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

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

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

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

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.

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

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

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 5.1%

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 5.2% Add: Paid under swap +LIBOR Less: Received under swap - 5% Net payment LIBOR+0.2%

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

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 4.7% Less: Paid under swap -5% Add: Received under swap +LIBOR Net income LIBOR-0.3%

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-0.20. 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%

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

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

Transform a Liability (Fin int. İnvolved) M.S Intel Loan payment LIBOR + 0.1% 5.2% Add: Paid under swap + 5.015 + LIBOR Less: Received under swap - LIBOR -4.985% Net Payment (Without fin. int.) 5.115% (5.1%) LIBOR+0.215 (LIBOR+ 0.2%)

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

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 + 4.985% Net Income (Without a fin. int) LIBOR-0.315% (LIBOR-0.3%) 4.785% (4.8%)

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

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.

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

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

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.

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%)

The swap agreement appears to improve the position of both company. Total gain is: 0.25+0.25=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 = 1.2-0.7=0.5%

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

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

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

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

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

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.

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.

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

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

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

Valuation Using Bonds Time Bfix cash flow Bfl cash flow Disc factor PV 0.25 4.0 105.100 0.9753 3.901 102.505 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

Valuation Using Bonds Vswap= 98.238-102.505= -4.267

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

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

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

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

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

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

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

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

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%

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

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

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

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 0.009557 0.5734 -0.2266 -0.2071 2 0.010047 0.6028 -0.1972 -0.1647 3 0.010562 0.6337 -0.1663 -0.1269 -10.0 1200 12.6746 +2.6746 2.0417 Total 1.5430 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

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

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

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