SWAPS Mario Cerrato

Interest Rate Swaps (Hull 2008 is a good reference for this topic). Definition: an interest rate swap is an agreement between two parties to exchange (US$) interest payments for a specific maturity on an agreed (notional) amount. Definition: an interest rate swap is an agreement between two parties to exchange (US$) interest payments for a specific maturity on an agreed (notional) amount. A plain vanilla interest rate swap consists in an agreement to pay interest at a floating rate an receive payments at a fixed rate, usually expressed in the same currency. A plain vanilla interest rate swap consists in an agreement to pay interest at a floating rate an receive payments at a fixed rate, usually expressed in the same currency.

Using Swaps to Transform a Liability Microsoft borrows $100m at LIBOR+0.1% Microsoft borrows $100m at LIBOR+0.1% 1) Microsoft pays LIBOR+0.1 to its lender 1) Microsoft pays LIBOR+0.1 to its lender 2) Microsoft receives LIBOR from INTEL 2) Microsoft receives LIBOR from INTEL 3) Microsoft pays 5% to INTEL 3) Microsoft pays 5% to INTEL Microsoft transforms its borrowings at LIBOR+0.1 into a fixed borrowings of 5.1% Microsoft transforms its borrowings at LIBOR+0.1 into a fixed borrowings of 5.1% SWAP MICROSOFT?????INTEL

Using Swaps to Transform a Liability INTEL: the swap can change its fixed rate borrowings into a floating rate borrowings. Suppose INTEL borrows $100m at fixed rate 5.2%. INTEL: the swap can change its fixed rate borrowings into a floating rate borrowings. Suppose INTEL borrows $100m at fixed rate 5.2%. 1)INTEL pays 5.2% to its lender 1)INTEL pays 5.2% to its lender 2)Pays LIBOR under the swap 2)Pays LIBOR under the swap 3)receives 5% under the swap 3)receives 5% under the swap INTEL borrowing at LIBOR+0.2% INTEL borrowing at LIBOR+0.2% SWAP MICROSOFT????INTEL

Using Swaps to Transform an Asset Suppose that Microsoft owns now $100m in bonds that provide interest 4.7% p.a. over the next three years. Suppose that Microsoft owns now $100m in bonds that provide interest 4.7% p.a. over the next three years. Microsoft can transform its fixed rate asset into a floating rate asset. Microsoft can transform its fixed rate asset into a floating rate asset. 1) Microsoft receives 4.7% on bonds 1) Microsoft receives 4.7% on bonds 2) Receives LIBOR under the swap 2) Receives LIBOR under the swap 3) Pays 5%p.a. under the swap 3) Pays 5%p.a. under the swap Microsoft receives LIBOR-0.3% Microsoft receives LIBOR-0.3%

Day Count Conventions when we calculate the party`s positions in a swap we have to consider day count convention when we calculate the party`s positions in a swap we have to consider day count convention LIBOR is quoted on actual/360. So if LIBOR =4.2 LIBOR is quoted on actual/360. So if LIBOR =4.2 Numb.of days = 184, notional amount=100m. Numb.of days = 184, notional amount=100m. Payment would be =100*0.042*184/360 Payment would be =100*0.042*184/360 In general: payment = (principal)*(LIBOR)*(days) In general: payment = (principal)*(LIBOR)*(days)

Comparative Advantage Motive Why doing a swap? Assume that A and B require $100m for 5 years. To reduce their financing risks A would like to borrow at fixed rate, B at floating. The costs to each party are the followings: A and B can both take advantage from a swap. B paying floating and receiving fixed… BorrowerFixed rateFloating rate A-BBB-rated8.5%6- M.LIB.+0.5% B-AAA-rated7.0%6-M.LIB.

7.52% 7.48% LIBOR LIBOR LIBOR+0.5% 7% A F.INS. B Floating Rate lender Eurobond

Quoted Swaps Rates For Euro- Swap Market

Typical Valuation Screen Used by Traders

Cash Flow Analysis

Swap Rates and the LIBOR Zero Curve The previous example(s) show that an interest rate swap can be characterized as the difference between two bonds. If we define with Bfx the value of the fixed rate bond underlying the swap and Bfl, the value of the floating rate bond, the value of the swap to the company receiving floating and paying fixed (i.e.A) is V=Bfl-Bfx Generally market makers quote, for different maturities a bid-offer prices for the fixed rate they are prepared to exchange for the floating. Bid price = fixed rate in a contract were they receive floating and pay fixed. Offer = fixed rate in a contract were they receive fixed and pay floating

Swap Rates and the LIBOR Zero Curve Therefore one approach to price this instrument is to price the previous portfolio of two bonds. Therefore one approach to price this instrument is to price the previous portfolio of two bonds. Otherwise we can consider the swap as a sequence of Forward Rates Agreements (FRA) and price this FRA portfolio. Otherwise we can consider the swap as a sequence of Forward Rates Agreements (FRA) and price this FRA portfolio. If Cash Flows between parties are exchanged at maturity of the forward rate one can show that the cash flows are not affected by the forward rate volatility. If Cash Flows between parties are exchanged at maturity of the forward rate one can show that the cash flows are not affected by the forward rate volatility. If the forward rate maturity does not coincide with the date when cash flows are exchanged then one can show that the volatility of the forward rate should be considered (We shall not look at these issues in this course). If the forward rate maturity does not coincide with the date when cash flows are exchanged then one can show that the volatility of the forward rate should be considered (We shall not look at these issues in this course).