Lecture_5Swaps(衍生金融工具-人民银行研究院,何佳).ppt

Lecture 5 Swaps Aswapisanagreementbetweentwoormorepartiestoexchangesetsofcashflowsoveraperiodinthefuture Thepartiesthatagreetotheswapareknownascounter parties Thecashflowsthatthecounter partiesmakearegenerallytiredtothevalueofdebtinstrumentsortothevalueofforeigncurrencies Therefore thetwobasickindsofswapsareinterestrateswapsandcurrencyswaps TheSwapsMarket Swapsarecustomtailoredtotheneedsofthecounter parties Theswapsmarkethasvirtuallynogovernmentregulation Defaultrisk ValueofOutstandingSwaps BillionofPrincipal PlainVanillaSwapsInterestrateswapsCurrencySwaps Motivationsforswaps Commercialneeds Asanexampleofprimecandidateforaninterestrateswaps consideratypicalsavingsandloanassociation Savingsandloanassociationsacceptdepositsandlendthosefundsforlong termmortgages Becausedepositorscanwithdrawtheirfundsonshotnoticedepositratesmustadjusttochanginginterestrateconditions MostmortgagorswishtoborrowatafixedrateforalongtimeinUS Isthereanyinterestrisk Canswapscontracthelp Comparativeadvantage Inmanysituations onefirmmayhavebetteraccesstothecapitalmarketthananotherfirm Forexample aU S firmmaybeabletoborroweasilyintheU S butitmightnothavesuchfavorableaccesstothecapitalmarketinGermany Similarly aGermanfirmmayhavegoodborrowingopportunitiesdomesticallybutpooropportunitiesintheStates InterestRateSwaps TwoPartiesexchangeperiodicinterestpaymentsoveraperiod Typically oneparty spaymentsarebasedonafixedratewhereasitscounterparty spaymentsarebasedonafloatingrate Interestpaymentsarecomputedusinganotionalprincipal Example BothAandBneedtoborrow 100millionfor3years Thefinancingratesfacingthemaresummarizedasfollows ItiscomparativelycheaperforAtousethefloatingratedebt ForB fixedrateborrowingwillbecheaper Why 1 IfAdesiresthefloatingratedebtandBprefersthefixedratedebt thereisnoneedforthemtoengageinaswap 2 IfAdesiresthefixedratedebtandBprefersthefloatingratedebt AshouldstillborrowfloatingrateandBborrowfixedrate Theycanthenenteraswaptobetterbothparties 6 3 Company Company LIBOR A B6 3 0 85 LIBORa CompanyA Borrowsfloatingrateandenterstheaboveswap b CompanyB Borrowsfixedrateandenterstheaboveswap TheresultsCompanyA Onasemiannualbasis receives LIBOR 6 3 50mfromtheswap andpaysthefloatingratedebtservice LIBOR 0 85 50m Thenetpaymentis7 15 50m whichislessthan7 5 50m CompanyB Onasemiannualbasis receives 6 3 LIBOR 50mfromtheswap andpaysthefixedratedebtservice6 3 50m ThenetpaymentisLIBOR 50m whichislessthan LIBOR 0 25 50m Note Swapratereferstofixedrateswap Swapsthroughanintermediary6 4 6 25 Company Swap Company LIBOR A Dealer B6 3 0 85 LIBORLIBOR TheresultsCompanyA Onasemiannualbasis receives LIBOR 6 4 50mfromtheswap andpaysthefloatingratedebtservice LIBOR 0 85 50m Thenetpaymentis7 25 50m whichislessthan7 5 50m CompanyB Onasemiannualbasis receives 6 25 LIBOR 50mfromtheswap andpaysthefixedratedebtservice6 3 50m Thenetpaymentis LIBOR 0 05 50m whichislessthan LIBOR 0 25 50m Swapdealer Makes 6 4 6 25 50m 75 000 PricingSchedulesThefixedrateintheswapisquotedasacertainnumberofbasispointsabovetheT noteyield Table Indicationpricingforinterestrateswapsat1 30pm NewYorkTimeonMay11 1995 Netting interestpaymentsaremadebyonecounter partytotheotherafternettingoutthefixedandfloatinginterestpayments Assume Notionalamount Q fixedratepayment k Floatingrateusedintimet Rt 1 LIBORattimet 1 NETpaymentattimet Fixedrateattimet Fixed ratepayerreceives Rt 1Q k andfloating ratepayerreceives k Rt 1Q Thefollowingisapossiblescenarioofcashflowsforthefixed ratepayerundera 100million 5 yearswapat5 6 withsemiannualcashflowexchanges Whatistheimplicationofnettingaboutcredit defaultrisk Pricinginterestrateswaps Setthefixedrateofswapsothattheswaphasazerovalueatthetimeofinitiation Thisiscalledparswap Supposethatpaymentdatesaret1 t2 tn Thevalueofaswapattimet Vt fromtheperspectiveofthefloating ratepayer Vt B1t B2t B1t valueoffixed ratebondunderlyingtheswapwhenti t ti 1 B1t nj i 1ke r t tj tj t Qe r t tn tn t B2t valueoffloating ratebondunderlyingtheswap Atthefloatingrateresettingday i e t t1 t2 tn immediatelyafterthepaymentismade B2t Q Why Inbetween i e ti t ti 1 B2t Q k exp r t ti 1 ti 1 t wherek isthefloatingratepaymentattimeti 1alreadyknownattimet Determiningtheswaprateattime0 V0 k ni 1kexp r 0 tj tj Qexp r 0 tn tn Q 0 Q ni 1kexp r 0 tj tj Qexp r 0 tn tn Thatis setanappropriatecouponratesothatthebondispricedatpar Example Counter partyAinathree yearswappays6 monthLIBORandreceivesafixedrateonanotionalprincipalof 100million Theswaphas1 25yearstomaturity Theswapratewasdeterminedoneyearandnine monthago Atthetimeofinitiation 3 year8 bondwaspricedatpar TheLIBORatthelastpaymentdatewas10 2 semiannualcompounding Discountratesfor3 month 9 monthand15 monthmaturitiesare10 10 5 and11 respectively Thefixedrate 8 perannum B1 4e 0 25 0 1 4e 0 75 0 105 104e1 25 0 11 98 24 B2 100 5 1 e 0 25 0 1 102 51 V 98 24 102 51 4 27 million toAand4 27millionB Portfolioofforwards Aswap semiannualinterestexchanges canbeviewedasasequenceofforwardswithmaturities t1 t2 tnwithacommonforwardprice DefinePt asthetime tvalueofzero couponbondmaturingattime for 1facevalue Forti t ti 1 1 Atti 1 k k evaluatedatt k k Pt ti 1 2 Atti 2 k 0 5R ti 1 Q evaluatedatt PVt t i 2 k 0 5R ti 1 Q k 0 5R ti 1 ti 2 Q exp r t ti 2 ti 2 t whereR ti 1 ti 2 istheforwardrate semiannualcompounding attimetover ti 1 ti 2 Why 3 Similarlyforti 3 ti 4 4 Thetotalvalueoftheswapattimet k k exp r t ti 1 ti 1 t nj i 1 k 0 5R tj tj 1 Q exp r t tj 1 tj 1 t Example ContinuethepreviousexampleR 3m 9m 2 exp 0 5 0 75 0 105 0 25 0 1 0 75 0 25 1 11 04 R 9m 15m 2 exp 0 5 1 25 0 11 0 75 0 105 1 25 0 75 1 12 10 V 4 5 1 e 0 1 0 25 4 0 5 0 1104 100 e 0 105 0 75 4 0 5 0 121 100 e 0 11 1 25 4 27 Variationofinterestrateswaps Indexamortizedswaps thenotionalprincipalisreducedoverthelifeoftheswap Constantyieldswaps bothpartsarefloating Forexample onepartmaybelinkedtotheyieldonthe30 yearT bondandtheothermaybelinkedonthe10 yearT note Rate cappedswaps floatingrateiscapped PutableandCallableswaps oneorbothcounter partieshavetherighttocanceltheswapatcertaintimeswithoutadditionalcosts Forwardswaps theswaprateissetbuttheswapdoesnotcommenceuntilalaterdate Currencyswaps Twopartiesexchangeperiodicinterestpaymentsandprincipalsintwocurrencies Example BothAandBneedtoborrowUSD50million orDEMequivalentof84millionbasedon1 68DEM USD forthree year Thefinancingratesfacingthemaresummarizedasfollows ItiscomparativelycheaperforAtousetheDEMdebt ForB USDborrowingwillbecheaper Why 1 IfAdesirestheDEMdebtandBpreferstheUSDdebt thereisnoneedforthemtoengageinaswap 2 IfAdesirestheUSDdebtandBpreferstheDEMdebt AshouldstillborrowDEMandBborrowUSD Theycanenteracurrencyswaptobetterbothparties Interestpaymentflows6 9 USDCompany Company 4 2 DEMA B6 9 USD3 9 DEM b Initialprincipalflow84mDEMCompany Company 84DEMA B50mUSD50mUSD b Terminalprincipalflow84mDEMCompany Company 84DEMA B50mUSD50mUSDb CompanyA BorrowsDEMdebtandenterstheaboveswap c CompanyB BorrowsUSDdebtandenterstheaboveswap d Theresults 1 CompanyA Beginning ExchangeDEM84millionforUSD50million afairtransactionatthecurrentexchangerate DEM168 USD1 In between Onasemiannualbasis receivesDEM4 2m 3 9 andpaysUSD25m 6 9 duetotheswap andpaysDEM42m 4 2 duetoitsDEMdebt ThenetpaymentisUSD25m 6 9 DEM42m 0 3 comparingtoUSD25m 7 5 End ExchangeUSD50mforDEM84m notafairexchangeattheprevailingexchangerate 2 CompanyB Beginning ExchangeUSD50millionforDEM84million afairtransactionatthecurrentexchangerate DEM168 USD1 In between Onasemiannualbasis receivesUSD25m 6 9 andpaysDEM4 2m 3 9 duetotheswap andpaysUSD25m 6 9 duetoitsUSDdebt ThenetpaymentisDEM42m 3 9 whichislessthanDEM42m 4 0 End ExchangeDEM84mforUSD50m notafairexchangeattheprevailingexchangerate Swapthroughanintermediary7 4 6 9 Company Swap Company 4 2 DMA Dealer B9 USD4 2 DM3 9 DM Theresults1 CompanyA Beginning ExchangeDEM84millionforUSD50million afairtransactionatthecurrentexchangerate DEM168 USD1 In between Onasemiannualbasis receivesDEM4 2m 4 2 andpaysUSD25m 7 4 duetotheswap andpaysDEM42m 4 2 duetoitsDEMdebt ThenetpaymentisUSD25m 7 4 whichislessthanUSD25m 7 5 End ExchangeUSD50mforDEM84m notafairexchangeattheprevailingexchangerate 2 CompanyB Beginning ExchangeUSD50millionforDEM84million afairtransactionatthecurrentexchangerate DEM168 USD1 In between Onasemiannualbasis receivesUSD25m 6 9 andpaysDEM4 2m 3 9 duetotheswap andpaysUSD25m 6 9 duetoitsUSDdebt ThenetpaymentisDEM42m 3 9 whichislessthanDEM42m 4 0 End ExchangeDEM84mforUSD50m notafairexchangeattheprevailingexchangerate3 Swapdealer Onasemiannualbasis earnsUSD 7 4 6 9 25mandlossDEM 4 2 3 9 2m PricingcurrencyswapsSetthetwofixedratesofaswapsothattheswaphasazerovalueatthetimeofinitiation Supposethatpaymentdatesaret1 t2 tn Thevalueofaswapattimet Vt basedonthedomesticcurrency Vt StBFt BDtSt exchangerate domesticpriceofoneunitforeigncurrency attimet BDt valueofdomesticfixed ratebondunderlyingtheswapwhenti t ti 1 BDt nj i 1kDe rd t tj tj t QDe rd t tn tn t wherekDisthepaymentinthedomesticcurrency QDistheprincipalamountinthedomesticcurrency BFt valueofforeignfixed ratebondunderlyingtheswap measuredintheforeigncurrency whenti t ti 1 BFt nj i 1kFe rf t tj tj t QFe rf t tn tn t wherekFisthepaymentintheforeigncurrency QFistheprincipalamountintheforeigncurrency Determiningthefixedrateattime0SetkDandkFsuchthatQD nj 1kDe rd 0 tj tj QDe rd 0 tn tnQF nj i 1kFe rf 0 tj tj QFe rf 0 tn tnThisimpliesV0 S0BF0 BD0 S0QF QD 0Thatis settwoappropriatecouponratessothatbothbondsarepricedatpar Example Counter partyAinathree yearswappaysafixedrateonaprincipalofUSD100mandreceivesafixedrateonaprincipalofDEM168m Thepaymentsaremadeonasemiannualbasis Theprincipalsweresetaccordingtotheexchangerateatthetimeofinitiation Thecurrentexchangerateis1 52DEM USD Theswaphas1 25yearstomaturity Theswapratewasdeterminedoneyearandnine monthago Atthetimeofinitiation 3 year7 2 USDbondwaspricedatpar and3 year4 2 DEMbondwasalsopricedatpar ThecurrenttermstructureforUSDandDEMarebothflatat8 and4 respectively BD 3 6e 0 25 0 08 3 6e 0 75 0 08 103 6e 1 25 0 08 100 66mBF 1 68 2 1e 0 25 0 04 2 1e 0 75 0 04 102 1e 1 25 0 04 170 08mToA V 1708 1 52 100 66 USD11 23mandtoB V USD11 23mPortfolioofforwards Acurrencyswapcanbeviewedasasequenceofforwardswithmaturities t1 t2 tnwithacommonforwardprice Forti t ti 1 1 Atti 1 St i 1 kF kD evaluatedatt ithasavalueequalto Ft ti 1 kF kD exp rDt ti 1 ti 1 t 2 Atti 2 St i 2 kF kD evaluatedatt ithasavalueequalto Ft ti 2 kF kD exp rDt ti 2 ti 2 t 3 Similarlyforti 3 ti 4 ti n 14 Atti n St i n kF QF kD QD evaluatedatt ithasavalueequalto Ft ti n kF QF kD QD exp rDt ti n ti n t 5 Thetotalvalueoftheswapattimetisthesumofalltheterms Example Continuethepreviousexample F 0 25 1 1 52exp 0 08 0 04 0 25 0 6645 F 0 75 1 1 52exp 0 08 0 04 0 75 0 6679 F 1 25 1 1 52exp 0 08 0 04 1 25 0 6916V 0 6645 2 1 1 68 3 6 e 0 08 0 25 0 6779 2 1 1 68 3 6 e0 08 0 75 0 6916 102 1 1 68 103 6 e 0 08 1 25 1 2308 1 1380 13 5986 USD11 2298m Equityswaps Twopartiesexchangeperiodicpaymentsoverafixedduration Typically oneparty spaymentsarebasedonastockindexreturnwhereasitscounter party spaymentsarebasedonabenchmark floatingrate Paymentsarecomputedusinganotionalprincipal Example Notionalprincipal 100m Counter partyAreceives3 monthLIBORandpaysS P500indexreturnplusaswapspreadof 0 1 S P500return 0 1 Company CompanyA BLIBOR ThevalueofequityswapThevalueofthisequityswapwaszeroonJan2 thetimeofinitiation ThesameistrueforApril2 July2 Oct2andJan2immediatelyafterthepaymentismade Why Thevalueofthisequityswapon sayMarch1 willnotbezero however AssumethatthefuturespriceofS P500indexfuturescontractmaturinginAprilcontractfinishedat460 1onthatday ThediscountrateonMarch1forthematurityofApril2is9 1 WhatisthevalueofswaptotheLIBORpayer TheLIBORpaymentonApril2isknowntobe225 000 Itspresentvalueis225 000 exp 0 091 32 365 223 212 ThereceiptonApril2subjecttotheS P500indexperformanceis IA2 IJ2 IJ2 0 1 100m Itspresentvalueis 460 1 469 75 0 001 469 75 100m 469 75 exp 0 091 32 365 2 137 166 Thetotalvalue 223 212 2 137 166 2 360 378 Commodityswaps Inatypicalcommodityswap onecounter partymakesperiodicpaymentstothesecondcounter partyatafixedpriceperunitforagivennotionalquantityofsomecommodity Thesecondcounter partypaysthefirstcounter partyafloatingpriceforagivennotionalquantityofsomecommodity Thecommoditiesareusuallythesame Thefloatingpriceisusuallycalculatedasanaverageprice CreditDefaultSwaps Willbediscussedinthesectionofcreditrisk Procter Gamble BankersTrustLeveragedSwap 1ThestoryOnNovember2 1993 P GandBTenteredafiveyear semiannualsettlement 200millionnotionalprincipalinterestrateswapcontractknownasthe 5 30 swap BTpaysafixedrateof5 30 andP Gpaysafloatingratedependsonthirty daycommercialpaper CP dailyaverageratelessthen75basispoints plussomespread Thekeyfactorsintheagreementarethespreadandthe75basispoints aplainvanillaswapwouldhavebeen5 3 versustheCPdailyaveragerateflat TheswapwasscheduledtolockinonMay4 1994 Becausethespreadonthelock in datewas2 750basispoints P Gexperiencedsignificantlossesandfiledalawsuit Anout of courtsettlementwasreachedinMay1996 BTagreedtoabsorb 157million 2TheP G BTleveragedswapTerm 5yearFrequency SemiannualpaymentsFixedratepayer BankersTrustat5 3 Floatingpayer P Gat30 daycommercialpaperdailyaverageratesless75Basispointsplusaspread 3ThespreadThespreadiszeroforthefirst6 monthsettlementperiod andthenwouldbefixedfortheremainingninesemiannualperiods dependingonTreasuryyieldsandpricesonthefirstsettlementdate May4 1994 accordingtotheformula Spread max 0 98 5 5 yearCMT 5 78 30 yearTYSPrice 100 5 yearCMT istheyieldonthe5 yearconstant maturityTreasurynote The30 yearTreasury TSY bondpriceisthemidpointofthebidandofferpricesonthe6 25 T bondmaturinginAugust2023 notincludingaccruedinterest ThespreadonNovember2 1993waszerobecause 98 5 5 02 5 78 102 57811 100 0 1703 ThespreadonMay4 1994wasMax 0 98 5 6 71 5 78 86 84375 100 0 2750Thusinreturnforreceivingafixedrateof5 3 theP Gwouldhavebeenobligatedtopaythe30 dayCPdailyaveragerateplus26 75 27 50 0 75 forthenextfourandonehalfyearsonthe 200millionswapiftheformulahadnotbeenamendedpriortoMay1994 4TheamendmentTheswapwasamendedinJanuary1994tomovethedeterminationdateofthespreadfromMay4 1994toMay19 1994inexchangefor13basispointsimprovementinthefloatingratesideoftheswap i e 75basispointshasbeenchangedto88basispoints Interestingly thereisaFederalOpenMarketCommitteemeetingscheduledonMay17 twodaysbeforethenewspreaddeterminationdate P GdecidedinMarch1994tolockinthespread insteadofwaitingforMay19determination Thiswasdoneinthreestageswith 50milliononMarch10 50onMarch14 andtheremaining 100milliononMarch29Allinall thespreadwaslockedinat15 Thelosscanbeestimatedatabout 106 541millioninpresentvalueterms 5WascorporatetreasurygroupatP Gabletoascertaintheriskitwasbeatinguponenteringthetransaction Alossofover 100milliononaswapwithanotionalprincipalof 200millionisextraordinary arealtestamenttothepowerofleverage Thespreadformulacanbesimplifiedto Spread max 0 0 170415 5 year CMT 0 01 30 year TSYprice Spread 0 170415 CMT 0 01 TSYPrice Using6 15 asthesix monthforwardyieldinNov 1993ontheT bondonAugust1 2023 wehave TSYPrice 13 6442 YLD Spread 0 170415 CMT 0 136442 YLD Aparallelshiftintermstructure yieldcurve willcausethespreadtomovebyafactorof0 306857 Onebasispointincreaseraisesthespreadby30 6857basispoints averybigleverage Amoveofonly58basispointsfromNovember2 1993curvewouldbeabletocoverthe75basispointcushion Eachadditionalbasispointmovedrivesthemarketvalueoftheleverageswapdownbyabout 2 389million Inaddition P GisfacingboththeCPrateandthespread Bothcomponentsarepositivelyrelatedtotheinterestrtelevel P Ggethittwiceiftheinterestratemovestogether Thisswapis therefore poorlystructure