Ch05_Swaps(互换)(金融工程学,华东师大).ppt
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1、Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.1,Swaps(互换)Chapter 5,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.2,Nature of Swaps,A swap is an agreement to exchange cash f
2、lows(现金流)at specified future times according to certain specified rules,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.3,Terminology,LIBOR the London InterBank Offer RateIt is the rate of interest offered by banks on deposits from other
3、banks in Eurocurrency markets,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang 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”toRECEIVE 6-month LIBOR andPAY a fixed rate of 5%paevery 6 months for 3 ye
4、ars on a notional principal of$100 millionNext slide illustrates cash flows,wherePOSITIVE flows are revenues(inflows)andNEGATIVE flows are expenses(outflows),Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.5,Cash Flows to Company B(See Ta
5、ble 5.1,page 123),Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang 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 dateThe principle is only used for the
6、calculation of interest payments.However,the principle itself is not exchangedMeaning 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
7、Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.7,Typical Uses of anInterest Rate Swap,Converting a liabilityfrom a FIXED rate liability to aFLOATING rate liabilityFLOATING rate liabilityto a FIXED rate liability,Converting an investmentfrom a FIXED rate investmen
8、t to aFLOATING rate investment FLOATING rate investment to a FIXED rate investment,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang 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 wher
9、eCompany B agrees to pay Company A 5%pa on$100 millionCompany A agrees to pay Company B 6-mth LIBOR on$100 millionSuppose Company B has arranged to borrow$100 million LIBOR+80bp,LIBOR+0.8%,5.2%,Note:1 basis point(bp)=one-hundredth of 1%,Options,Futures,and Other Derivatives,4th edition 2000 by John
10、C.HullTang 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 Swa
11、pIn 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.HullTang 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%,Options,Fut
12、ures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.11,Financial Institution is Involved(Figure 5.4,page 126),A,F.I.,B,LIBOR,LIBOR,LIBOR+0.8%,4.985%,5.015%,5.2%,“Plain vanilla”fixed-for-float swaps on US interest rates are usually structured so that the
13、 financial institutions earns 3 to 4 basis points on a pair of offsetting transactions,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.12,A and B Transform an Asset(Figure 5.3,page 125),A,B,LIBOR,5%,LIBOR-0.25%,4.7%,Options,Futures,and Ot
14、her Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.13,Financial Institution is Involved(See Figure 5.5,page 126),A,F.I.,B,LIBOR,LIBOR,4.7%,5.015%,4.985%,LIBOR-0.25%,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal U
15、niversity,5.14,The Comparative Advantage Argument(Table 5.4,page 129),Company A wants to borrow floatingCompany B wants to borrow fixed,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.15,The Comparative Advantage(continued),One possible s
16、wap isCompany A has 3 sets of cash flows 1.Pays 10%pa to outside lenders 2.Receives 9.95%pa from B Pays LIBOR+0.05%3.Pays LIBOR to B a 25bp gainCompany B has 3 sets of cash flows 1.Pays LIBOR+1.00%pa to outside lenders 2.Receives LIBOR from A Pays 10.95%pa 3.Pays 9.95%to A a 25bp gain,Options,Future
17、s,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.16,The Swap(Figure 5.6,page 130),A,B,LIBOR,LIBOR+1%,9.95%,10%,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.17,The Swap when a Financial Ins
18、titution is Involved(Figure 5.7,page 130),A,F.I.,B,10%,LIBOR,LIBOR,LIBOR+1%,9.93%,9.97%,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.18,Total Gain from anInterest Rate Swap,The total gain from an interest rate swap is always|a-b|wherea
19、 is the difference between the interest rates in thefixed-rate market for the two parties,andb is the difference between the interest rates in thefloating-rate market for the two partiesIn this example a=1.20%and b=0.70%,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yinca
20、i,Shanghai Normal University,5.19,Criticism of the Comparative Advantage Argument,The 10.0%and 11.2%rates available to A and B in fixed rate markets are 5-year ratesThe LIBOR+0.3%and LIBOR+1%rates available in the floating rate market are six-month ratesBs fixed rate depends on the spread above LIBO
21、R it borrows at in the future,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.20,Valuation of an Interest Rate Swap,Interest rate swaps can be valued as the difference between-the value of a fixed-rate bond&-the value of a floating-rate b
22、ondAlternatively,they can be valued as a portfolio of forward rate agreements(FRAs),Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.21,Valuation of an Interest Rate Swap as a Package of Bonds,The fixed rate bond is valued in the usual way
23、(page 132)The floating rate bond is valued by noting that it is worth par immediately after the next payment date(page 132),Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.22,Valuation of an Interest Rate Swap as a Package of Bonds(contin
24、ued),Define Vswap:value of the swap to the financial institution Bfix:value of the fixed-rate bond underlying the swap Bfl:value of the floating-rate bond underlying the swap L:notional principal in a swap agreement ti:time when the ith payments are exchanged ri:LIBOR zero rate for a maturity tiThen
25、,Vswap=Bfix-Bfl and if k is the fixed-rate coupon and k*is the floating,Options,Futures,and Other Derivatives,4th edition 2000 by John C.HullTang Yincai,Shanghai Normal University,5.23,Example of an Interest Rate Swap Valued as a Package of Bonds,Suppose,that you agreed to pay 6-month LIBOR and rece
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