In each case, assume that the interest rate call and put options each have exercise rates of \(2 \%\), a LIBOR reference rate, notional principals of \(\$ 20\) million, time period of0.25 per year, and premiums of \(\$ 25,000\). Evaluate at spot discount yields at expiration of \(0.5 \%,1.0 \%,1.5 \%,2.00 \%,2.50 \%,3.00 \%,3.50 \%\), and \(4.00\%\).

a. An interest rate call purchase

b. An interest rate put purchase

c. An interest rate call sale

d. An interest rate put sale