Question 3. A corporation enters into a 1.25-year interest rate swap with a bank, where the corporation pays the 3-month LIBOR as the floating rate and receives quarterly payments at a fixed rate '% p.a. (quarterly compounding) on a notional principal of $100 million. The fixed rate is negotiated such that the swap has 0 value at the time it is entered into. The risk-free rate given by LIBOR for maturities 3, 6, 9, 12, 15 months are 1.5%, 1.6%, 1.7%, 1.8%, 1.9% p.a. (continuous compounding), respectively. Take the perspective of the corporation. (a) By finding the amount that $1 invested at 1.5% p.a. continuously compounding grows to after 1 year, show that the equivalent quarterly compounding rate is 1.502816% p.a. (b) Show that the swap rate is f' = 1.902611% p.a. [1 mark] [4 marks] Draw a cashflow diagram of this swap. For the floating rate payments, use y (T) to denote LIBOR at time t for maturity time T. [1 mark] (d) It is now 8 months after the swap was entered into. At this time, the risk-free rate given by LIBOR for maturities 1, 4, 7 months are 1.6%, 1.7%, 1.8% p.a. (continuous compounding), respectively. Also, 6 months after the swap was entered into, the risk-free rate for maturity 3 months is 1.65% p.a. Find the value of the swap. [4 marks]