# Swaps

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```							            Financial Risk Management
Zvi Wiener
Following
P. Jorion, Financial Risk Manager Handbook
http://pluto.huji.ac.il/~mswiener/zvi.html     FRM       972-2-588-3049
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
A                                                 B
Floating rate
Based on a presentation of Global Risk Strategy Group of Deutsche Bank
Swaps                                    Zvi Wiener                      slide 3
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.)

Swaps                        Zvi Wiener                  slide 4
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%

Swaps                 Zvi Wiener            slide 5
7.4%
7.0%                             Libor+85bp
AAA    Libor        BBB

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.

Swaps                 Zvi Wiener                slide 6
Basic terms of IRS
• Notional amount
• Fixed rate leg
• Floating rate leg
• Calculated period
• Day count fraction

Swaps               Zvi Wiener   slide 7
Basic terms of IRS
• Payer and receiver - quoted relative to fixed
interest (i.e. payer = payer of fixed rate)
• Short party = payer of fixed, (buyer)
• Long party = receiver of fixed, (seller)
• Valuation = net value NOT notional!!

Swaps                         Zvi Wiener              slide 8
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.
Swaps                       Zvi Wiener                 slide 9
Payments
Fixed payment =
(notional)(Fixed rate)(fixed rate day count convention)

Floating payment =
(notional)(Float. rate)(float. rate day count convention)

Swaps                    Zvi Wiener               slide 10
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 1 (1  rt ) (1  r5 ) 5
t

Swaps                            Zvi Wiener              slide 11
Swaps   Zvi Wiener   slide 12
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

Swaps                       Zvi Wiener              slide 13
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.

Swaps                        Zvi Wiener                 slide 14
Swaps   Zvi Wiener   slide 15
Swaps   Zvi Wiener   slide 16
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.

Swaps                        Zvi Wiener                  slide 17
• Zero coupon swap (reinvested payments)
• Amortizing swap (decreasing notional)
• Accreting swap (increasing notional)
• Rollercoaster (variable notional)

Swaps                        Zvi Wiener            slide 18
Amortizing swap

Decreasing notional affects coupon payments

Swaps                      Zvi Wiener             slide 19
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!!

Swaps                        Zvi Wiener                  slide 20
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)

Swaps                       Zvi Wiener              slide 21
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

Swaps                        Zvi Wiener                  slide 22
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.

Swaps                       Zvi Wiener             slide 23
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).

Swaps                        Zvi Wiener                 slide 24
IRS Markets
Daily average volume of trade (notional)
1995       1998      2001
\$63B       \$155B     \$331B

Swaps                       Zvi Wiener             slide 25
Mark to market
• daily repricing
• collateral
• reduces credit exposure

Swaps                       Zvi Wiener   slide 26
Reasons to use swaps by firms
• Lower cost of funds
• Home market effects
• Comparative advantage of highly rated firms

Swaps                      Zvi Wiener              slide 27
Swaps   Zvi Wiener   slide 28
Swaps   Zvi Wiener   slide 29
Swaps   Zvi Wiener   slide 30
Global Derivatives Markets 1999
Exchange traded \$13.5T                    OTC Instruments \$88T
IR contracts       11,669                 IR contracts         60,091
Futures            7,914                  FRAs                 6,775
Options            3,756                  Swaps                43,936
FX contracts       59                     Options              9,380
Futures            37                     FX contracts         14,344
Options            22                     Forwards             9,593
Stock-index contr. 1,793                  Swaps                2,444
Futures            334                    Options              2,307
World GDP in 99 = 30,000                  Forw. and swaps      283
All stocks and bonds = 70,000             Options              1,527
Liquidation value = 2,800                 Commodity contr. 548
Others               11,408
Swaps                          Zvi Wiener
Source BIS                           slide 31
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

Swaps                        Zvi Wiener               slide 32
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

Swaps                        Zvi Wiener               slide 33

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