© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-1 Interest Rate Swaps Companies use interest rate swaps to modify their interest rate exposure. The interest payments are based on the notional principle of the swap. The life of the swap is the swap term or swap tenor.

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-2 A Simple Interest Rate Swap XYZ Corp. has $200M of floating-rate debt at LIBOR, i.e., every year it pays that year’s current LIBOR. XYZ would prefer to have fixed-rate debt with 3 years to maturity. XYZ could enter a swap, in which they receive a floating rate and pay the fixed rate, which is %.

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-3 A Simple Interest Rate Swap (cont’d) On net, XYZ pays % XYZ net payment = – LIBOR + LIBOR – % = –6.9548% Floating payment Swap payment

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-4 Swap Rate and Bond Calculation The implied forward rate between times t 1 and t 2, r 0 (t 1, t 2 ), is given by the ratio of zero-coupon prices, i.e., By taking r 0 (t i–1, t i ) as the F 0,t i in Eq. (8.3), we have

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-5 Swap Rate and Bond Calculation (cont’d) After rearrangement, This is the valuation equation for a bond priced at par with a coupon rate of R. So, the swap rate is the coupon rate on a par coupon bond.

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-6 The Swap Curve A set of swap rates at different maturities is called the swap curve. The swap curve should be consistent with the interest rate curve implied by the Eurodollar futures contract, which is used to hedge swaps. Recall that the Eurodollar futures contract provides a set of 3-month forward LIBOR rates. In turn, zero-coupon bond prices can be constructed from implied forward rates. Therefore, we can use this information to compute swap rates.

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-7 The Swap Curve (cont’d)

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-8 The Swap Curve (cont’d) Sample calculation: The June Eurodollar futures price was The implied quarterly (nonannualized) interest rate for June to September was The implied June price for a $1 cash flow in September was therefore

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-9 The Swap Curve (cont’d) The forward interest rate from September to December: The price of a zero-coupon bond paying $1 in December is then

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-10 The Swap Curve (cont’d) For the June to December swap rate is The annualized swap rate = 4 x % = %

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-11 The Swap Curve (cont’d)

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-12 The Swap Curve (cont’d) Fig. 8.8 shows that the swap spread which is defined as the difference between swap rates and Treasury- bond yields for comparable maturities is positive.

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-13 Deferred Swaps A deferred swap is a swap that begins at some date in the future, but its swap rate is agreed upon today. The fixed rate on a deferred swap beginning in k periods is computed as Equation (8.8) is equal to equation (8.3), when k = 1.

© 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-14 Amortizing and Accreting Swaps An amortizing swap is a swap where the notional value is declining over time (e.g., floating rate mortgage). An accreting swap is a swap where the notional value is growing over time. The fixed swap rate is still a weighted average of implied forward rates, but now the weights also involve changing notional principle, Q t i (8.11)