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EDUCATION IN ECONOMICS SERIES

NO. 7

SWAP TRANSACTIONS

CENTRAL BANK OF NIGERIARESEARCH DEPARTMENT

2016

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Table of Contents

1.0 Introduction ............................................................................ 1

2.0 Definition and Concepts in Swap Transactions .................. 22.1 DefinitionofSwap .................................................................. 2

2.1.1 FeaturesofSwapTransactions ............................................. 32.2 ConceptsinSwapTransactions ........................................... 4

3.0 Why Swap? ............................................................................. 7

4.0 Types of Swap Contracts ....................................................... 84.1 InterestRateSwap ................................................................. 8

4.1.1VariantsofInterestRateSwap .............................................. 84.2 CurrencySwap ..................................................................... 12

4.2.1VariantsofCurrencySwap .................................................. 144.3 CommoditySwap ................................................................ 18

4.3.1VariantsofCommoditySwap ............................................. 194.4 EquitySwap ........................................................................... 21

4.4.1 VariantsoftheBasicEquitySwap ..................................... 22

5.0 Swap Pricing and valuation ................................................ 255.1. PricingandValuationofOtherSwaps .............................. 27

5.1.1CurrencySwap ..................................................................... 27

5.1.2CommoditySwap ............................................................... 28

6.0 Risks Associated with Swap ................................................30FurtherReading .............................................................................. 32

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List of Figures

Figure1:GraphicalIllustrationofScenario1 .............................. 11


Figure3:CurrencySwapCashFlow ............................................ 14

Figure4:Fixed-for-FixedCurrencySwap .................................. 16

Figure5:Fixed-for-FloatingCurrencySwap ................................ 17

Figure6:Floating-for-FloatingCurrencySwap ........................... 18



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SWAP TRANSACTIONS1

1.0 IntroductionThe concept of Swap is quite simple though oftenmisunderstood by many. It is as simple as exchanging(swapping) items or cash flows between two parties(individuals or institutions). Basically, swap refers to acontractinwhichtwoindividuals(orcounterparties)agreeto either exchange cash flows (that are linked to eitherinterest rates, commodity prices, currencies or equities)withinaspecifiedperiod.ThisEducationalSeriesattemptstodiscusstheconceptofswaptransactionsandtheirtypes;itspricingandvaluationandtherisksassociatedwiththem.Italsocontainsillustrationsandtablestoenhancereaders’understandingofthesubjectmatter.

The series is subdivided into six (6) sections. Following theintroductory section, section twocontainsdefinitionsandconceptsofSwap.Sectionthreediscussesthereasonsforswaptransactions,whilesectionfourexaminesthedifferenttypesofswapcontracts.Sectionfivecontainsthepricingandvaluationofswaps;whileSectionsixdiscussestherisksassociatedwithswaptransactions.

1 Thecontributorstothisseriesare:Yakub,MaajiUmar;Ikenna-Ononugbo,AzumiAwawu;Nwosu,ChiomaPeace;Elisha,JosiahDassaandOpiah,DominicChioma

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2.0 Definition and Concepts in Swap Transactions

2.1 Definition of SwapAswaptransactionisanagreementbetweentwopartiesto exchange sequences of cash flows for a set period.Usually, at the time the agreement is initiated, the cashflowisdeterminedbyuncertainvariables,suchasinterestrate, foreign exchange rate, equity price or commodityprice.Swaptransactionshavetwolegs:thefixedandthevariablelegs.Theholderofthefixedlegoftheswapmakespaymentsbasedonafixedinterestrate.Ontheotherhand,theholderof thevariable legmakespaymentbasedonavariable interest rate that isusuallymarket-determined.The London Interbank Offered Rate (LIBOR)2 is a typicalexampleofmarket-basedrate.

Theoriginofswapcanbetracedtothe1970swheninvestorsin the United Kingdom used back-to-back loans 3 to by-passtheBritishgovernment’spolicyonforeignexchangecontrolsandcapitalrestrictions.Aback-to-backloanallowscounterparties to have access to the foreign exchangeof another country without paying any foreign currencytaxes. The major shortcoming of the back-to-back loanagreement is thateach loanhasa separateagreement

2 Thisservesasthefirststepincalculatinginterestratesonvariousshorttermloansthroughoutthe world. It is an interbank rate that is widely used for swap transactions globally.

3 Back-to-backloansallowstwocounterpartiesindifferentcountriestoexchangeloansinthecurrencyoftheirindividualcountries

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such that one party could still be obligated to continuepaymentseveniftheotherpartydefaults.Tomitigatethisshortcoming,intheearly1980stheback-to-backloanwasstructured intoa formalised swapagreement referred toas currency swap. The first formalised swap agreementwas the currency swap between International BusinessMachines(IBM)andtheWorldBankin1981.Inlate1981,swapwasextendedtocreditmarketinstrumentsthatweredenominated in the samecurrency (PlainVanilla interestrate swap). Other forms of swap contracts (commodity,equity, etc.) haveemergedover the yearsowing to thesophisticationoftheglobalfinancialenvironment.

2.1.1 Features of Swap Transactions

Atypicalswaptransactionhasthefollowingcharacteristics:

• It is a bilateral agreement between individuals orentitiestoexchangecashflows(payments)overaspecifiedperiodandrate;

• Itmayinvolveanintermediaryora‘swapbank’whobringstogetherthecounterpartiesforapremium;

• The principal or notional amount may be re-exchangedattheendoftheswapcontract;

• They are traditionally over-the-counter (OTC)financialderivatives;and

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• Payment intervals in swapvarydependingon theterm structure of the swap agreement (quarterly,semi-annuallyorannually).

2.2 Concepts in Swap Transactions• Counterparties –Thesearetheparties(individualsor

entities)involvedintheswaptransaction.

• Notional/Principal Amount:Thisistheamountorvaluethat the underlying price (interest rate, exchangerate,equityorcommodityprice)isappliedontogetthestreamsoffuturepaymentsbybothpartiesinaswapagreement;

• Fixed Rate-Thisdeterminestheratethatwillbeusedto calculate the amount to be paid by the fixedpayer.Thisstreamofpaymentsisknownasthefixedlegoftheexchange;

• Fixed Payer –This is thepartyholdingthefixed-leginaswaptransaction.Hepaysthefixedratetotheotherparty;

• Floating Rate - Thisdefines the rate(coupon)usedforsettingthefloatingpaymentobligation.Themostcommonly used rate is the LIBOR or some stockindex.

• Swap Rate –Thisistherateofthefixedrateofaswaptransaction.

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• Equity Leg –Thisisthelegofanequityswapcontractthatisbasedontheperformanceofashare(stock)orstockmarketindex.

• Swap Bank – This is a financial institution that actsasanintermediaryinaswaptransactionandearnspremiumfortheirservices.

• Coupon – This is the annual interest rate paid ona swap transaction. It is usually expressed as apercentageofthenotionalamount.

• Coupon Frequency–Thisdefineshowoftencouponsare to be paid between the counterparties. Theterm of the index will oftenmatch the frequencyof the coupons. For example, 3-month LIBOR ispaidquarterly,whilea6-monthLIBORispaidsemi-annually.Othersareannualandmonthly.

• Day Count Conventions - These are used forcomputingtheportionsoftheyearwhencalculatingcouponamounts.

• Business Day Convention-Thisoutlineshowcoupondates are adjusted for weekends and holidays.Typical conventions are ‘Following Business Day’and‘ModifiedFollowing.’

• Modified-Following – This refers to the automaticchange in payment day on a swap or othercontractual transaction that does not fall on abusinessday.Ifforinstanceifthepaymentdayfalls

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on a non-business day, then the payment day isautomatically rolledover to thenextbusinessday.If the next business day, however, falls on a newmonth,thebusinessdaythatprecedesthepaymentdateisused.

• Following-Business-Day – This implies that thepaymentdateofacontracthasbeenmovedtothenextbusinessday.

• Effective Date-This isthecommencementdateoftheswap.Itdefineswheninterestaccumulationonthefirstcouponpaymentwillstart.

• Maturity Date–This is thedateof the lastcoupon.It defines when the obligations between the twopartiesend.

• Over-the-Counter (OTC) –Referstoadealernetworkdifferentfromaformalexchangeforthetradingofsecuritiesincludingswaps.

• Financial Derivatives –Thesearefinancialcontractsbetweenpartieswheremovementsinthepricesofthe underlying assets (commodities, interest rates,stocks, bonds and market indices) determine thecontracts’value.

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3.0 Why Swap?Thereareseveralreasonswhycounterpartiesmaywanttoengageinswaptransactions.Theyinclude:

• Risk Management: Swap transactions serve as arisk management tool in hedging against probablelossesemanatingfromthecharacteristicfluctuationincommodity prices, interest rates, exchange rate andequityprices;

• Financing Access: Swap transactions enable acompanytoaccesscheapfinancebytappingintothecashreservesofanotherfirm;

• Tool for Hedging:Swapsaretypicallyhedgingtools.Theyareusedtoguideagainstexposurestounanticipatedinterest rate, exchange rate, commodity price andequityrisks;

• Instrument of Unconventional Monetary Policy:Inrecenttimes, bilateral currency swap agreements betweeneconomieshavebeenutilizedasatoolformanagingliquidityandforeignexchangepressure;

• Flexibility: Swap agreements are both negotiableand renewable up to at least 10 years. Also, mostswapagreementsarenon-obligatory,thatis,ifapartydefaults, theotherparty isnotboundtocontinuethecountract;

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• Minimizes Transaction Costs and Taxes: Swapenablesusers to reduceand in somecasesavoid transactioncosts.Forinstance,investorscanaccessforeignmarketswithouthavingtocontendwithmargin,capitalcontrol,and institutional rules. Firms can also access financefromtheirsubsidiariesabroadthroughtheengagementofcounterparties inthehostcountryas inthecaseofacurrency swap, thus,bypassing stiff regulationsandavoidingtransactiontaxes.

4.0 Types of Swap Contracts

4.1 Interest Rate SwapAn interest rate swap is a bilateral agreement betweentwo parties/counterparties to exchange a stream offuture interest payments on a principal amount basedon specified interest rates for a set period. This type ofswap is structured such that onepartypaysa fixed rate(the“FixedPayer”),whiletheotherpartypaysavariablerate(the“FloatingPayer”).Conventionally,the‘buyer’ofthe swap is the ‘fixed ratepayer,’while the ‘seller’ is the‘floatingratepayer.’Itisworthyofnotethatinaninterestrateswap,thepartiesdonotexchangetheprincipal.Onthepaymentdate, it is only thedifferencebetween thefixedandvariableinterestamountsthatispaid;thereisnoexchangeofthefullinterestamounts.

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4.1.1 Variants of Interest Rate Swap

Therearethreemainvariantsofinterestrateswaps:

4.1.1.1 Fixed-for-Float: This is the exchange of a streamoffixedinterestpaymentsforastreamoffloating interestpayments. The fixed rate payment (known as the swaprate) ispredetermined,whilethefloatingratepayment islinkedtosomeindex(suchastheLIBOR)whichfluctuatesthroughout the length of the contract. The tenor of thisswaprangesfrom1to15years.

4.1.1.2 Float-for-Float:Thisinvolvestheexchangeoffloatinginterestpaymentsbasedonthesameordifferentindexes.Inthisregard,onepartypaysafloatinginterestrateanchoredonareferenceindexA,toreceiveafloatingratepaymentanchoredon the same/another reference index B, onagivennotionalamount,foraspecifiednumberofyears.

4.1.1.3 Fixed-for-Fixed: This is an arrangementwhere theinterest payments exchangedby the twocounterpartiesarebasedonapre-determined(fixed)rate.Theabsenceofvariabilityineitherofthetworatesmeansthepaymentswillnotchangethroughoutthetenoroftheswap.Thisisaspecialcaseofinterestrateswap(similartoacross-currencyswap)whereeachpartyusesadifferentcurrency.

ExampleAssumeJohnownsaN1,000,000investmentthatpayshimNIBOR+1%everymonthandSandraownsaN1,000,000

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investmentthatpaysher1.5%everymonth.AstheNIBORfluctuates, the payment John receives changes, whilethe payment Sandra receives remains the same. If Johndecides to lock-in a constant payment and Sandraagrees to take a chance of receiving higher payment,thenJohnandSandracanagreetoenterintoaninterestrateswapcontract.

Under thetermsof their contract, John agrees to paySandra NIBOR + 1% permonth on aN1,000,000notionalamount,whileSandraagreestopayJohn1.5%permonthonthesamenotionalamount.Let’sseewhatthisdeallookslikeundertwodifferentscenarios.

Scenario 1: NIBOR = 0.25%

Priortotheinitiationofthecontract,JohnreceivesamonthlypaymentofN12,500fromhisinvestment(N1,000,000x(0.25%+ 1%)), while, Sandra receives a monthly payment ofN15,000fromherinvestment(N1,000,000x1.5%).

With the swap contract, John owes Sandra N12,500(N1,000,000xNIBOR+1%),andSandraowesJohnN15,000(N1,000,000 x 1.5%). The two transactions partiallyoffsetssuchthatSandrapaysJohnthedifferenceofN2,500.

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Figure 1: Graphical Illustration of Scenario 1

Scenario 2: NIBOR = 1.0%

Now, assuming the NIBOR increases to 1%, John willreceive a payment of N20,000 (N1,00,000 x (1% + 1%))on his investment instead of the agreed N15,000 underthecontract, Sandra still receivesamonthlypaymentofN15,000 (N1,000,000 x 1.5%) on her investment. The twotransactionsoffsetwithJohngivingSandrathedifferencebetweentheswapinterestpaymentwhichisN5,000.

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WithNIBORat1%,Johnisobligatedunderthetermsoftheswaptopaythedifference.

Notethat the interest rate swap has allowed Johntoguaranteehimself a N15,000 payout; if NIBOR is low,Sandrawillowehimundertheswap,butifNIBORishigher,hewilloweSandramoney.Eitherway,hehaslockedina1.5%monthlyreturnonhisinvestment.Sandrahasexposedherselftovariationinhermonthlyreturns.

4.2 Currency Swap This is an agreement betweentwo partiesto exchangecash flows indifferentcurrenciesat somepredeterminedratesforaspecifiedperiod.Itinvolvesexchangingboththe

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principalandtheinterestpaymentsonaparticularloaninonecurrency for theprincipalandthe interestpaymentsfor the equivalent of the same loan amount in anothercurrency. It could also be an arrangement betweencounterparties in different countries aimed at financingeconomicactivities(e.g. trade,businessoperations,etc.)in their localcurrenciesat thepre-determinedexchangerates,withoutbringing inathirdcountrycurrency liketheUSDollar.Thepartiestoacurrencyswapusuallyexchangetheprincipalatthebeginningandattheendoftheswapperiod.

Atypicalcurrencyswaphasthreecashflows:

• Theexchangeofprincipalsatthebeginningofthecontract;

• The exchange of interest payments during thecontractperiod;and

• The re-exchange of principals at the end of thecontract.

The associated cash flows are denominated in differentcurrencies and the principal amounts are usuallyexchangedatthestartandmaturitydates.Theexchangerateand interest rateusedcaneitherbe fixedorat theprevailingexchangerate(Floatingorspotrate)atthetimeofthetransaction.

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Figure 3: Currency Swap Cash Flow

4.2.1 Variants of Currency Swap

Therearethree(3)mainvariantsofcurrencyswaps:fixed-for-fixed, fixed-for-floatingandfloating-for-floating. Theseformsofcurrencyswapsarebestillustratedwithexamples.Let us consider a four-year currency swap with a semi-annualpayment involvingaGhanaiancedibasedonaswaprateof3.84%andaNigerianNaira,basedonaswaprateof2.5%.Theprincipalamount isN12.71millionwhichisequivalenttoGH₵10.00millionataspotexchangerateof 0.79 (GH₵ /N). At the beginning of the contract, thecounterpartieswillexchangethetwoprincipalamounts.In

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thisregard,PartyOnesendsGH₵10.00milliontoPartyTwo,whilereceivingN12.71millionfromPartyTwo.

Let us consider the variants of currency swaps using thebackgroundinformationabove.

4.2.1.1 Fixed-for-fixed: In this variant, payments in bothcurrencies are based on the associated fixed interestrates. From thepreceding illustration, PartyOne receivesfrom Party Two Ghanaian cedi interest payment basedona 3.84% fixed rateapplied to thenotionalamountofGH₵10.00millionover thedurationof the swap.Similarly,PartyTworeceivesfromPartyOneNigerianNaira interestpaymentsbasedona2.50%fixedratethenotionalamountofN12.71millionoverthelifespanoftheswap.Atmaturity,andregardlessofwhethertherewasan initialexchange,the counterparties exchanges the original principalamounts.PartyOne receivesGH₵10.00million fromPartyTwoandreturnsN12.71milliontoPartyTwo.

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Figure 4: Fixed-for-Fixed Currency Swap

4.2.1.2 Fixed-for-Floating: This entails the payment of afixed interest rateononecurrencyand the receipt of afloating interest rate on another currency. Referring tothe earlier background information, Party One receivesfrom Party TwoGhanaian cedi interest payments basedona3.84%fixedrateonaprincipalamountofGH₵10.00 millionover the lifespanof theswap.Ontheotherhand,PartyTworeceivesfromPartyOneNigerianNaira interestpaymentbasedona floatingormarket-determined rateontheprincipalamountofN12.71million.Atmaturity,the

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originalprincipalamountsarere-exchangedbetweenthetwoparties.

Figure 5: Fixed-for-Floating Currency Swap

4.2.1.3 Floating-for-Floating: Under this arrangement, theinterest rates applied on the two currencies aremarket-determined (floating rates). Following our backgroundinformation,bothpartiesreceiveinterestpaymentsontheprincipal amounts (GH₵ 10.00million, for PartyOne andN12.71million forPartyTwo). As typicalofother formsofcurrencyswap, regardlessofwhether therewasan initialexchange, the counterparties would re-exchange theoriginalprincipalamounts.

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Figure 6: Floating-for-Floating Currency Swap

4.3 Commodity SwapA commodity swap is a two-sided contract wherebythe price of a commodity (an underlining commodity)is traded over a specified period. The contract has twolegs.Oneparty(the‘fixedpricepayer’)makesaperiodicpaymentbasedonanagreedfixedpriceforthespecifiedcommodity;whiletheotherparty(the‘floatingpricepayer’)makes a periodic payment based on a floating pricefor thesamecommodity. The floatingprice isusuallyanaveragespotpricecalculatedoversomepredeterminedperiod. Generally, the fixed price payers are consumerswho intend to protect themselves against price swings,

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whilethefloatingpricepayersareproducerswhoseektoguaranteetheircommodityprices.

4.3.1 Variants of Commodity Swap

4.3.1.1 Fixed-Float Commodity Swap: This is the mostcommonor basic formof commodity swap (also knownasthePlainVanillacommodityswap).Inthisregard,oneof the counterparties (the fixed price payer) agrees topaycash flowsbasedona fixedpriceof theunderlyingcommodity and receives cash flows in turn based on afloatingpriceoftheunderlyingcommodity.

4.3.1.2 Commodity for Interest Swap: Thisformofcommodityswap is similar to the equity swap in that the cash flowon the underlying commodity is exchanged for interestpayments,plusorminusaspread.Itderivesfromtheviewthat changes in interest rate induce fluctuations in thepricesofsomecommodities.

Example

A hypothetical airline company (Air Trek), enters anagreement to receiveonemillion litresof jet fuel for four(4)months.LetusassumethatAirTrektakesthefixedlegoftheswapforN100perlitre,whilethecounterpartyholdsthefloatinglegoftheswap.

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Scenario 1: Jet Fuel Price = N120

AnincreaseinthemarketpriceofjetfueltoN120perlitre,within the contract period, requires the counterparty topayAir-TrekthedifferenceofN20million((N120-N100)X1millionlitres).


Scenario 2: Jet Fuel Price = N90

Conversely,adeclineinjetfuelpricetoN90,wouldrequireAir-Trek,topaythecounterpartyN10million((N100-N90)X1million litres)on the settlementdate. Thus, fluctuations

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inthemarketpriceofjetfuelareeventuallyoffsetbytheagreementofbothpartiestotradethepricedifferences.


4.4 Equity SwapAn equity swap is an agreement that empowerscounterpartiestoexchangecashflowsfromtwodifferentassets.Inthisarrangement,partyoneagreestoexchangetherateof returnormarket indexofanequity(stock) forthecounterparty’s fixedor floating interest rateor returnsonanotherstockorindexatspecifiedfuturedates.Theleglinkedtotheinterestrateiscalledthe“floatingleg”,while

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thattotherateofreturnontheequityiscalledthe“equityleg”. Generally, notional amounts are not exchangedinequity swaps,and the returnon themarket indexcaneitherbepositiveornegative.

4.4.1 Variants of Equity Swap

Thevariantsofequityswapinclude:

• Equity Return Against a Fixed Rate:This isanequityswapwherebyonelegpaysthereturnonanequity(stock,share)ormarketindexoftheequityandtheotherlegpaysafixedrate.

• Equity Return Against a Floating Rate: Under thisarrangement,onepartypaysthereturnonanequity(stock, share) and the other party pays a floatingrate (the current market interest rate i.e. LIBOR).Theprevailingmarket rateat thebeginningof thecontractdeterminesthefirstpayment.

• Equity Return Against Another Equity Return: In thisscenario,bothpartiesbase theirpayment streamson the returns of two different domestic equitymarketindices(forinstance,inNigeria,onepartyintheswaptransactionpaysthereturnonthefinancialsector stock index,while the other party pays thereturnsontheindustrialsectorstockindex).

• Equity Return Against a Foreign Equity Return: Thisisanequity swapwherebybothpartiesbase their

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payments on the return of two different equitymarketindices.AnexampleiswhenonepartypaysthereturnsontheNigerianStockmarketindexwhilereceivingthereturnsontheS&P500indexfromthecounterparty.

• Equity Swaps with Changing Notional Capital:Inthebasic equity swap, the notional amounts are notexchanged,but in thiscase, thenotionalamountsare exchanged. The two notional principals willbe required at the beginning of the swap, andtheir value may differ because of the prevailingexchangerateatthebeginningoftheswap.

Example

Considertwoassetmanagers(AandB)managingFundAandFundB.AssetManagerAwhoseFundportfoliotrackstheNigeriaAllShareIndex(NASI)decidestoenteraswapwithFundBwithanotionalprincipalofN100millionandthetotalreturnsontheNASI,whileFundBpaysafixedinterestrateof6%.Paymentsaretobemadebi-annually,andtheswapisexpectedtomatureafter3years.

Fromthisillustration,assetmanagerApaysassetmanagerB a floating rate pegged to the NASI, whilemanager Bmakesperiodic 6% interest ratepayment tomanagerA,onthegivennotionalamountofN100million,fora3-yearperiod.

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IftheNASIreturnsarepositive,FundApaysNASIreturnstoFundBandFundBpaysthefixedratetoFundA.WhentheNASIreturnsarenegative,FundApaysnothingtoFundB,butFundBpaysthefixedrateandthepercentagelossontheNASIreturntoFundA.

Assumingat thebeginningof thecontract, theNASIwas2500andlatermovedto2600and2570attheendofJuneand December, respectively. Thus, at end-June, Fund ApaysFundBthereturnonNASIof4% and December, respectively. Thus, at end-June, Fund A

ontheprincipalamountofN100.0million.FundB,therefore,receives, N4,000,000{i.e.N100,000*4%},

while Fund A receives fixed rate of 6% on the principalN2,991,780{i.e.N100,000*182*6%}.

In the second tranche of the payment, end-December,FundApaysnothingsincethereturnontheindexisnegativeFundApaysnothingsincethereturnontheindexisnegative

butFundBpays the fixed interestontheprincipalplusafloatingrateontheprincipali.e.theloss on the return on NASI {N100,000*1.154%=N1,154,000}. Thus,FundAreceivesfromFundBatotalofN4,162,219.00{N3,008,219+N1,154,000}.

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5.0 Swap Pricing and valuationThis section provides a simplified framework forunderstandingswappricingandvaluation.The‘price’and‘value’ofaswaparetwodistinctconcepts.Thepriceofaswapreferstotheinterestrateusedtodeterminethefixedratepaymentsinaswaptransaction,while,thevalueofaswapreferstothedifferencebetweencashflowsbasedonthefixedandfloatingratepayments.Thevalueofaswapcanbeexpressedas:

Where(multipliedby)isthetotalvalueofthecashstreamsonafixedratebondand(multipliedby)isthetotalvalueofcashstreamsonafloatingratebond;whileisthenotionalamount of the swap transaction. The expression aboverepresentsthevalueofa‘receive fixed, pay floating’swapinwhichcasetheparty takesa longposition in thefixedratebondanda shortposition in the floating ratebond.Conversely, the value of a ‘pay fixed, receive floating’ swapisexpressedas:

The above expressions suggest that the value a swaptransactionisderivedfromitspricing.

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Attheoriginationoftheswap(timezero),thepriceofthefixedratebondandthefloatingratebondareequal,sothatthevalueoftheswapcontractequalszero4.Beyondtheoriginationoftheswap,thevalueofcanbepositiveornegative.

Some important information required to price a swapinclude: the tenor, frequency of settlement, dates ofpaymentandthedaycountconventions.

Thepricingofaswaptransactionmakestwoassumptions:

• atorigination,thevalueoftheswapiszero,and

• thefacevalueofafloatingratebondisthesameatissuance.

ThestandardconventionisthatthefloatingrateisLiborrateatthestartofthecontract.Assumingthenotionalamountisequaltoone(sayN1);applyingthefirstassumption,andtakingtobeequaltoN1asinthesecondassumption,wehave:

Thisisinlinewiththegeneralprinciplethatstatesthatthepriceofaswapistherate(coupon)thatequatesthevalue

4 Mathematically: suchthatthepresentvalueofcash flows from the fixed ratepayments equals thepresent valueof cashflowsfromthefloatingratepayments.

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of the fixed ratebond to thatof the floating ratebond,sothatatthebeginningofthecontract,thevalueoftheswapiszero.

ThispricingandvaluationframeworkdirectlyappliestothePlainVanilla formsof interest rateandequityswaps. Thepricingandvaluationofothertypesofswaprequiresomemodificationstotheoriginalframeworkandarediscussedbelow.

5.1. Pricing and Valuation of Other Swaps

5.1.1 Currency Swap

The earlier framework discussed provides some intuitioninto the pricing and valuation of a currency swap. Thefollowingassumptionshold:

• The swapcontractcomprises twobonds –a fixedratebondandafloatingratebond;

• Atinitiation,thevalueoftheswapiszerogiventhatthevalueofthefixedratebondequalsthevalueofthefloatingratebond;and

• Thefloatingbondratesellsatface-value(say,N1).Amajordistinctionbetweentheinterestrateswapandthecurrency swap is that, in the latter, theprincipal are notjust ‘notional,’ they are actually exchangedboth at thebeginningandatmaturity.

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LetS0bethespotexchangeratebetweentwocurrencies,and represent the initial value ofthebonds (with fixedor floatingcash flows)expressed indomestic and foreign currencies, respectively. Thus, thevalueofthecurrencyswapcanbeexpressedas:

… value at time ofinception

… value for a ‘receivedomestic/payforeign’swap

… value for a ‘receiveforeign/paydomestic’swap

At other periods other than period zero, the value of acurrency swap can be positive (greater than zero) ornegative(lessthanzero).

Inlinewiththebasicframeworkofswappricing,thepricingof currency swap can be determined from its value atorigination. Theprices or valueof eachbond,P, at theinceptionofacurrencyswap,alsoequaltotheirprincipal.

5.1.2 Commodity Swap

Thepriceandvalueofacommodityswaparederivedbysomemathematicalderivationsthatequatethecashflowsoffixedandfloatingbondpricesresultingintheexpression:

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Theequationaboveexpresses thevalueof theswap(V)for a series of forward contracts (periods t=1, 2,… n). is the zero coupon rate used to discount the streams offuture cash flows (say, forward prices of the underlyingcommodity),while and are the fixedand floatingpricesofthecommodity.Atthebeginningofthecontract,thevalueoftheswaptransactioniszero,sothatitispossibletosolveforthefixedpriceoftheswap.

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6.0 Risks Associated with SwapAnumberof risksareassociatedwith swap transactions.Theserisksinclude:

Credit Risks:Thisistheriskthatcounterpartiesmaydefaulton payments. It is the basic risk associated with swaptransaction. Inmost financialcontracts, this typeof risk isalsoknownasdefaultrisk;

Interest Rate Risk:Thisistheriskthattheworth/valueofaninvestmentwill changedue to variations in the absolutelevelofinterestratesandthespreadbetweentworates.Thevaluesofbondsaremoredirectlyaffectedbyinterestraterisksthanstocks;hence,itisamajorthreattobondholders;

Search Cost: This is the cost associated with finding awilling counterparty. The process might be expensiveregarding fees charged by an intermediary or the costofmanagementtimeinnegotiation.Therearealso, legalchargesfordrawingupthecurrencyswapagreement;

Mismatch Risk: This arises from the inability to find acounterpart that wants to initiate a swap for the sameamountandatthesameperiod(maturity);

Exit Restriction: Should one party wish to exit the swapbeforematurity,theexitingpartymustsecuretheconsentofitscounterpartybeforepursuingamutuallyagreedexitstrategywhichmightbedifficulttoachieve;

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Sovereign Risk:Thisriskarisesfromtheimpositionofexchangeraterestrictionsbyeitherofthetwocountriesinvolvedinaswaptransaction.Thismightaffecttheperformanceoftheswap.

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Further ReadingChance,D.andDon,R.(1998),“ThePricingofEquitySwaps

andSwaptions,”JournalofDerivativesVol.5,Summer,pp.19-31.

Fletcher,D., and Sultan, J. (1997), “CrossCurrency SwapRatesandDeviationsfromInterestRateParity,”JournalofFinancialEngineering,6,pp.47-69.

Kolb,R.andJames,O.(2007),Futures,Options,andSwaps,5thEdition,Malden,MA:BlackwellPublishing.

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