Interest rate swaps and agreements
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Interest Rate Swaps and Agreements. Chapter 28. Swaps. CBs and IBs are major participants dealers traders users regulatory concerns regarding credit risk exposure five generic types of swaps interest rate swaps currency swaps credit swaps commodity swaps equity swaps.

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Interest Rate Swaps and Agreements

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Interest rate swaps and agreements

Interest Rate Swaps and Agreements

Chapter 28



  • CBs and IBs are major participants

    • dealers

    • traders

    • users

  • regulatory concerns regarding credit risk exposure

  • five generic types of swaps

    • interest rate swaps

    • currency swaps

    • credit swaps

    • commodity swaps

    • equity swaps

Interest rate swaps

Interest Rate Swaps

  • OTC instruments

    • investors can go through securities firm or commercial bank

    • firms can act as brokers or dealers for investor

  • counterparty risk can be significant

  • Swap can be viewed as

    • package of forward/future contracts

    • package from CFs from buying and selling cash market instruments

      • fixed rate payer has position similar to long position in floating rate bond and short in fixed rate (borrowing by issuing fixed rate bond)

      • floating payer has position like purchasing fixed rate bond and financing purchase at floating rate

Interest rate swaps1

Interest Rate Swaps

  • counterparties agree to exchange periodic interest payments with dollar amount based on notional principal

    • plain vanilla – fixed-rate payer and floating-rate payer

      • reset frequency

      • reference rates

Plain vanilla interest rate swap example

Plain Vanilla Interest Rate Swap Example

  • Consider money center bank that has raised $100 million by issuing 4-year notes with 10% fixed coupons. On asset side: C&I loans linked to LIBOR. Duration gap is negative.

    DA - kDL < 0

  • Second party is savings bank with $100 million in fixed-rate mortgages of long duration funded with CDs having duration of 1 year.

    DA - kDL > 0

Interest rate swaps2

Interest Rate Swaps

  • We depict this fixed-floating rate swap transaction in the following

Interest rate swaps3

Interest Rate Swaps

  • The expected net financing costs for the FIs are shown below

Interest rate swaps4

Interest Rate Swaps

  • Assume that the realized path of LIBOR over the 4 year life of the contract would be as follows 9%, 9%, 7%, and 6% at the end of each of the 4 years. The money center bank’s variable payments to the thrift are indexed to these rates by the formula:

    (LIBOR + 2%) * $100m

  • The annual payments made by the thrift were the same each year

    10% * $100m.

Interest rate swaps5

Interest Rate Swaps

Interest rate swaps6

Interest Rate Swaps

  • example

    • notional of $50m where X is fixed rate payer and Y is floating rate payer – X pays 10% per year and Y pays the 6-month LIBOR – payments every 6 months for next 5 years

      • what will payments be if 6-month LIBOR is 7%





  • trade date

  • effective date

  • maturity date

  • dates can differ for counterparties in same swap

  • terminology to describe position



  • fixed rate payer is short the bond market – explain

  • fixed rate payer – position that is exposed to the price sensitivities of a longer-term liability and a floating-rate bond

  • floating rate payer – position that is exposed to the price sensitivities of a fixed-rate bond and a floating-rate liability



  • dealer quotes fixed payer to pay 8.85% and receive LIBOR “flat” – bid price dealer quotes floating payer is to pay LIBOR flat and receive 8.75% - spread is 10bp

  • fixed rate is spread above Treasury yield curve – say 10 year Treasury yield is 8.35% - offer price dealer quoted is 10 year Treasury plus 50bp vs. receiving LIBOR flat

  • bid price dealer quoted for floating payer is LIBOR flat vs. 10 year Treasury plus 40bp

  • dealer quotes swap as 40-50 – dealer willing to enter into swap to receive LIBOR and pay fixed rate equal to 10-yr Treas. plus 40bp – willing to enter into swap to pay LIBOR and receive fixed rate equal to 10-yr. Treas. plus 50bp

Swap rate

Swap Rate

  • to determine rate, remember that no upfront CFs are made, so PV of payments must be equal

    • swap rate for floating payer must be rate that makes PV of payments on fixed-rate side equal to payments on floating rate side

    • what rate do we use to discount CFs to find PV?

  • example

    • swap settlement date is January 1 at year 1

    • floating-rate payments made quarterly based on actual/360

    • reference rate is 3-month LIBOR

    • notional amount is $100m

    • term of swap is 3 years

Swap example

Swap Example

  • today 3-month LIBOR is 4.05%

  • floating payment is

    • fixed rate payer receives payment on March 31 of

    • next payment from April 1 to June 30 – 91 days

    • 3 month Eurodollar CD futures contract for settlement on June 30 of year 1 is 95.85 so Eurodollar futures rate is 4.15%

Swap example1

Swap Example

  • for the fixed-rate payment

  • suppose swap rate is 4.98% and quarter has 90 days

Swap rate1

Swap Rate

  • key principle in finding swap rate is no arbitrage opportunity – PV of payments received must equal PV of payments made

  • rate used for discounting?

  • forward discount factor is PV of $1 received at period t

    • find forward discount factor for period using forward rates – but adjust rates for number of days in quarter

Forward discount factors

Forward Discount Factors

  • for period 1

  • for period 2

  • for period 3

Swap rate2

Swap Rate

  • no arbitrage – PV of fixed = PV of floating

  • fixed rate pmt for period t

  • PV of fixed rate payment for period t is

  • PV of fixed rate payments

  • no arbitrage so

Valuing a swap

Valuing a Swap

  • one year later, rates change so payments by floating rate side change – how does this affect value?

Asset liability management

Asset/Liability Management

  • bank has portfolio of $50m of 5-year loans with fixed rate of 10% - loans are interest only with semiannual pmts and principal due at end of 5 yrs – CF is $2.5m every 6 months

    • to fund, bank will issue 6 month CDs on which it pays 6-month LIBOR plus 40bp

    • at what LIBOR rate is bank in trouble?

    • bank wants to lock in spread over cost of funds

Asset liability management1

Asset/Liability Management

  • life insurance firm pays 9% over next 5 years on GIC – amount is $50m

    • firm can invest $50m in 5 year floating rate security on which rate is 6-month LIBOR plus 160bp with coupon reset every 6 months

    • risk for insurance firm?

Asset liability management2

Asset/Liability Management

  • swap available in market has terms:

    • every 6 months bank pays 8.45% (annual rate)

    • every 6 months bank receives LIBOR

    • every 6 months insurance firm pays LIBOR

    • every 6 months insurance firm receives 8.40%

  • what does swap do for each party?

    • bank locks in spread of 155bp

    • insurance firm locks in spread of 100bp

For the bank

For the bank

For the insurance firm

For the insurance firm

Asset liability management3

Asset/Liability Management

  • bank – alters CF of assets from fixed to floating

  • life insurance firm – alters CF of assets from floating to fixed

  • asset swap – in above example

  • liability swap

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