7
Options, Swaps
Chapter Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.1
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 6th Edition, Copyright John C. Hull 2005
7.2
An 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 6th Edition, Copyright John C. Hull 2005
7.3
Cash Flows to Microsoft
(See Table 7.1, page 151)
---------Millions of Dollars--------LIBOR FLOATING FIXED Date Mar.5, 2004 Sept. 5, 2004 Mar.5, 2005 Sept. 5, 2005 Mar.5, 2006 Sept. 5, 2006 Mar.5, 2007 Rate 4.2% 4.8% 5.3% 5.5% 5.6% 5.9% 6.4% +2.10 +2.40 +2.65 +2.75 +2.80 +2.95 2.50 2.50 2.50 2.50 2.50 2.50 0.40 0.10 +0.15 +0.25 +0.30 +0.45
7.4
Net
Cash Flow Cash Flow Cash Flow
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
Typical Uses of an Interest Rate Swap
Converting
a liability from fixed rate to floating rate floating rate to fixed rate an investment from fixed rate to floating rate floating rate to fixed rate
7.5
Converting
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
Intel and Microsoft (MS) Transform a Liability
(Figure 7.2, page 152)
5% 5.2%
Intel
LIBOR
MS
LIBOR+0.1%
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.6
Financial Institution is Involved
(Figure 7.4, page 153)
4.985% 5.2%
5.015%
Intel
LIBOR
F.I.
LIBOR
MS
LIBOR+0.1%
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.7
Intel and Microsoft (MS) Transform an Asset
(Figure 7.3, page 153)
5% 4.7%
Intel
LIBOR-0.2% LIBOR
MS
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.8
Financial Institution is Involved
(See Figure 7.5, page 154)
4.985%
5.015% 4.7 %
Intel
LIBOR-0.2% LIBOR
F.I.
LIBOR
MS
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.9
Quotes By a Swap Market Maker
(Table 7.3, page 155) Maturity 2 years 3 years 4 years 5 years 7 years 10 years Bid (%) 6.03 6.21 6.35 6.47 6.65 6.83 Offer (%) 6.06 6.24 6.39 6.51 6.68 6.87 Swap Rate (%) 6.045 6.225 6.370 6.490 6.665 6.850
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.10
The Comparative Advantage Argument (Table 7.4, page 157)
AAACorp wants to borrow floating BBBCorp wants to borrow fixed
Fixed AAACorp BBBCorp 4.0% 5.20%
Floating 6-month LIBOR + 0.30% 6-month LIBOR + 1.00%
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.11
The Swap (Figure 7.6, page 158)
3.95% 4% AAACorp
BBBCorp
LIBOR+1% LIBOR
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.12
The Swap when a Financial Institution is Involved
(Figure 7.7, page 158)
3.93% 4% AAACorp
3.97%
F.I.
LIBOR LIBOR
BBBCorp LIBOR+1%
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.13
Criticism of the Comparative Advantage Argument
The 4.0% and 5.2% 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 sixmonth rates BBBCorp's fixed rate depends on the spread above LIBOR it borrows at in the future
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.14
The Nature of Swap Rates
Six-month LIBOR is a short-term AA borrowing rate The 5-year swap rate has a risk corresponding to the situation where 10 six-month loans are made to AA borrowers at LIBOR This is because the lender can enter into a swap where income from the LIBOR loans is exchanged for the 5-year swap rate
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.15
Using Swap Rates to Bootstrap the LIBOR/Swap Zero Curve
Consider a new swap where the fixed rate is the swap rate When principals are added to both sides on the final payment date the swap is the exchange of a fixed rate bond for a floating rate bond The floating-rate rate bond is worth The par. swap is worth zero. The fixed-rate bond must therefore also be worth par This shows that swap rates define par yield bonds that can be used to bootstrap the LIBOR (or LIBOR/swap) zero curve
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.16
Valuation of an Interest Rate Swap that is not New
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 6th Edition, Copyright John C. Hull 2005
7.17
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 6th Edition, Copyright John C. Hull 2005
7.18
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 6th Edition, Copyright John C. Hull 2005
7.19
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 6th Edition, Copyright John C. Hull 2005
7.20
Exchange of Principal
In
an interest rate swap the principal is not exchanged In a currency swap the principal is usually exchanged at the beginning and the end of the swap's life
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.21
The Cash Flows (Table 7.7, page 166)
Dollars Pounds $ ------millions-----15.00 +10.00 +0.60 0.70 +0.60 0.70 +0.60 0.70 +0.60 0.70 +15.60 -10.70
Year 2004 2005 2006 2007 2008 2009
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.22
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 6th Edition, Copyright John C. Hull 2005
7.23
Comparative Advantage Arguments for Currency Swaps (Table 7.8, page 167)
General Motors wants to borrow AUD Qantas wants to borrow USD
USD General Motors Qantas 5.0% 7.0% AUD 12.6% 13.0%
Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 2005
7.24
Valuation of Currency Swaps
Like interest rate swaps, currency swaps ca...