Question

2) You entered into a plain vanilla swap a while back where you pay 10% per annum with quarterly compounding on a notional principal of $100,000,000 with payments made quarterly. In exchange, you receive a payment of LIBOR. Your swap has 0.8 years left until its termination date. The LIBOR rate was 14.5% per annum with quarterly compounding when you made your last payment. If today's discount rates are per annum with continuous compounding as followed what is the value of your position? Years Rate 0.3 7.25% 0.55 7.30% 0.8 7.35%

Answer 1

Notional Principal = $ 100000000, The swap holder receives LIBOR and pays fixed 10% per annum, On last payment date LIBOR was 14.5 % per annum which implies that at the swap termination, the swap holder will receive 14.5% in the floating leg payment. Further, the swap has a remaining tenure of 0.8 years. Payment Frequencies for both legs are quarterly

0.8 Year Discount Rate = 7.35 %

Therefore, Position Value = Present Value of Floating Leg (Receipt) - Present Value of Fixed Leg (Payment)

Floating Leg Cash Flow = 0.145 x 100000000 x 0.25 = $ 3625000 and Fixed Leg Cash Flow = 0.1 x 100000000 x 0.25 = $ 2500000

Position Value = [3625000 / e^(0.0735 x 0.8)] - [2500000 / e^(0.0735 x 0.8)] = $ 1060757.25