http://pluto.huji.ac.il/~mswiener/zvi.html

972-2-588-3049FRM

Zvi Wiener

02-588-3049http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

Swaps

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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

A BFixed rate

Floating rate

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 OriginsAAA wants to borrow in floating and BBB wants to borrow in fixed.

Fixed Floating

AAA 7.00% LIBOR+5bps

BBB 8.50% LIBOR+85bps

difference 1.5% 0.8%

Net differential 70bps = 0.7%

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Comparative Advantage

Cost of funds for AAA=Libor - 40bp (45bps saved)

Cost of funds for BBB=8.25% (25bps saved)

Swap rate = 7.40%

Swap rate is the fixed rate which is paid against receiving Libor.

AAA BBBLibor

7.4%7.0% Libor+85bp

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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/(1+r)t

• Future value FV = CFt(1+r)t

• Net present value NPV = sum of all PV

-PV 5 5 5 5 105

55

4

1 )1(

105

)1(

5

rrPV

tt

t

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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)

A B8%

LIBOR

A C6%

LIBOR

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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 00:47Which 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 yearB. Sell USD against DEM in a 1 year forward contract.C. Sell a 1-year DEM CapD. Purchase a 1-year Certificate of Deposit

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FRM-GARP 00:47Which 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 yearB. Sell USD against DEM in a 1 year forward contract.C. Sell a 1-year DEM CapD. Purchase a 1-year Certificate of Deposit

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Global Derivatives Markets 1999

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

OTC Instruments $88TExchange traded $13.5TIR contracts 11,669Futures 7,914Options 3,756FX contracts 59Futures 37 Options 22Stock-index contr. 1,793Futures 334Options 1,459

Source BIS

World GDP in 99 = 30,000BAll stocks and bonds = 70,000Liquidation value = 2,800B

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Global Derivatives Markets 2001

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

OTC Instruments $111TExchange traded $23.5TIR contracts 21,614Futures 9,137Options 12,477FX contracts 89Futures 66 Options 23Stock-index contr. 1,838Futures 295Options 1,543

Source BIS