Chapter 7 Swaps Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 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, 10th Edition, Copyright John C. Hull 2017 2 An Example of a Plain Vanilla Interest Rate Swap An agreement by Apple to receive 6-month LIBOR & pay a fixed rate of 3% 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, 10th Edition, Copyright John C. Hull 2017 3 Cash Flows to Apple (See Table 7.1, page 157 ---------Millions of Dollars--------LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow

Mar. 8, 2016 2.2% Sept. 8, 2016 2.8% +1.10 1.50 0.40 Mar. 8, 2017 3.3% +1.40 1.50 0.10

Sept. 8, 2017 3.5% +1.65 1.50 +0.15 Mar. 8, 2018 3.6% +1.75 1.50 +0.25 Sept. 8, 2018 3.9%

+1.80 1.50 +0.30 Mar. 8, 2019 3.4% +1.95 1.50 +0.45 Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 4 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 fixed rate to floating rate floating rate to fixed rate Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 5 Interest Rate Swap Between Apple and Citigroup (Figure 7.1, page 156) 3.0% Citi Apple LIBOR Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 6

Apple Transforms a Liability from Floating to Fixed (Figure 7.2, page 158) 3.0% Citi Apple LIBOR+0.1% LIBOR Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 7 Interest Rate Swap Between Citigroup and Intel (Figure 7.3, page 159) 2.97%

Citi Intel LIBOR Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 8 Intel Transforms a Liability from Fixed to Floating (Figure 7.4, page 159) 2.97% Citi Intel 3.2% LIBOR Options, Futures, and Other Derivatives, 10th Edition,

Copyright John C. Hull 2017 9 Apple Transforms an Asset from Fixed to Floating (Figure 7.5, page 159) 3.0% Citi Apple 2.7% LIBOR Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 10 Intel Transforms an Asset from Floating to Fixed (Figure 7.6, page 160) 2.97%

Citi Intel LIBOR0.2% LIBOR Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 11 Quotes By a Swap Market Maker (Table 7.3, page 161) Maturity 2 years Bid (%) 2.55 Offer (%) 2.58

Swap Rate (%) 2.565 3 years 2.97 3.00 2.985 4 years 3.15 3.19 3.170 5 years 3.26

3.30 3.280 7 years 3.40 3.44 3.420 10 years 3.48 3.52 3.500 Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 12

Day Count A day count convention is specified for fixed and floating payments For example, LIBOR is likely to be actual/360 in the U.S. because LIBOR is a money market rate Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 13 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 CCPs are used for most standard swaps between two financial institutions Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017

14 The Comparative Advantage Argument (Table 7.4, page 163) AAACorp wants to borrow floating BBBCorp wants to borrow fixed Fixed Floating AAACorp 4.00% 6-month LIBOR 0.1% BBBCorp 5.20% 6-month LIBOR + 0.6%

Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 15 A Swap where Companies Trade Directly with Each Other (Figure 7.7, page 164) 4% 4.35% BBBCorp AAACorp LIBOR+0.6% LIBOR Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017

16 The Swap when a Financial Institution (F.I.) is Involved (Figure 7.7, page 164) 4% 4.33% AAACorp 4.37% BBBCorp F.I. LIBOR LIBOR+0.6% LIBOR Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017

17 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 LIBOR0.1% and LIBOR+0.6% rates available in the floating rate market are sixmonth rates BBBCorps fixed rate depends on the spread above LIBOR it borrows at in the future Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 18 Valuation of an Interest Rate Swap Initially interest rate swaps are worth close to zero At later times they can be valued as a portfolio of forward rate agreements (FRAs) The procedure is to Calculate LIBOR forward rates

Calculate the swap cash flows that will occur if LIBOR forward rates are realized Discount these swap cash flows at OIS rates Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 19 Example 7.1 (page 166) Swap involves paying 3% per annum and receiving LIBOR every six months on $100 million Swap has 15 months remaining (exchanges in 3, 9, and 15 months) LIBOR rate applicable to exchange in 3 months was determined 3 months ago and is 2.9% Forward LIBOR rates for 3-9 month period and 9-15 month periods are 3.429% and 3.734%, respectively OIS zero rates for maturities of 3, 9, and 15 months are 2.8%, 3.2%, and 3.4%, respectively Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 20

Calculations ($ million) Time (yrs) Fixed cash flow Floating cash flow Net cash flow Discoun PV of net t factor cash flow 0.25 1.5000 +1.450

0 0.050 0 0.9930 0.0497 0.75 1.5000 +1.714 5 +0.214 5 0.9763 +0.2094 1.25

1.5000 +1.867 2 +0.367 2 0.9584 +0.3519 Value of swap is $0.5117 million +0.5117 Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 21 Bootstrapping LIBOR forward rates: Example 7.2 (page 167)

6,12,18, and 24 month OIS rates are 3.8%, 4.3%, 4.6%, and 4.75% respectively with cont. comp. 6-month LIBOR rate is 4% (sa comp.) Suppose forward LIBOR rates for 6-12 and 12-18 months have already been calculated as 5% and 5.5%, respectively (sa comp) The two year swap rate is 5% The next step is to calculate the LIBOR forward rate, F, for the18-24 month period. Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 22 Bootstrapping LIBOR forward rates: Calculations A 2-year swap where 5% is paid and LIBOR is received on $100 is worth zero. Value of first three exchanges are 0.5(0.04 0.05)100e0.0380.5 = 0.4906 0.5(0.05 0.05)100e0.0431.0 = 0 0.5(0.055 0.05)100e0.0461.5 = +0.2333 The value of the fourth payment must be +0.2573 so that

the total value is zero 0.5(F0.05)100e0.04752.0 = 0.2573 F = 0.05566 or 5.566% per annum Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 23 An Example of a Fixed-forFixed Currency Swap (Figure 7.10, page 169) Five year agreement by BP to Pay 3% on a US dollar principal of $15,000,000 Receive 4% on a sterling principal of 10,000,000 Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 24 Exchange of Principal In an interest rate swap the

principal is not exchanged In a currency swap the principal is exchanged at the beginning and the end of the swap Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 25 The Cash Flows (Table 7.5, page 170) Date Dollar Cash Flows (millions) Sterling cash flow (millions) Feb 1, 2016 +15.00

10.00 Feb 1, 2017 0.45 +0.40 Feb 1, 2018 0.45 +0.40 Feb 1, 2019 0.45 +0.40 Feb 1, 2020 0.45

+0.40 Feb 1, 2021 15.45 +10.40 Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 26 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, 10th Edition, Copyright John C. Hull 2017

27 Comparative Advantage May Be Real Because of Taxes General Electric wants to borrow AUD Quantas wants to borrow USD Borrowing costs after adjusting for the differential impact of taxes could be: USD AUD General Electric 5.0% 7.6% Quantas 7.0% 8.0%

Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 28 Valuation of Fixed-for-Fixed Currency Swaps Fixed for fixed currency swaps can be valued either using forward rates or as the difference between 2 bonds Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 29 Examples 7.3 and 7.4 (pages 172-174) All Japanese interest rates are 1.5% per annum (cont. comp.) All USD interest rates are 2.5% per annum (cont. comp.) 3% is received in yen; 4% 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, 10th Edition, Copyright John C. Hull 2017 30 Valuation in Terms of Forward Rates (page 173) Tim Dollar e Cash Flow 1 2 3 Tota l Forward rate Dollar

value of yen cash flow +36 0.00918 2 0.4 10. 4 0.4 Yen cash flow Net cash flow Present

value 0.3306 0.069 4 0.0677 +36 0.00927 5 0.3339 0.066 1 0.0629 +123 6

0.00936 8 11.5786 +1.178 6 +1.0934 Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 +0.9629 31 Valuation in Terms of Bonds (page 174) Time Cash Flows ($ millions) PV

($ millions) 1 0.4 0.3901 36 35.46 2 0.4 0.3805 36 34.94 3

10.4 9.6485 1,236 1,181.61 Total Cash flows (millions of yen) 10.4191 PV ( millions of yen) 1,252.01 Value = 1,252.01/11010.4191 = +0.9629 millions of dollars

Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 32 Other Currency Swaps Fixed-for-floating: equivalent to a fixed-forfixed currency swap plus a fixed for floating interest rate swap Floating-for-floating: equivalent to a fixed-forfixed currency swap plus two floating interest rate swaps Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 33 Swaps & Forwards A swap can be regarded as a convenient way of packaging forward contracts When a swap is initiated the swap has zero value, but typically some forwards have a positive value and some have a negative value

Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 34 Credit Risk When derivatives transactions with a counterparty are cleared bilaterally, they are netted There is exposure if the net value of outstanding transactions is greater than the collateral posted Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 35 Credit Default Swaps: A Quick First Look Notional principal (e.g. $100 million) and maturity (e.g. 5 yrs) specified Protection buyer pays a fixed rate (e.g. 150 bp) on the notional principal (the CDS spread)

If the reference entity (a country or company) defaults protection seller buys bonds issued by the reference entity for their face value and the spread payments stop. Total face value of bonds bought equals notional principal Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 36 Other Types of Swaps Amortizing/ step up Compounding swap Constant maturity swap LIBOR-in-arrears swap Accrual swap Equity swap Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 37 Other Types of Swaps continued

Cross currency interest rate swap Floating-for-floating currency swap Diff swap Commodity swap Variance swap Options, Futures, and Other Derivatives, 10th Edition, Copyright John C. Hull 2017 38