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Interest Rate Swaps and Agreements Chapter 28

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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 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

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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

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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. D A - kD L < 0 Second party is savings bank with $100 million in fixed-rate mortgages of long duration funded with CDs having duration of 1 year. D A - kD L > 0

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Interest Rate Swaps We depict this fixed-floating rate swap transaction in the following

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Interest Rate Swaps The expected net financing costs for the FIs are shown below

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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.

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Interest Rate Swaps

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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%

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Swaps

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trade date effective date maturity date dates can differ for counterparties in same swap terminology to describe position

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Swaps 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

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Swaps 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

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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

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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%

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Swap Example for the fixed-rate payment suppose swap rate is 4.98% and quarter has 90 days

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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

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Forward Discount Factors for period 1 for period 2 for period 3

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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

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

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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

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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?

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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

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For the bank

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For the insurance firm

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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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