1. Chapter 7 Swaps
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

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, 8th Edition, Copyright © John C. Hull 2012

3. 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 that could occur (Day count conventions are not considered)
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

4. One Possible Outcome for Cash Flows to Microsoft (Table 7.1, page 150)
Date
LIBOR
Floating Cash Flow
Fixed Cash Flow
Net Cash Flow
Mar 5, 2012
4.20%
Sep 5, 2012
4.80%
+2.10
−2.50
−0.40
Mar 5, 2013
5.30%
+2.40
−0.10
Sep 5, 2013
5.50%
+2.65
+ 0.15
Mar 5, 2014
5.60%
+2.75
+0.25
Sep 5, 2014
5.90%
+2.80
+0.30
Mar 5, 2015
+2.95
+0.45
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

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
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

6. Intel and Microsoft (MS) Transform a Liability (Figure 7.2, page 151)
LIBOR 5%
LIBOR+0.1%
5.2%
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

7. Financial Institution is Involved (Figure 7.4, page 152)
LIBOR
LIBOR+0.1%
4.985%
5.015%
5.2%
Intel MS
Financial Institution has two offsetting swaps
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

8. Intel and Microsoft (MS) Transform an Asset (Figure 7.3, page 152)
LIBOR 5%
LIBOR-0.2%
4.7%
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

9. Financial Institution is Involved (See Figure 7.5, page 153)
Intel
F.I. MS
LIBOR
4.7%
5.015%
4.985%
LIBOR-0.2%
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

10. Quotes By a Swap Market Maker (Table 7.3, page 154)
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, 8th Edition, Copyright © John C. Hull 2012

11. Day Count
A day count convention is specified for for fixed and floating payment
For example, LIBOR is likely to be actual/360 in the US because LIBOR is a money market rate
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

12. Confirmations Confirmations specify the terms of a transaction
The International Swaps and Derivatives has developed Master Agreements that can be used to cover all agreements between two counterparties
Governments now require central clearing to be used for most standardized derivatives
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

13. The Comparative Advantage Argument (Table 7.4, page 156)
AAACorp wants to borrow floating
BBBCorp wants to borrow fixed
Fixed
Floating
AAACorp
4.0%
6 month LIBOR − 0.1%
BBBCorp
5.2%
6 month LIBOR + 0.6%
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

14. The Swap (Figure 7.6, page 157) BBBCorp 4.35% 4% AAACorp LIBOR+0.6%
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

15. The Swap when a Financial Institution is Involved (Figure 7
The Swap when a Financial Institution is Involved (Figure 7.7, page 157)
AAACorp
F.I.
BBBCorp 4%
LIBOR
LIBOR+0.6%
4.33%
4.37%
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

16. 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, 8th Edition, Copyright © John C. Hull 2012

17. 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, 8th Edition, Copyright © John C. Hull 2012

18. 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
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

19. Example of Bootstrapping the LIBOR/Swap Curve (Example 7.1, page 160)
6-month, 12-month, and 18-month LIBOR/swap rates are 4%, 4.5%, and 4.8% with continuous compounding.
Two-year swap rate is 5% (semiannual)
The 2-year LIBOR/swap rate, R, is 4.953%
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

20. Valuation of an Interest Rate Swap
Initially interest rate swaps are worth close to zero
At later times they 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, 8th Edition, Copyright © John C. Hull 2012

21. 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, 8th Edition, Copyright © John C. Hull 2012

22. Valution of Floating-Rate Bondt*
Valuation Date
First Pmt
Date
Floating Pmt =k*
Second
Pmt Date
Maturity Date
Value = L
Value = L+k*
Value = PV of L+k* at t*
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

23. 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% (s.a. compounding)
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

24. Valuation Using Bonds (page 161)
Time
Bfix cash flow
Bfl cash flow
Disc factor PV
Bfix
Bfl
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
Swap value = − = −4.267
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

25. 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, 8th Edition, Copyright © John C. Hull 2012

26. Valuation of Example Using FRAs (page 163)
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, 8th Edition, Copyright © John C. Hull 2012

27. Overnight Indexed Swaps
Fixed rate for a period is exchanged for the geometric average of the overnight rates
Should OIS rate equal the LIBOR rate? A bank can
Borrow $100 million in the overnight market, rolling forward for 3 months
Enter into an OIS swap to convert this to the 3-month OIS rate
Lend the funds to another bank at LIBOR for 3 months
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

28. Overnight Indexed Swaps continued
...but it bears the credit risk of another bank in this arrangement
The OIS rate is now regarded as a better proxy for the short-term risk-free rate than LIBOR
The excess of LIBOR over the OIS rate is the LIBOR-OIS spread. It is usually about 10 basis points but spiked at an all time high of 364 basis points in October 2008
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

29. 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, 8th Edition, Copyright © John C. Hull 2012

30. 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, 8th Edition, Copyright © John C. Hull 2012

31. The Cash Flows (Table 7.7, page 166)
Date
Dollar Cash Flows
(millions)
Sterling cash flow
Feb 1, 2011
-18.0
+10.0
Feb 1, 2012
+1.08
−0.50
Feb 1, 2014
Feb 1, 2015
Feb 1, 2016
+19.08
−10.50
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

32. Typical Uses of a Currency Swap
Convert a liability in one currency to a liability in another currency
Convert an investment in one currency to an investment in another currency
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

33. Comparative Advantage May Be Real Because of Taxes
General Electric wants to borrow AUD
Quantas wants to borrow USD
Cost after adjusting for the differential impact of taxes
USD
AUD
General Electric
5.0%
7.6%
Quantas
7.0%
8.0%
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

34. 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, 8th Edition, Copyright © John C. Hull 2012

35. 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, 8th Edition, Copyright © John C. Hull 2012

36. Valuation in Terms of Bonds (Table 7.9, page 169)
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
Value of Swap = /110 − =
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

37. Valuation in Terms of Forwards (Table 7.10, page 170)
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, 8th Edition, Copyright © John C. Hull 2012

38. Swaps & Forwards
A swap can be regarded as a convenient way of packaging forward contracts
Although the swap contract is usually worth close to zero at the outset, each of the underlying forward contracts are not worth zero
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012

39. 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, 8th Edition, Copyright © John C. Hull 2012

40. 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, 8th Edition, Copyright © John C. Hull 2012