华东师范大学：《金融工程》英文版 Chapter 5 Swaps (互换)

Swaps (互换) Chapter 5 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.1 Swaps (互换) Chapter 5

5.2 Nature of Swaps A swap is an agreement to exchange cash flows(现金流) at specified future times according to certain specified rules Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.2 Nature of Swaps • A swap is an agreement to exchange cash flows (现金流) at specified future times according to certain specified rules

53 Terminology LIBOR the london inter Bank offer rate It is the rate of interest offered by banks on deposits from other banks in Eurocurrency markets Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.3 Terminology • LIBOR the London InterBank Offer Rate It is the rate of interest offered by banks on deposits from other banks in Eurocurrency markets

5.4 An Example of a"Plain vanilla Interest Rate Swap(大众型利率互换) An agreement by"Company B"to RECEIVE 6-month libor and PAY a fixed rate of 5% pa every 6 months for 3 years on a notional principal of $100 million Next slide illustrates cash flows, Where POSIT/VE flows are revenues(inflows) and NEGATIVE flows are expenses(outflows) Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.4 An Example of a “Plain Vanilla” Interest Rate Swap(大众型利率互换) • An agreement by “Company B” to RECEIVE 6-month LIBOR and PAY a fixed rate of 5% pa every 6 months for 3 years on a notional principal of $100 million • Next slide illustrates cash flows, where POSITIVE flows are revenues (inflows) and NEGATIVE flows are expenses (outflows)

Cash Flows to Company B 5.5 (See Table 5.1, page 123) -----Millions of dollars LIBOR FLOATING FIXED Date Rate Cash flow Cash Flow Cash Flow Mar.1,199942% Sept.1,19994.8% +2.10-2.50 0.40 Mar.1.20005.3% +2.40 2.50 0.10 Sept.1,20005.5% +2.65 2.50 +0.15 Mar.1,200156% 2.75 2.50 +0.25 Sept.1,200159% +2.80 -2.50 +0.30 Mar.1,.20026.4% +2.95 2.50 +0.45 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.5 ---------Millions of Dollars--------- LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1999 4.2% Sept. 1, 1999 4.8% +2.10 –2.50 –0.40 Mar.1, 2000 5.3% +2.40 –2.50 –0.10 Sept. 1, 2000 5.5% +2.65 –2.50 +0.15 Mar.1, 2001 5.6% +2.75 –2.50 +0.25 Sept. 1, 2001 5.9% +2.80 –2.50 +0.30 Mar.1, 2002 6.4% +2.95 –2.50 +0.45 Cash Flows to Company B (See Table 5.1, page 123)

5.6 More on table 5.1 The floating- rate payments are calculated using the six-month LIBOR rate prevailing six month before the payment date The principle is only used for the calculation of interest payments. However, the principle itself is not exchanged-Meaning for Notional principle The swap can be regarded as the exchange of a fixed-rate bond for a float -rate bond Company B(A)is long(short)a floating-rate bond and short (long)a fixed-rate bond Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.6 More on Table 5.1 • The floating-rate payments are calculated using the six-month LIBOR rate prevailing six month before the payment date • The principle is only used for the calculation of interest payments. However, the principle itself is not exchanged—Meaning for “Notional principle” • The swap can be regarded as the exchange of a fixed-rate bond for a float-rate bond. Company B (A) is long (short) a floating-rate bond and short (long) a fixed-rate bond

5.7 Typical Uses of an Interest Rate Swap Converting a liability Converting an investment from a from a FIXED rate liability to a FXED rate investment to a 户 LOATING rate liability FLOATING rate investment FLOATING rate liability FLOATING rate investment to a F XED rate liability to a fXed rate investment Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.7 Typical Uses of an Interest Rate Swap • Converting a liability from a – FIXED rate liability to a FLOATING rate liability – FLOATING rate liability to a FIXED rate liability • Converting an investment from a – FIXED rate investment to a FLOATING rate investment – FLOATING rate investment to a FIXED rate investment

58 Transforming a Floating-rate Loan to a Fixed-rate Consider a 3-year swap initialized on March 1, 2000 Where Company B agrees to pay Company A 5%pa on $100 million Company a agrees to pay Company B 6-mth LIBOR on $100 million Suppose Company B has arranged to borrow $100 million LIBOR+ 80bp 5% Company C ompany 5.2% LIBOR B LIBOR+0.8% Note: 1 basis point(bp )= one-hundredth of 1%0 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.8 Transforming a Floating-rate Loan to a Fixed-rate • Consider a 3-year swap initialized on March 1, 2000 where Company B agrees to pay Company A 5%pa on $100 million Company A agrees to pay Company B 6-mth LIBOR on $100 million • Suppose Company B has arranged to borrow $100 million LIBOR + 80bp Company B Company A 5% 5.2% LIBOR LIBOR+0.8% Note: 1 basis point (bp) = one-hundredth of 1%

5.9 Transforming a Floating-rate Loan to a Fixed-rate (continued) After Company B has entered into the swap, they have 3 sets of cash flows Pays LiBOR plus 0.8% to outside lenders 2. Receives LIBOR from Company a in the swap 3. Pays 5% to Company A in the Swap In essence. b has transformed its variable rate borrowing at LIBOR 80bp to a fixed rate of 5.8% Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.9 Transforming a Floating-rate Loan to a Fixed-rate (continued) • After Company B has entered into the swap, they have 3 sets of cash flows 1. Pays LIBOR plus 0.8% to outside lenders 2. Receives LIBOR from Company A in the swap 3. Pays 5% to Company A in the Swap • In essence, B has transformed its variable rate borrowing at LIBOR + 80bp to a fixed rate of 5.8%

5.10 a and B transform a liability (Figure 5.2, page 125) 5.2 A B LIBOR+0.8% LIBOR Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University

Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 5.10 A and B Transform a Liability (Figure 5.2, page 125) A B LIBOR 5% LIBOR+0.8% 5.2%