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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Swaps
Chapter 7
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Nature of Swaps
A swap is an agreement toexchange cash flows at specifiedfuture times according to certainspecified rules
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
An Example of a Plain Vanilla
Interest Rate Swap
An agreement by Microsoft to receive6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3years on a notional principal of $100millionNext slide illustrates cash flows
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
---------Millions of Dollars---------
LIBOR FLOATING FIXED Net
Date Rate Cash Flow Cash Flow Cash Flow
Mar.5, 2010 4.2%Sept. 5, 2010 4.8% +2.10 2.50 0.40
Mar.5, 2011 5.3% +2.40 2.50 0.10
Sept. 5, 2011 5.5% +2.65 2.50 +0.15
Mar.5, 2012 5.6% +2.75 2.50 +0.25
Sept. 5, 2012 5.9% +2.80 2.50 +0.30
Mar.5, 2013 6.4% +2.95 2.50 +0.45
Cash Flows to Microsoft(See Table 7.1, page 159
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Typical Uses of an
Interest Rate SwapConverting a liability from
fixed rate to floating ratefloating rate to fixed rate
Converting an investment fromfixed rate to floating ratefloating rate to fixed rate
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Intel and Microsoft (MS)Transform a Liability(Figure 7.2, page 160)
Intel MS
LIBOR
5%
LIBOR+0.1%
5.2%
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Financial Institution is Involved(Figure 7.4, page 162)
F.I.
LIBOR LIBOR
LIBOR+0.1%
4.985% 5.015%
5.2%Intel MS
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Intel and Microsoft (MS)Transform an Asset(Figure 7.3, page 161)
Intel MS
LIBOR
5%
LIBOR-0.2%
4.7%
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Financial Institution is Involved(See Figure 7.5, page 163)
Intel F.I. MS
LIBOR LIBOR
4.7%
5.015%4.985%
LIBOR-0.2%
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Quotes By a Swap Market Maker(Table 7.3, page 163)
Maturity Bid (%) Offer (%) Swap Rate (%)2 years 6.03 6.06 6.045
3 years 6.21 6.24 6.225
4 years 6.35 6.39 6.370
5 years 6.47 6.51 6.490
7 years 6.65 6.68 6.66510 years 6.83 6.87 6.850
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
The Comparative AdvantageArgument (Table 7.4, page 166)
AAACorp wants to borrow floatingBBBCorp wants to borrow fixed
Fixed Floating
AAACorp 4.00% 6- month LIBOR 0.1%
BBBCorp 5.20% 6-month LIBOR + 0.6%
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
The Swap (Figure 7.6, page 166)
AAACorp BBBCorp
LIBOR
LIBOR+0.6%
4.35%
4%
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
The Swap when a Financial
Institution is Involved(Figure 7.7, page 167)
AAA F.I. BBB4%
LIBOR LIBOR
LIBOR+0.6%
4.33% 4.37%
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Criticism of the ComparativeAdvantage Argument
The 4.0% and 5.2% rates available to AAACorpand BBBCorp in fixed rate markets are 5-year ratesThe LIBOR0.1% and LIBOR+0.6% ratesavailable in the floating rate market are six-month rates
BBBCorps fixed rate depends on the spreadabove LIBOR it borrows at in the future
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
The Nature of Swap Rates
Six-month LIBOR is a short-term AAborrowing rateThe 5-year swap rate has a riskcorresponding to the situation where 10 six-month loans are made to AA borrowers atLIBOR
This is because the lender can enter into aswap where income from the LIBOR loans isexchanged for the 5-year swap rate
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Using Swap Rates to Bootstrap theLIBOR/Swap Zero Curve
Consider a new swap where the fixed rate is the swaprateWhen principals are added to both sides on the finalpayment date the swap is the exchange of a fixed ratebond for a floating rate bondThe floating-rate rate bond is worth par. The swap isworth zero. The fixed-rate bond must therefore also beworth par
This shows that swap rates define par yield bonds thatcan be used to bootstrap the LIBOR (or LIBOR/swap)zero curve (See Example 7.2 on page 169.)
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Valuation of an Interest RateSwap
Interest rate swaps can be valued asthe difference between the value of afixed-rate bond and the value of afloating-rate bond
Alternatively, they can be valued as a
portfolio of forward rate agreements(FRAs)
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Valuation in Terms of Bonds
The fixed rate bond is valued in the usualway
The floating rate bond is valued by notingthat it is worth par immediately after thenext payment date
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Value of Floating Rate Bond( L =Principal)
Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
0 t *
ValuationDate
First PmtDate
FloatingPmt = k *
SecondPmt Date Maturity
Date
Value = LValue = L +k *
Value = PVof L +k * at t *
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Example
Pay six-month LIBOR, receive 8% (s.a.compounding) on a principal of $100 millionRemaining life 1.25 yearsLIBOR rates for 3-months, 9-months and 15-months are 10%, 10.5%, and 11% (cont comp)6-month LIBOR on last payment date was
10.2% (s.a. compounding)
Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010 20
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Valuation using Bonds (page 172)
Swap value = 98.238 102.505= 4.267
Time Fixed Floating Disc PV fixed PV floatingBond Bond Factor Bond Bond
0.25 4 105.1 0.9753 3.901 102.50450.75 4 0.9243 3.6971.25 104 0.8715 90.64
98.238 102.505
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Valuation in Terms of FRAs
Each exchange of payments in an interest
rate swap is an FRAThe FRAs can be valued on theassumption that todays forward rates are
realized
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Example (page 173)
Time Fixed Floating Net Disc PV of Net
Cash Flow Cash Flow Cash Flow Factor Cash Flow0.25 4 -5.100 -1.100 0.9753 -1.0730.75 4 -5.522 -1.522 0.9243 -1.4071.25 4 -6.051 -2.051 0.8715 -1.787
-4.267
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
An Example of a Currency Swap
An agreement to pay 5% on a sterlingprincipal of 10,000,000 & receive 6%on a US$ principal of $15,000,000every year for 5 years
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Exchange of Principal
In an interest rate swap theprincipal is not exchangedIn a currency swap theprincipal is exchanged at thebeginning and the end of theswap
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
The Cash Flows (Table 7.5, page 176)
Year
Dollars Pounds$
------millions------2010 18.00 +10.002011 +1.08 0.52012 +1.08 0.52013 +1.08 0.5
2014 +1.08 0.52015 +19.08 10.5
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Typical Uses of aCurrency Swap
Conversion from a liability in one currencyto a liability in another currency
Conversion from an investment in onecurrency to an investment in another
currency
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Comparative Advantage Argumentsfor Currency Swaps (Table 7.6, page 176)
General Electric wants to borrow AUDQantas wants to borrow USD
USD AUD
General Motors 5.0% 7.6%
Qantas 7.0% 8.0%
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Valuation of Currency Swaps
Like interest rate swaps,currency swaps can be valuedeither as the difference between2 bonds or as a portfolio of forward contracts (SeeExamples 7.6 and 7.7)
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Example (pages 178-180)
All Japanese LIBOR/swap rates are 4% All USD LIBOR/swap rates are 9%5% is received in yen; 8% is paid in dollars.Payments are made annuallyPrincipals are $10 million and 1,200 million yenSwap will last for 3 more yearsCurrent exchange rate is 110 yen per dollar
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Valuation in Terms of Bonds
Time Cash Flows ($) PV ($) Cash flows (yen) PV (yen)
1 0.8 0.7311 60 57.65
2 0.8 0.6682 60 55.393 0.8 0.6107 60 53.22
3 10.0 7.6338 1,200 1,064.30
Total 9.6439 1,230.55
Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Value = 1230.55/1109.6439 = 1.5430
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Valuation in Terms of Forwards
Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Time $ cashflow
Yen cashflow
ForwardExch rate
Yen cashflow in $
NetCash
Flow
Presentvalue
1 -0.8 60 0.009557 0.5734 -0.2266 -0.2071
2 -0.8 60 0.010047 0.6028 -0.1972 -0.1647
3 -0.8 60 0.010562 0.6337 -0.1663 -0.1269
3 -10.0 1200 0.010562 12.6746 +2.6746 2.0417
Total 1.5430
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Swaps & Forwards
A swap can be regarded as aconvenient way of packaging forwardcontractsWhen a swap is initiated the swap haszero value, but typically some forwardshave a positive value and some have anegative value
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Credit Risk
A swap is worth zero to a companyinitially
At a future time its value is liable to beeither positive or negativeThe company has credit risk exposure
only when its value is positive
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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010
Other Types of Swaps
Amortizing/ step upCompounding swap
Constant maturity swapLIBOR-in-arrears swap
Accrual swap
Equity swap
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O ti F t d Oth D i ti 7th Ed Ch 7 C ight J h C H ll 2010
Other Types of Swaps continued
Cross currency interest rate swapFloating-for-floating currency swap
Diff swapCommodity swapVariance swap
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