Chapter 7 Swaps Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 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, 8th Edition, Copyright © John C. Hull 2012 2 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 3 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 −2.50 −0.10 Sep 5, 2013 5.50% +2.65 −2.50 + 0.15 Mar 5, 2014 5.60% +2.75 −2.50 +0.25 Sep 5, 2014 5.90% +2.80 −2.50 +0.30 Mar 5, 2015 +2.95 −2.50 +0.45 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 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, 8th Edition, Copyright © John C. Hull 2012 5 Intel and Microsoft (MS) Transform a Liability (Figure 7.2, page 151) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 6 Intel MS LIBOR 5% LIBOR+0.1% 5.2% Financial Institution is Involved (Figure 7.4, page 152) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 7 F.I. LIBOR LIBOR LIBOR+0.1 % 4.985% 5.015% 5.2% Intel MS Financial Institution has two offsetting swaps Intel and Microsoft (MS) Transform an Asset (Figure 7.3, page 152) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 8 Intel MS LIBOR 5% LIBOR-0.2% 4.7% Financial Institution is Involved (See Figure 7.5, page 153) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 9 Intel F.I. MS LIBOR LIBOR 4.7% 5.015%4.985% LIBOR-0.2% 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 10 [...]... Time Fixed cash flow Floating cash flow Net Cash Flow Disc factor PV Bfl 0.25 4.0 -5.100 -1.100 0. 975 3 -1. 073 0 .75 4.0 -5.522 -1.522 0.9243 -1.4 07 1.25 4.0 -6.051 -2.051 0. 871 5 -1 .78 7 Total -4.2 67 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C Hull 2012 26 Overnight Indexed Swaps Fixed rate for a period is exchanged for the geometric average of the overnight rates Should OIS... Futures, and Other Derivatives, 8th Edition, Copyright © John C Hull 2012 13 The Swap (Figure 7. 6, page 1 57) 4.35% 4% AAACorp BBBCorp LIBOR+0.6% LIBOR Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C Hull 2012 14 The Swap when a Financial Institution is Involved (Figure 7. 7, page 1 57) 4.33% 4. 37% 4% AAACorp LIBOR F.I BBBCorp LIBOR+0.6% LIBOR Options, Futures, and Other Derivatives,... Copyright © John C Hull 2012 23 Valuation Using Bonds (page 161) Time Bfix cash flow Bfl cash flow Disc factor PV Bfix PV Bfl 0.25 4.0 105.100 0. 975 3 3.901 102.505 0 .75 4.0 0.9243 3.6 97 1.25 104.0 0. 871 5 90.640 Total 98.238 102.505 Swap value = 98.238 − 102.505 = −4.2 67 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C Hull 2012 24 Valuation in Terms of FRAs Each exchange of payments... 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 33 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,... per dollar Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C Hull 2012 35 Valuation in Terms of Bonds (Table 7. 9, page 169) Time Cash Flows ($) PV ($) Cash flows (yen) PV (yen) 1 0.8 0 .73 11 60 57. 65 2 0.8 0.6682 60 55.39 3 0.8 0.61 07 60 53.22 3 10.0 7. 6338 1,200 1,064.30 Total 9.6439 1,230.55 Value of Swap = 1230.55/110 − 9.6439 = 1.5430 Options, Futures, and Other Derivatives,... 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 30 The Cash Flows (Table 7. 7, page 166) Date Dollar Cash Flows (millions) Sterling cash flow (millions) Feb 1, 2011 -18.0 +10.0 Feb 1, 2012 +1.08 −0.50 Feb 1, 2012 +1.08 −0.50 Feb 1, 2014 +1.08 −0.50 Feb 1, 2015 +1.08 −0.50 Feb... 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 12 The Comparative Advantage Argument (Table 7. 4, page 156) • AAACorp wants to... into an OIS swap to convert this to the 3month 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 27 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... 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 17 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... can be used to bootstrap the LIBOR (or LIBOR/swap) zero curve Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C Hull 2012 18 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) 2.5e −0.04×0.5 + 2.5e −0.045×1.0 + 2.5e −0.048×1.5 . Chapter 7 Swaps Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 1 Nature of Swaps A swap is an agreement to exchange. 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. Involved (Figure 7. 7, page 1 57) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 15 AAACorp F.I . BBBCorp 4% LIBOR LIBOR LIBOR+0.6% 4.33% 4. 37% Criticism of