1. Swaps
Chapter 7
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

2. Nature of Swaps
A swap is an agreement btw two parties to exchange cash flows at specified future times according to certain specified rules. - A forward contract is equivalent to the exchange of CFs on just one future date, swaps lead to CF exchanges taking a place on several future dates. The most common swap contracts are; - plain vanilla interest rate swap - fixed-for-fixed currency swap
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

3. Mechanics of Interest Rate Swaps
Plain vanilla swap: Company agrees to pay CFs equal to interest at a predetermined fixed rate on a notional principal for a number of years. In return, it receives interest at a floating rate on the same notional principal for the same period of time.
LIBOR is used as the floating rate in most interest rate swaps.
Notional: Principal is not exchanged

4. An Example of a “Plain Vanilla” Interest Rate Swap
An interst rate swap btw Microsoft and Intel. 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.
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

5. Exp. Cont.
Microsoft is long a floating rate bond and short a fixed rate bond.
Intel is long a fixed rate bond and short a floating rate bond.
On a floating rate bond, interest is generally set at the beginning of the period to which it will apply and is paid at the end of the period.

6. Cash Flows to Microsoft
Millions of Dollars
LIBOR
FLOATING
FIXED
Net
Date
Rate
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
–0.10
Sept. 5, 2011
5.5%
+2.65
+0.15
Mar.5, 2012
5.6%
+2.75
+0.25
Sept. 5, 2012
5.9%
+2.80
+0.30
Mar.5, 2013
6.4%
+2.95
+0.45
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

7. 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
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

8. Using a swap to transform a liability
Microsoft has agrees to borrow $100 million at LIBOR+0.1%, wants to transform a floating rate loan into a fixed rate loan. After it has entered into a swap:
Loan payment: LIBOR+0.1%
Add:Paid under swap + 5%
Less:Received under swap - LIBOR
Net Payment %

9. For Intel swap is used to transform fixed rate into floating rate
For Intel swap is used to transform fixed rate into floating rate. Suppose it has 3-year $100 million loan on which it pays 5.2%
Loan payment %
Add: Paid under swap +LIBOR
Less: Received under swap - 5%
Net payment LIBOR+0.2%

10. Intel and Microsoft (MS) Transform a Liability
LIBOR 5%
LIBOR+0.1%
5.2%
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

11. Using the swap to transform an asset (nature of an asset)
Suppose MS owns $100 million in bonds that will provide 4.7% per annum over the next 3 years. MS enters into a swap, wants to switch its assets from fixed to floating rate.
Investment income %
Less: Paid under swap -5%
Add: Received under swap +LIBOR
Net income LIBOR-0.3%

12. Intel is transforming an asset earning floating to fixed
Intel is transforming an asset earning floating to fixed. Suppose Intel has an investment $100 million that yields LIBOR After it has entered into the swap:
Investment income LIBOR-0.20
Less: Paid under swap - LIBOR
Add: Received under swap + 5%
Net Investment income 4.8%

13. Intel and Microsoft (MS) Transform an Asset (Figure 7.3, page 151)
LIBOR 5%
LIBOR-0.2%
4.7%
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

14. Role of Financial Intermediary
Suppose fin. intermediary enters into two offsetting swap transactions with Intel and MS and receives 0.03% fee per year:
0.03% x 1 million = $30,000

15. Transform a Liability (Fin int. İnvolved)
M.S
Intel
Loan payment
LIBOR + 0.1%
5.2%
Add: Paid under swap
+ LIBOR
Less: Received under swap
- LIBOR
-4.985%
Net Payment
(Without fin. int.)
5.115%
(5.1%)
LIBOR+0.215
(LIBOR+ 0.2%)

16. Financial Institution is Involved (Figure 7.4, page 151)
LIBOR
LIBOR+0.1%
4.985%
5.015%
5.2%
Intel MS
Financial Institution has two offsetting swaps
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

17. Transform an Asset (Fin. Inter. involved)
M.S
Intel
In. Income
4.7%
LIBOR-0.2%
Less: Paid under swap
-5.015
-LIBOR
Add: Received under swap
+ LIBOR %
Net Income
(Without a fin. int)
LIBOR-0.315%
(LIBOR-0.3%)
4.785%
(4.8%)

18. Financial Institution is Involved
Intel
F.I. MS
LIBOR
4.7%
5.015%
4.985%
LIBOR-0.2%
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

19. Market Makers
It is unlikely that two companies will contact a fin. intermediary at the same time and want to take opposite positions in exactly the same swap. For this reason many large fin. intermediaries act as market makers for swaps.
Swap Rate: is the average the bid and offer fixed rates.

20. Quotes By a Swap Market Maker
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
6.665
10 years
6.83
6.87
6.850
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

21. The Comparative Advantage Argument
AAACorp and BBBCorp wish to borrow $10 million for 5 years
AAACorp wants to borrow floating
BBBCorp wants to borrow fixed
Fixed
Floating
AAACorp
4.0%
6-month LIBOR − 0.10%
BBBCorp
5.2%
6-month LIBOR + 0.6%
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

22. BBBCorp has a comparative advantage in floating market and AAACorp has a comparative advantage in fixed rate market.
They can enter into a swap that AAACorp ends up with floating rate funds and BBBCorp ends up with fixed rate funds.
Suppose AAACorp agrees to pay interest at 6 month LIBOR on $10 million and BBBCorp agrees to pay 4.35% per annum on $10 million.

23. AAACorp
BBBCorp
Loan payment 4%
LIBOR+0.6%
Add: Paid under swap
+ LIBOR
+ 4.35%
Less: Received under swap
-4.35%
-LIBOR
Net Payment
(Before)
LIBOR-0.35%
(LIBOR-0.10%)
(0.25% gain)
4.95%
(5.2%)

24. The swap agreement appears to improve the position of both company.
Total gain is: =0.50%
If a is the difference btw the interest rates in fixed market and if b is the difference between the interest rates in floating market.
Total gain is; a-b
a = 1.2% (5.2%-5%)
b= 0.7% ( LIBOR+0.6%-(LIBOR-0.1%))
a-b = =0.5%

25. The Swap agreement btw two parties
AAACorp
BBBCorp
LIBOR
LIBOR+0.6%
4.35% 4%
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

26. The Swap when a Financial Institution is Involved
AAACorp
F.I.
BBBCorp 4%
LIBOR
LIBOR+0.6%
4.33%
4.37%
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

27. 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−0.1% and LIBOR+0.6% 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, 7th International Edition, Copyright © John C. Hull 2008

28. 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, 7th International Edition, Copyright © John C. Hull 2008

29. 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 par. The 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
Traders use swap rates for longer-term zero rates.
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

30. Example 7.2
Suppose that the 6-month, 12-month and 18 month LIBOR/swap zero rates have been determined as 4%, 4.5%, and 4.8% with cont.compounding and that the 2-year swap rate (for a swap where payments are made semiannually) is 5%.
Note: This 5% swap rate means that a bond with a principal of $100 million and semiannual coupon of 5% per annum sells for par.
Find the 2-year zero rate.

31. Example 7.3
The 400-day LIBOR zero rate has been calculated as 4.8% with cont.compounding and, from a Eurodollar futures quote, it has been calculated that the forward rate for a 91-day period beginning in 400 days is 5.3% with cont. compounding. Find the 491-day rate.

32. 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, 7th International Edition, Copyright © John C. Hull 2008

33. 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, 7th International Edition, Copyright © John C. Hull 2008

34. Example
Pay six-month LIBOR, receive 8% (s.a. compounding) on a principal of $100 million
Remaining life 1.25 years
LIBOR 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% (semiann compounding)
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

35. Valuation Using Bonds Time Bfix cash flow Bfl cash flow Disc factor PV
0.25
4.0
0.9753
3.901
0.75
0.9243
3.697
1.25
104.0
0.8715
90.640
Total
98.238
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

36. Valuation Using Bonds
Vswap= =

37. 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, 7th International Edition, Copyright © John C. Hull 2008

38. Valuation of Example Using FRAs (page 162)
Time
Fixed cash flow
Floating cash flow
Net Cash Flow
Disc factor PV
Bfl
0.25
4.0
-5.100
-1.100
0.9753
-1.073
0.75
-5.522
-1.522
0.9243
-1.407
1.25
-6.051
-2.051
0.8715
-1.787
Total
-4.267
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

39. Currency Swaps
Exchanging principal and interest payments in one currency for principal and interest payments in another currency.

40. An Example of a Currency Swap
An agreement to pay 5% on a sterling principal of £10,000,000 & receive 6% on a US$ principal of $18,000,000 every year for 5 years.
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

41. 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, 7th International Edition, Copyright © John C. Hull 2008

42. The Cash Flows (Table 7.7, page 164)
Dollars
Pounds $
Year
------millions------
2004
–18.00
+10.00
2005
+1.08
–0.50
2006
+1.08
–0.50
2007
+1.08
–0.50
2008
+1.08
–0.50
2009
+19.08
−10.50
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

43. 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, 7th International Edition, Copyright © John C. Hull 2008

44. Comparative Advantage Arguments for Currency Swaps
General Electric wants to borrow 20 miilion AUD and Qantas wants to borrow 15 million USD (Exchange rate is $0.75 per AUD)
USD
AUD
General Motors
5.0%
7.6%
Qantas
7.0%
8.0%
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

45. GE has a comparative advantage in USD and Qantas has a comparative advantage in AUD. So that GE borrows USD and Qantas borrows AUS then they enter into a currency swap to transform GE’s loan into a AUD and Qantas loan into a USD.
Total gain to all parties: 2%-0.4% = 1.6%

46. 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, 7th International Edition, Copyright © John C. Hull 2008

47. Example 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 annually
Principals are $10 million and 1,200 million yen
Swap will last for 3 more years
Current exchange rate is 110 yen per dollar
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

48. Valuation in Terms of Bonds
Time
Cash Flows ($)
PV ($)
Cash flows (yen)
PV (yen) 1
0.8
0.7311 60
57.65 2
0.6682
55.39 3
0.6107
53.22
10.0
7.6338
1,200
1,064.30
Total
9.6439
1,230.55
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

49. Valuation in Terms of Forwards
Time
$ cash
flow
Yen cash flow
Forward Exch rate
Yen cash flow in $
Net Cash Flow
Present value 1
-0.8 60
0.5734 2
0.6028 3
0.6337
-10.0
1200
2.0417
Total
1.5430
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

50. Swaps & Forwards
A swap can be regarded as a convenient way of packaging forward contracts
Although the swap contract is usually worth zero at the outset, each of the underlying forward contracts are not worth zero
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

51. 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
Some swaps are more likely to lead to credit risk exposure than others
What is the situation if early forward rates have a positive value?
What is the situation when the early forward rates have a negative value?
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

52. 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, diff swaps, cross currency interest rate swaps, equity swaps, extendable swaps, puttable swaps, swaptions, commodity swaps, volatility swaps……..
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008