Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.1
Swaps
Chapter 6
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.2
Nature of Swaps
A swap is an agreement to
exchange cash flows at specified
future times according to certain
specified rules
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.3An Example of a,Plain Vanilla”
Interest Rate Swap
? An agreement by Microsoft to receive
6-month LIBOR & pay a fixed rate of
5% per annum every 6 months for 3
years on a notional principal of $100
million
? Next slide illustrates cash flows
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.4
---------Millions of Dollars---------
LIBOR FLOATING FIXED Net
Date Rate Cash Flow Cash Flow Cash Flow
Mar.5,2001 4.2%
Sept,5,2001 4.8% +2.10 –2.50 –0.40
Mar.5,2002 5.3% +2.40 –2.50 –0.10
Sept,5,2002 5.5% +2.65 –2.50 +0.15
Mar.5,2003 5.6% +2.75 –2.50 +0.25
Sept,5,2003 5.9% +2.80 –2.50 +0.30
Mar.5,2004 6.4% +2.95 –2.50 +0.45
Cash Flows to Microsoft
(See Table 6.1,page 127)
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.5
Typical Uses of an
Interest Rate Swap
? Converting a
liability from
–fixed rate to
floating rate
–floating rate to
fixed rate
? Converting an
investment from
–fixed rate to
floating rate
–floating rate to
fixed rate
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.6Intel and Microsoft (MS)
Transform a Liability
(Figure 6.2,page 128)
Intel MS
LIBOR
5%
LIBOR+0.1%
5.2%
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.7
Financial Institution is Involved
(Figure 6.4,page 129)
F.I.
LIBOR LIBOR
LIBOR+0.1%
4.985% 5.015%
5.2%
Intel MS
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.8Intel and Microsoft (MS)
Transform an Asset
(Figure 6.3,page 128)
Intel MS
LIBOR
5%
LIBOR-0.25%
4.7%
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.9
Financial Institution is Involved
(See Figure 6.5,page 129)
Intel F.I,MS
LIBOR LIBOR
4.7%
5.015%4.985%
LIBOR-0.25%
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.10
The Comparative Advantage
Argument (Table 6.4,page 132)
? AAACorp wants to borrow
floating
? BBBCorp wants to borrow
fixed
Fixed Floating
AAACorp 10.00% 6-month LIBOR + 0.30%
BBBCorp 11.20% 6-month LIBOR + 1.00%
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.11
The Swap (Figure 6.6,page 132)
AAA BBB
LIBOR
LIBOR+1%
9.95%
10%
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.12The Swap when a Financial
Institution is Involved
(Figure 6.7,page 133)
AAA F.I,BBB
10%
LIBOR LIBOR
LIBOR+1%
9.93% 9.97%
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.13
Criticism of the Comparative
Advantage Argument
? The 10.0% and 11.2% rates available to
AAACorp and BBBCorp in fixed rate markets
are 5-year rates
? The LIBOR+0.3% and LIBOR+1% rates
available in the floating rate market are six-
month rates
? BBBCorp’s fixed rate depends on the spread
above LIBOR it borrows at in the future
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.14
Valuation of an Interest Rate
Swap
? Interest rate swaps can be valued as
the difference between the value of a
fixed-rate bond and the value of a
floating-rate bond
? Alternatively,they can be valued as a
portfolio of forward rate agreements
(FRAs)
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.15
Valuation in Terms of Bonds
? The fixed rate bond is valued in the
usual way
? The floating rate bond is valued by
noting that it is worth par immediately
after the next payment date
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.16
Valuation in Terms of FRAs
? Each exchange of payments in an
interest rate swap is an FRA
? The FRAs can be valued on the
assumption that today’s forward rates
are realized
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.17
An Example of a Currency Swap
An agreement to pay 11% on a
sterling principal of ￡10,000,000 &
receive 8% on a US$ principal of
$15,000,000 every year for 5 years
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.18
Exchange of Principal
? In an interest rate swap the
principal is not exchanged
? In a currency swap the
principal is exchanged at the
beginning and the end of the
swap
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.19
The Cash Flows (Table 6.6,page 140)
Year
Dollars Pounds
$
------millions------
2001 –15.00 +10.00
2002 +1.20 –1.10
2003 +1.20 –1.10
2004 +1.20 –1.10
2005 +1.20 –1.10
2006 +16.20 -11.10
￡
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.20
Typical Uses of a
Currency Swap
? Conversion from
a liability in one
currency to a
liability in
another currency
? Conversion from
an investment in
one currency to
an investment in
another currency
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.21
Comparative Advantage Arguments
for Currency Swaps (Table 6.7,page 141)
General Motors wants to borrow AUD
Qantas wants to borrow USD
USD AUD
General Motors 5.0% 12.6%
Qantas 7.0% 13.0%
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.22
Valuation of Currency Swaps
Like interest rate swaps,
currency swaps can be valued
either as the difference
between 2 bonds or as a
portfolio of forward contracts
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.23
Swaps & Forwards
? A swap can be regarded as a
convenient way of packaging forward
contracts
? The,plain vanilla” interest rate swap in
our example consisted of 6 FRAs
? The,fixed for fixed” currency swap in
our example consisted of a cash
transaction and 5 forward contracts
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.24
Swaps & Forwards
(continued)
? The value of the swap is the sum of the
values of the forward contracts underlying
the swap
? Swaps are normally,at the money” initially
– This means that it costs nothing to enter
into a swap
– It does not mean that each forward
contract underlying a swap is,at the
money” initially
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
6.25
Credit Risk
? A swap is worth zero to a company
initially
? At a future time its value is liable to be
either positive or negative
? The company has credit risk exposure
only when its value is positive