1.1

1
550.444Modeling and AnalysisSecurities and
Markets

• Week of October 20, 2008
• Swaps

2
Where we are

• Previously Interest Rate Futures (Chapter 6,
  OFOD)
• Last Week Mid Term
• This Week Swaps (Chapter 7, OFOD)
• Next Week Option Markets and Stock Options
  (Chapter 8-9, OFOD)

3
Assignment

• For This Week (Oct 20)
• Read Hull Chapter 7
• Problems
• Chapter 7 1,3,5,6,9,12,1820,21
• For Next Week (Oct 27)
• Read Hull Chapter 8-9
• Problems
• Chapter 9 7,14,15,18,19 23
• Optional Look at DerivaGem 9.21 9.26

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Plan for This Week

• Exam Discussion (Briefly)
• Swaps
• Interest Rate Swap
• Structure and Uses
• The Swap Curve
• Valuation of IR Swap Bond Viewpoint as PF of
  FRA
• Currency Swap
• Valuation of Currency Swap As bond PF of
  Forward FX Contracts
• Other Swaps and Compounding Swaps
• Whats Ahead Options (8-9) Binomial Trees (11)
  Wiener Process Ito Lemma (12)
  Black-Scholes-Merton Model (13)

5
Nature of Swaps

• A swap is an agreement to exchange cash flows at
  specified future times according to certain
  specified rules

6
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

7
Cash Flows to Microsoft
8
Cash Flow Diagram of Swap MS

• Pay Fixed at 5
• Receive Floating at LIBOR
• Payment at ti, fixed at ti-1
• Net Cash exchanged

-
t1
t2
t3
t4
t5
t6
t0

-
9
Swap Characteristics

• Cash Flows (Fixed and Floating) could be
  described (augmented) by showing notional amount
  exchanged at maturity
• Allows for the description of the Swap as
• Short a Fixed-Rate Bond, BFIX
• Long a Floating-Rate Bond, BFLT
• For a New Swap, by Definition, BFIX BFLT
• Be Aware of Day Count Conventions, Fixed vs.
  Floating
• LIBOR Act/360
• Fixed 30/360 or Act/360 or etc.

10
Typical Uses of anInterest 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

11
Intel and Microsoft (MS) Transform a Liability
5
5.2
MS
Intel
LIBOR0.1
LIBOR

• Intel has issued a 3-year, 100mm note at a rate
  of 5.2
• -- Net of the Swap, Intel has transformed
  this to a borrowing of LIBOR20bps
• - Micro has borrowed 100mm for 3-years at
  LIBOR10bps
• -- Net of the Swap, Micro has transformed
  this to a fixed, 3-year
• borrowing at 5.1

12
Financial Institution is Involved - The Swap
Dealer (AAA)

4.985
5.015
5.2
Intel
F.I.
MS
LIBOR0.1
LIBOR
LIBOR
Net of the Dealer - Intel has LIBOR21.5bps
financing - MS has 5.115 fixed financing
13
Intel and Microsoft (MS) Transform an Asset

5
4.7
Intel
MS
LIBOR-0.2
LIBOR
Intel has an investment that pays LIBOR-20bps
over the next 3-years - Net of the Swap, Intel
has transformed this into an investment paying a
fixed 4.80 Micro has an investment that pays a
fixed rate of 4.7 over 3-years - Net of the
Swap, MS has converted this into a floating rate
deposit at LIBOR-30bps
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Financial Institution is Involved

5.015
4.985
4.7
MS
F.I.
Intel
LIBOR-0.2
LIBOR
LIBOR
Net of the Dealer - Intel has a 4.78 fixed rate
asset - MS has a LIBOR-31.5bps floating rate asset
15
Swap Confirmation
16
Quotes By a Swap Market Maker March 01, 2007
17
Swap Curve March 01, 2007
18
US Treasury March 01, 2007
19
Swap Spreads March 01, 2007
20
SWAP ED Analysis March 01,07
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The Comparative Advantage - Why Swaps are so
Popular

• One Curious Property Underscoring the Utility of
  Swaps is the Ability of Counterparties to take
  advantage of their Comparative Advantage in the
  Debt Markets
• Different Credit Quality Borrowers may have a
  Comparative Advantage in Fixed or Floating
  Markets
• For New Financing, Borrowers go to the Cash
  Market where they have a Comparative Advantage
• As a Result a Company may
• Borrow Fixed when it wants Floating
• Borrow Floating when it wants Fixed
• BUT, It can Adjust the result through the Swap
  Market

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The Comparative Advantage

• AAACorp wants to borrow floating
• Has a Comparative Advantage in Fixed Market
• 120bps better than BBBCorp
• BBBCorp wants to borrow fixed
• Has a Comparative Advantage in Floating Market
• 70bps worse than AAACorp

A120 B70 Can always structure
swap pick-up as A-B 50
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The Comparative Advantage

3.95
4
AAA Corp
BBB Corp
LIBOR1
LIBOR

• AAACorp Creates a Synthetic LIBOR5 Floater
  through the Swap Market
• - 25bp improvement over the Cash Market
• BBBCorp Creates a Synthetic 4.95 Fixed Rate
  through the Swap Market
• - 25bp improvement over the Cash Market

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The Comparative Advantage with Swap Dealer

3.93
3.97
4
AAA Corp
BBB Corp
F.I.
LIBOR1
LIBOR
LIBOR

• - AAACorp Creates LIBOR7 with Dealer Charges
  included
• BBBCorp Creates 4.97 with Dealer Charges
  included
• The 4bps the Dealer takes out reduces AAACorp
  credit exposure and
• makes the facility available to BBBCorp

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The Comparative Advantage

• The 4.0 and 5.2 rates available to AAACorp and
  BBBCorp in fixed rate markets are 5-year rates
• Spread reflects credit issues for the long haul
• The LIBOR0.3 and LIBOR1 rates available in
  the floating rate market are six-month rates
• Credit issue is diminished as credit weakening is
  mitigated by the lenders ability to charge a
  higher spread or not to roll
• BBBCorps fixed rate depends on the spread above
  LIBOR it borrows at in the future
• If short term borrowing cost goes up to
  LIBOR200bps
• Fixed rate borrowing goes up to 5.97
• Well above the 5.20 that could have been
  locked-in via Cash Market

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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
• This is more favorable than the 5-year Cash
  Market where the borrower is sure to be AA only
  at the beginning of the 5-years
• Also, the Swap Dealer is only exposed to the net
  of the exchange on the Swap, not the notional
  amount
• No Arbitrage on Swap-to-Cash since there is no
  risk on the Notional Amount (Principal Amount in
  the Cash Mkt.)
• 5-year swap rates are therefore lower than 5-year
  AA rates

27
Using Swap Rates to Bootstrap the LIBOR/Swap Zero
Curve

• Consider a new Swap where Fixed side 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 bond is worth Par (at fixing)
• The Swap is worth zero
• Therefore, the Fixed-Rate Bond must 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

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Valuation of an Interest Rate Swap that is not New

• Interest Rate Swap can be valued as the
  difference between the value of a fixed-rate bond
  and a floating-rate bond VSwapBFIX - BFLOAT
• Alternatively, they can be valued as a portfolio
  of forward rate agreements (FRAs)
• where FiForward rate,i0
• F0Current LIBOR
• EXAMPLE Consider the
• SWAP
• Pay 6M LIBOR Receive 8 PA on 100mm
• 15-months to go
• Market
• LIBOR (cc) 3M10 9M10.5 15M11
• 6M LIBOR 3M ago 10.2

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Valuation in Terms of Bonds

• The Fixed-Rate Bond is valued in the usual way
• Using the LIBOR/Swap Zero Curve
• The Floating-Rate Bond is valued by noting that
  it is worth par when the coupon is re-set
• VSwapBFIX - BFLOAT
• VSwap -4.267

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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
  todays 6-mo forward rates (in 3- 9-mos) are
  realized
• 3x9 rate e.1x.25xeF(C3)x.5 e.105x.75
• 9x15 rate e.105x.75xeF(C9)x.5 e.11x1.25
• Converting continuous compounding back to SA

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Valuation in Terms of FRAs

• 1st Row CF in 3-mos, already determined
• 2nd 3rd Row CF in 9- 15-mos assumes forward
  rates
• 2nd Row FRA is (8-11.044)(.5)xe-0.105x0.75
• 3rd Row FRA is (8-12.102)(.5)xe-0.11x1.25

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The Currency Swap

• Exchange of Cash Flows across 2 Currencies
• Principal and Interest in one Currency for
  Principal and Interest in another Currency
• Principal Amounts are (usually) Exchanged at the
  Beginning and at the End of the life of the Swap
• At Initiation, the market exchange rate is used
  to set the principal amounts
• At the End, the principal amount in each currency
  is the same, but the value can be quite different
  due to then prevailing exchange rates
• Consider the Interest in a Fixed-for-Fixed
  Currency Swap payments are made once a year

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An Example of a Currency Swap

• An agreement to pay 7 on a sterling principal
  of 10,000,000 receive 4 on a US principal of
  15,000,000 every year for 5 years
• 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
  swaps life

34
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

35
Comparative Advantage Arguments for Currency Swaps

• General Motors wants to borrow 20 million in AUD
• Has a Comparative Advantage in USD
• 200bps better than Quantas
• Qantas wants to borrow 12 million in USD
• Has a Comparative Advantage in AUD
• Only 40bps worse than GM
• Implied FX is 1.66 AUD per USD
• Borrowing Rates for each, adjusted for the
  differential impact of taxes

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The Comparative Advantage with US Swap Dealer

USD 5.0
USD 6.3
USD 5
1.3 ------------------- US Swap Dealer ---------
------------ -1.1
General Motors
Quantas
AUD 13.0
AUD 13.0
AUD 11.9

• - GM Creates AUD 11.9, Pick-up of 70bps over AUD
  borrowing
• Quantas Creates USD 6.3, Pick-up of 70bps over
  USD costs
• The Dealer gains 1.3 (156,000) on USD leg and
  looses 1.1 (220,000) on AUD leg
• Dealer takes out 20bps (So all 160bps is
  accounted for)
• FX risk can be avoided by buying AUD 220,000 PA
  in the Forward FX market for
• each year to lock-in the 24,000 spread
  156,000-220,000x1.66724,000

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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
• Let the Swap be where USD is received and foreign
  currency is paid
• Similarly, for a portfolio of forward FX
  contracts where USD is received
• EXAMPLE
• SWAP 3-year tenor, annual pay
• Pay USD at 8PA on 10 million
• Receive YEN at 5PA on Y1,200 million
• Market
• LIBOR/Swap Curve is flat in both US (at 9PA)
  Japan (at 4PA)
• FX spot market has Y110 1

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Valuation in Terms of Bonds

• The USD Fixed-Rate Bond is valued in the usual
  way
• Using the USD LIBOR/Swap Zero Curve
• The JPY Fixed-Rate Bond is valued the same way
• Using the JPY LIBOR/Swap Zero Curve
• Since the USD is Paid, VSwap S0 BF BD
• VSwap 1,230.55/110 9.6439 1.543 million

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Valuation as a Portfolio of Forward FX Contracts

• Current Spot FX is Y1101 or 0.009091
• Forward FX F(Ti)S0 x exp.05 x Ti
• PV the Net USD CF
• PV(Ti) USD(Ti) JPY(Ti) x F(Ti) expRi x
  Ti

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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 5
  forward contract
• 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

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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
• The credit risk exposure is limited to the value
  of the contract, not the notional amount.

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Other Types of Swaps

• Floating-for-floating interest rate swaps
• Amortizing swaps
• Step up swaps
• Forward swaps
• Constant maturity swaps
• Compounding swaps
• LIBOR-in-arrears swaps
• Accrual swaps
• Differential swaps
• Cross currency interest rate swaps
• Equity swaps
• Extendable swaps Puttable swaps
• Swaptions
• Commodity swaps
• Volatility swaps..

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The End for Today

• Questions?