Question

An interest rate swap has three years of remaining life. Payments are exchanged annually. Interest at 3.2% is paid and 12-month LIBOR is received. An exchange of payments has just taken place. The one-year, two-year and three-year LIBOR/swap zero rates are 1.5%, 2.5 and 3.75%. All rates an annually compounded. What is the value of the swap as a percentage of the principal when OIS and LIBOR rates are the same? (Assume Principal =$100)

Answer 1

Pay Leg: Fixed Interest Rate = 3.2 % and Notional = $ 100

Receive Leg: Floating 12-Month LIBOR Rate, Notional = $ 100

1-Year LIBOR zero rate = 1.5%, 2 -Year LIBOR zero rate = 2.5 % and 3-Year LIBOR zero rate = 3.75 %

Floating Interest Rate for Year 1 = 1.5 %, Floating Interest Rate for Year 2 (1-Year LIBOR Rate at the beginning of Year 2) = [(1.025)^(2) / (1.015)] - 1 = 0.0351 or 3.51 %

Floating Interest Rate for Year 3 (1-Year LIBOR Rate at the beginning of Year 3) = [(1.0375)^(3) / (1.025)^(2)] - 1 = 0.06296 or 6.296 %

Year 1:

Fixed Leg Cash Flow = 0.032 x 100 = $ 3.2 and Floating Leg Cash Flow = 0.015 x 100 = $ 1.5

Net Cash Received = 1.5 - 3.2 = - $ 1.7

Year 2:

Fixed Leg Cash Flow = 0.032 x 100 = $ 3.2 and Floating Leg Cash Flow = 0.0351 x 100 = $ 3.51

Net Cash Received = 3.51 - 3.2 = $ 0.31

Year 3:

Fixed Leg Cash Flow = 0.032 x 100 = $ 3.2 and Floating Leg Cash Flow = 0.06296 x 100 = $ 6.296

Net Cash Received = 6.296 - 3.2 = $ 3.096

Swap Value = Total Present Value of Net Cash Flow Receipts = [-1.7/(1.015)] + [0.31/(1.025)^(2)] + [3.096/(1.0375)^(3)] = $ 1.39246 ~ $ 1.39