Swaps
Zvi Wiener
02-588-3049
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
http://pluto.huji.ac.il/~mswiener/zvi.html
FRM
972-2-588-3049
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
Fixed rate
B
A
Floating rate
Based on a presentation of Global Risk Strategy Group of Deutsche Bank
Credit Derivatives
Zvi Wiener
slide 2
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.)
Credit Derivatives
Zvi Wiener
slide 3
IRS Origins
AAA 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%
Credit Derivatives
Zvi Wiener
slide 4
Comparative Advantage
7.4%
7.0%
AAA
Libor
BBB
Libor+85bp
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.
Credit Derivatives
Zvi Wiener
slide 5
Basic terms of IRS
• Notional amount
• Fixed rate leg
• Floating rate leg
• Calculated period
• Day count fraction
Credit Derivatives
Zvi Wiener
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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!!
Credit Derivatives
Zvi Wiener
slide 7
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.
Credit Derivatives
Zvi Wiener
slide 8
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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Zvi Wiener
slide 9
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
4
5
105
PV  

t
5
(
1

r
)
(
1

r
)
t 1
t
5
Credit Derivatives
Zvi Wiener
slide 10
Credit Derivatives
Zvi Wiener
slide 11
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
Credit Derivatives
Zvi Wiener
slide 12
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.
Credit Derivatives
Zvi Wiener
slide 13
Credit Derivatives
Zvi Wiener
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Credit Derivatives
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slide 15
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.
Credit Derivatives
Zvi Wiener
slide 16
• Zero coupon swap (reinvested payments)
• Amortizing swap (decreasing notional)
• Accreting swap (increasing notional)
• Rollercoaster (variable notional)
Credit Derivatives
Zvi Wiener
slide 17
Amortizing swap
Decreasing notional affects coupon payments
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Zvi Wiener
slide 18
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!!
Credit Derivatives
Zvi Wiener
slide 19
Unwinding
8%
A
LIBOR
B
6%
A
LIBOR
C
Net of the two offsetting swaps is 2% for the
life of the contract. (sometimes novation)
Credit Derivatives
Zvi Wiener
slide 20
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
Credit Derivatives
Zvi Wiener
slide 21
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.
Credit Derivatives
Zvi Wiener
slide 22
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).
Credit Derivatives
Zvi Wiener
slide 23
IRS Markets
Daily average volume of trade (notional)
1995
1998
2001
$63B
$155B
$331B
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Zvi Wiener
slide 24
Mark to market
• daily repricing
• collateral
• adjustments
• reduces credit exposure
Credit Derivatives
Zvi Wiener
slide 25
Reasons to use swaps by firms
• Lower cost of funds
• Home market effects
• Comparative advantage of highly rated firms
Credit Derivatives
Zvi Wiener
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Credit Derivatives
Zvi Wiener
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Zvi Wiener
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Credit Derivatives
Zvi Wiener
slide 29
FRM-GARP 00:47
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
Credit Derivatives
Zvi Wiener
slide 30
FRM-GARP 00:47
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
Credit Derivatives
Zvi Wiener
slide 31
Global Derivatives Markets 1999
Exchange traded $13.5T
IR contracts
11,669
Futures
7,914
Options
3,756
FX contracts
59
Futures
37
Options
22
Stock-index contr. 1,793
Futures
334
Options
1,459
World GDP in 99 = 30,000B
All stocks and bonds = 70,000
Liquidation value = 2,800B
Credit Derivatives
Zvi Wiener
Source
BIS
OTC Instruments $88T
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
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Global Derivatives Markets 2001
Exchange traded $23.5T
IR contracts
21,614
Futures
9,137
Options
12,477
FX contracts
89
Futures
66
Options
23
Stock-index contr. 1,838
Futures
295
Options
1,543
Credit Derivatives
Zvi Wiener
Source
BIS
OTC Instruments $111T
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
slide 33