Zvi Wiener

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Swaps

• Zvi Wiener
• 02-588-3049
• http//pluto.mscc.huji.ac.il/mswiener/zvi.html

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Interest Rate Swaps Concept

• An agreement between 2 parties to exchange
  periodic payments calculated on the basis of
  specified interest rates and a notional amount.
• Plain Vanilla Swap

Based on a presentation of Global Risk Strategy
Group of Deutsche Bank
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IRS

• In a standard IRS, one leg consists of fixed
  rate payments and the other depends on the
  evolution of a floating rate.
• Typically long dated contracts 2-30 years
• Sometimes includes options, amortization, etc.
• Interest compounded according to different
  conventions (eg 30/360, Act/Act. Act/360, etc.)

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IRS Origins

• AAA wants to borrow in floating and BBB wants to
  borrow in fixed.
• Fixed Floating
• AAA 7.00 LIBOR5bps
• BBB 8.50 LIBOR85bps
• difference 1.5 0.8
• Net differential 70bps 0.7

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Comparative Advantage
7.0
Libor85bp
BBB
AAA

• Cost of funds for AAALibor - 40bp (45bps saved)
• Cost of funds for BBB8.25 (25bps saved)
• Swap rate 7.40
• Swap rate is the fixed rate which is paid against
  receiving Libor.

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Basic terms of IRS

• Notional amount
• Fixed rate leg
• Floating rate leg
• Calculated period
• Day count fraction

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Basic terms of IRS

• Payer and receiver - quoted relative to fixed
  interest (i.e. payer payer of fixed rate)
• buyer payer, seller receiver
• Short party payer of fixed, (buyer)
• Long party receiver of fixed, (seller)
• Valuation net value NOT notional!!

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Various swaps

• Coupon swaps - fixed against floating.
• Basis or Index swaps - exchange of two streams
  both are computed using floating IR.
• Currency swap - interest payments are
  denominated in different currencies.
• Asset swap - to exchange interest received on
  specific assets.
• Term swap maturity more then 2 years.
• Money Market swap - less then 2 years.

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Payments

• Fixed payment
• (notional)(Fixed rate)(fixed rate day count
  convention)
• Floating payment
• (notional)(Float. rate)(float. rate day count
  convention)

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Time Value of Money

• present value PV CFt/(1r)t
• Future value FV CFt(1r)t
• Net present value NPV sum of all PV

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Swap Pricing

• A swap is a series of cash flows.
• An on-market swap has a Net Present Value of
  zero!
• PV(Fixed leg) PV(Floating leg) 0

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Pricing

• Floating leg is equal to notional amount at each
  day of interest rate settlement (by definition of
  LIBOR).
• Fixed leg can be valued by standard NPV, since
  the paid amount is known.

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Forward starting swaps

• interest starts accruing at some date in the
  future.
• Valuation is similar to a long swap long and a
  short swap short.

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• Zero coupon swap (reinvested payments)
• Amortizing swap (decreasing notional)
• Accreting swap (increasing notional)
• Rollercoaster (variable notional)

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Amortizing swap
Decreasing notional affects coupon payments
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Unwinding an existing swap

• Enter into an offsetting swap at the prevailing
  market rate.
• If we are between two reset dates the offsetting
  swap will have a short first period to account
  for accrued interest.
• It is important that floating payment dates
  match!!

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Unwinding
Net of the two offsetting swaps is 2 for the
life of the contract. (sometimes novation)
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Risks of Swaps

• Interest rate risk - value of fixed side may
  change
• Credit risk - default or change of rating of
  counterparty
• Mismatch risk - payment dates of fixed and
  floating side are not necessarily the same
• Basis risk and Settlement risk

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Credit risk of a swap contract

• Default of counterparty (change of rating).
• Exists when the value of swap is positive
• Frequency of payments reduces the credit risk,
• similar to mark to market.
• Netting agreements.
• Credit exposure changes during the life of a swap.

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Duration of a swap

• Fixed leg has a long duration (approximately).
• Short leg has duration about time to reset.
• Duration is a measure of price sencitivity to
  interest rate changes (approximately is equal to
  average time to payment).

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IRS Markets

• Daily average volume of trade (notional)
• 1995 1998 2001
• 63B 155B 331B

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Mark to market

• daily repricing
• collateral
• adjustments
• reduces credit exposure

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Reasons to use swaps by firms

• Lower cost of funds
• Home market effects
• Comparative advantage of highly rated firms

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FRM-GARP 0047

• Which one of the following deals has the largest
  credit exposure for a 1,000,000 deal size.
  Assume that the counterparty in each deal is a
  AAA-rated bank and there is no settlement risk.
• A. Pay fixed in an interest rate swap for 1 year
• B. Sell USD against DEM in a 1 year forward
  contract.
• C. Sell a 1-year DEM Cap
• D. Purchase a 1-year Certificate of Deposit

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FRM-GARP 0047

• Which one of the following deals has the largest
  credit exposure for a 1,000,000 deal size.
  Assume that the counterparty in each deal is a
  AAA-rated bank and there is no settlement risk.
• A. Pay fixed in an interest rate swap for 1 year
• B. Sell USD against DEM in a 1 year forward
  contract.
• C. Sell a 1-year DEM Cap
• D. Purchase a 1-year Certificate of Deposit

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Global Derivatives Markets 1999
OTC Instruments 88T
Exchange traded 13.5T

• IR contracts 60,091
• FRAs 6,775
• Swaps 43,936
• Options 9,380
• FX contracts 14,344
• Forwards 9,593
• Swaps 2,444
• Options 2,307
• Equity-linked contr. 1,809
• Forw. and swaps 283
• Options 1,527
• Commodity contr. 548
• Others 11,408

IR contracts 11,669 Futures 7,914 Options 3,756
FX contracts 59 Futures 37 Options 22 Stock-in
dex contr. 1,793 Futures 334 Options 1,459
World GDP in 99 30,000B All stocks and bonds
70,000 Liquidation value 2,800B
Source BIS
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Global Derivatives Markets 2001
OTC Instruments 111T
Exchange traded 23.5T

• IR contracts 77,513
• FRAs 7,737
• Swaps 58,897
• Options 10,879
• FX contracts 16,748
• Forwards 10,336
• Swaps 3,942
• Options 2,470
• Equity-linked contr. 1,881
• Forw. and swaps 320
• Options 1,561
• Commodity contr. 598
• Others 14,375

IR contracts 21,614 Futures 9,137 Options 12,47
7 FX contracts 89 Futures 66 Options 23 Stock-i
ndex contr. 1,838 Futures 295 Options 1,543
Source BIS