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OPTIONS,FUTURES, ANDOTHERDERIVATIVES

JohnC.Hull

MapleFinancialGroupProfessorofDerivativesandRiskManagement

JosephL.RotmanSchoolofManagement UniversityofToronto

SankarshanBasu

ProfessorofFinanceandAccounting IndianInstituteofMarketingBangalore

TENTHEDITION

Published by Pearson India Education Services Pvt. Ltd, CIN: U72200TN2005PTC057128.

No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s prior written consent.

This eBook may or may not include all assets that were part of the print version. The publisher reserves the right to remove any material in this eBook at any time.

ISBN: 978-93-528-6659-5 eISBN: 9789353063016

Head Office: 15th Floor, Tower-B, World Trade Tower, Plot No. 1, Block-C, Sector-16, Noida 201 301,Uttar Pradesh, India.

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ToMichelle ToNilanjana

2.Futuresmarketsandcentralcounterparties...

3.Hedgingstrategiesusingfutures ......................................................................64 4.Interestrates. ...............................................................................................94

5.Determinationofforwardandfuturesprices.

23.Estimatingvolatilitiesandcorrelations.....

28.Martingalesandmeasures. ...........................................................................690

29.Interestratederivatives:Thestandardmarketmodels... ....................................708

30.Convexity,timing,andquantoadjustments... ..................................................728

31.Equilibriummodelsoftheshortrate .............................................................741

32.No-arbitragemodelsoftheshortrate...... ......................................................754

33.HJM,LMM,andmultiplezerocurves..... ......................................................777

34.SwapsRevisited.... ......................................................................................796

35.Energyandcommodityderivatives... .............................................................811

36.Realoptions. .............................................................................................829

37.Derivativesmishapsandwhatwecanlearnfromthem. ....................................843 Glossaryofterms. ......................................................................................857 DerivaGemsoftware..... ...............................................................................880

Majorexchangestradingfuturesandoptions ..................................................885 Tablesfor N ðxÞ ...........................................................................................886 Credits.. ....................................................................................................888 Authorindex. .............................................................................................889 Subjectindex.

ListofBusinessSnapshots

Chapter1.Introduction.

1.1Exchange-tradedmarkets..

1.2Over-the-countermarkets..

1.3Forwardcontracts.

1.4Futurescontracts..

1.5Options.

1.6Typesoftraders....

1.7Hedgers.

1.9Arbitrageurs..

1.10OverviewoftheIndianDerivativesMarket...

2.4Theoperationofmarginaccounts....

2.5OTCmarkets

2.6NewspaperQuotes

2.7Delivery

2.8Typesoftradersandtypesoforders.

2.9Regulation....

2.10Accountingandtax......

2.11Forwardvs.futurescontracts....

Chapter3.Hedgingstrategiesusingfutures.. ......................................................................64

3.1Basicprinciples... .................................................................................64

3.2Argumentsforandagainsthedging. ........................................................66

3.3Basisrisk.... ........................................................................................69

3.4Crosshedging..... .................................................................................73

3.5Stockindexfutures.. .............................................................................77

3.6Stackandroll......................................................................................84

Chapter4.Interestrates..

4.1Typesofrates.....

4.2Swaprates...........................................................................................99

4.3Therisk-freerate.

4.4Measuringinterestrates..

4.5Zerorates.........................................................................................104

4.6Bondpricing......

4.7Determiningzerorates....

4.9Forwardrateagreements.

4.10Duration.....

4.11Convexity....

4.12Theoriesofthetermstructureofinterestrates....

5.1Investmentassetsvs.consumptionassets....

5.2Shortselling

5.3Assumptionsandnotation......

5.4Forwardpriceforaninvestmentasset.

5.6Knownyield

5.7Valuingforwardcontracts......

5.8Areforwardpricesandfuturespricesequal?......

5.9Futurespricesofstockindices.

5.10Forwardandfuturescontractsoncurrencies......

5.11Futuresoncommodities..

5.12Thecostofcarry.

5.13Deliveryoptions..

5.14Futurespricesandexpectedfuturespotprices....

6.1Daycountandquotationconventions.

6.2Treasurybondfutures.....

6.3Eurodollarfutures. ..............................................................................167

6.4Duration-basedhedgingstrategiesusingfutures.... ...................................173

6.5Hedgingportfoliosofassetsandliabilities ..............................................174

Chapter7.Swaps.. .......................................................................................................180

7.1Mechanicsofinterestrateswaps...... .....................................................183

7.2Daycountissues... ..............................................................................188

7.3Conﬁrmations...... ..............................................................................189

7.4Thecomparative-advantageargument...... ..............................................190

7.5Valuationofinterestrateswaps. ............................................................194

7.6Howthevaluechangesthroughtime .....................................................196

7.7Fixed-for-ﬁxedcurrencyswaps.. ............................................................197

7.8Valuationofﬁxed-for-ﬁxedcurrencyswaps... ..........................................200

7.9Othercurrencyswaps... .......................................................................202

7.10Creditrisk.... .....................................................................................203

7.11Creditdefaultswaps..... .......................................................................204

7.12Othertypesofswaps....

Chapter8.Securitizationandthecreditcrisisof2007... .....................................................212

8.1Securitization

8.2TheU.S.housingmarket..

Chapter9.XVAs..

9.1CVAandDVA...................................................................................227

Chapter10.Mechanicsofoptionsmarkets..

10.8Theoptionsclearingcorporation....

10.9Regulation.. ......................................................................................253

10.10Taxation..... ......................................................................................253

10.11Warrants,employeestockoptions,andconvertibles.... .............................254

10.12Over-the-counteroptionsmarkets...

Chapter11.Propertiesofstockoptions.. ...........................................................................261

11.1Factorsaﬀectingoptionprices.

11.3Upperandlowerboundsforoptionprices.. ...........................................266

11.4Put–callparity.... ...............................................................................268

11.5Callsonanon-dividend-payingstock.. ..................................................271

11.6Putsonanon-dividend-payingstock...

11.7Eﬀectofdividends.. ...........................................................................276

Chapter12.Tradingstrategiesinvolvingoptions..... .............................................................282

12.1Principal-protectednotes. ....................................................................282

12.2Tradinganoptionandtheunderlyingasset

Chapter13.Binomialtrees .............................................................................................302

13.1Aone-stepbinomialmodelandano-arbitrageargument .........................302

13.2Risk-neutralvaluation..... ....................................................................306

13.3Two-stepbinomialtrees.. ....................................................................308

13.4Aputexample.... ...............................................................................311

13.5Americanoptions ...............................................................................312

13.6Delta... .............................................................................................313

13.7MatchingvolatilitywithUandD...

13.8Thebinomialtreeformulas.....

13.9Increasingthenumberofsteps .............................................................316

13.10UsingDerivaGem... ...........................................................................317

13.11Optionsonotherassets... ....................................................................318

Chapter14.WienerprocessesandIto ’slemma ...................................................................330

14.1TheMarkovproperty... .......................................................................330

14.2Continuous-timestochasticprocesses .....................................................331

14.3Theprocessforastockprice.... ............................................................336

14.4Theparameters..... ..............................................................................339

14.5Correlatedprocesses..... .......................................................................340

14.6Ito ’slemma. .....................................................................................341

14.7Thelognormalproperty .......................................................................342 Summary...... .....................................................................................343

Appendix:AnonrigorousderivationofIto ’slemma... ............................347

Chapter15.TheBlack–Scholes–Mertonmodel ...................................................................349

15.1Lognormalpropertyofstockprices.. .....................................................350

15.2Thedistributionoftherateofreturn .....................................................351

15.3Theexpectedreturn...... .......................................................................352

15.4Volatility...... .....................................................................................353

15.5TheideaunderlyingtheBlack–Scholes–Mertondiﬀerentialequation ..........357

15.6DerivationoftheBlack–Scholes–Mertondiﬀerentialequation.. .................359

15.7Risk-neutralvaluation.. .......................................................................362

15.8Black–Scholes–Mertonpricingformulas... ..............................................363

15.9Cumulativenormaldistributionfunction.. ..............................................366

15.10Warrantsandemployeestockoptions...... ..............................................367

15.11Impliedvolatilities. ..............................................................................369 15.12Dividends..... .....................................................................................371

Chapter16.Employeestockoptions....

16.1Contractualarrangements.. ...................................................................383

16.2Dooptionsaligntheinterestsofshareholdersandmanagers?... .................385

16.3Accountingissues. ..............................................................................386

16.4Valuation......

16.5Backdatingscandals.....

Chapter17.Optionsonstockindicesandcurrencies ............................................................396

17.1Optionsonstockindices... ...................................................................396

17.2Currencyoptions.. ..............................................................................398

17.3Optionsonstockspayingknowndividendyields.. ...................................401

17.4ValuationofEuropeanstockindexoptions... ..........................................403

17.5ValuationofEuropeancurrencyoptions... ..............................................406

17.6Americanoptions. ..............................................................................407

Chapter18.FuturesoptionsandBlack’smodel...... .............................................................412

18.1Natureoffuturesoptions ....................................................................412

18.2Reasonsforthepopularityoffuturesoptions..... ....................................415

18.3Europeanspotandfuturesoptions. ......................................................415

18.4Put–callparity.... ...............................................................................416

18.5Boundsforfuturesoptions..... .............................................................417

18.6Driftofafuturespricesinarisk-neutralworld..

18.7Black’smodelforvaluingfuturesoptions... ...........................................419

18.8UsingBlack’smodelinsteadofBlack–Scholes–Merton... .........................420

18.9Valuationoffuturesoptionsusingbinomialtrees ....................................421

18.10Americanfuturesoptionsvs.Americanspotoptions..

18.11Futures-styleoptions ...........................................................................424

Chapter19.TheGreekletters...

19.3Greeklettercalculation... ....................................................................431 19.4Deltahedging.....

19.7Relationshipbetweendelta,theta,andgamma....

19.10ApproximationforCalculationsoftheGreeksforanAmericanOption.

19.12Scenarioanalysis. ...............................................................................449

19.13Extensionofformulas.....

Chapter20.Volatilitysmiles.....

20.1Whythevolatilitysmileisthesameforcallsandputs

20.4Alternativewaysofcharacterizingthevolatilitysmile..

20.5Thevolatilitytermstructureandvolatilitysurfaces.....

20.6Minimumvariancedelta. ....................................................................471

20.7Theroleofthemodel.....

20.8Whenasinglelargejumpisanticipated......

Furtherquestions.. ..............................................................................476

Appendix:Determiningimpliedrisk-neutraldistributionsfrom volatilitysmiles. ...................................................................478

Chapter21.Basicnumericalprocedures...... .......................................................................481

21.1Binomialtrees...... ..............................................................................481

21.2Usingthebinomialtreeforoptionsonindices,currencies,andfutures contracts ............................................................................................489

21.3Binomialmodelforadividend-payingstock. ..........................................491

21.4Alternativeproceduresforconstructingtrees. ..........................................496

21.5Time-dependentparameters...... ............................................................499

21.6MonteCarlosimulation .......................................................................500

21.7Variancereductionprocedures.. ............................................................506

21.8Finitediﬀerencemethods.. ...................................................................509 Summary...... .....................................................................................519 Furtherreading.... ..............................................................................520 Practicequestions.. ..............................................................................521 Furtherquestions.. ..............................................................................523

Chapter22.Valueatriskandexpectedshortfall..... ............................................................525

22.1TheVaRandESmeasures ...................................................................526

22.2Historicalsimulation.... .......................................................................527

22.3Model-buildingapproach.. ...................................................................533

22.4Thelinearmodel.. ..............................................................................536

22.5Thequadraticmodel.... .......................................................................541

22.6MonteCarlosimulation .......................................................................544

22.7Comparisonofapproaches ...................................................................545

22.8Backtesting.. .....................................................................................545

22.9Principalcomponentsanalysis... ............................................................545 Summary...... .....................................................................................549 Furtherreading.... ..............................................................................550 Practicequestions.. ..............................................................................551 Furtherquestions.. ..............................................................................552

Chapter23.Estimatingvolatilitiesandcorrelations.. ............................................................554

23.1Estimatingvolatility..... .......................................................................554

23.2Theexponentiallyweightedmovingaveragemodel ...................................556

23.3TheGARCH(1,1)model. ...................................................................558

23.4Choosingbetweenthemodels... ............................................................559

23.5Maximumlikelihoodmethods... ............................................................560

23.6UsingGARCH(1,1)toforecastfuturevolatility.. ...................................565

23.7Correlations.. .....................................................................................568

23.8ApplicationofEWMAtofour-indexexample...... ...................................571 Summary...... .....................................................................................573 Furtherreading.... ..............................................................................573 Practicequestions.. ..............................................................................573 Furtherquestions.. ..............................................................................575

Chapter24.Creditrisk... ................................................................................................577

24.1Creditratings .....................................................................................577

24.2Historicaldefaultprobabilities.. ............................................................578

24.3Recoveryrates...... ..............................................................................579

24.4Estimatingdefaultprobabilitiesfrombondyieldspreads...... .....................580

24.5Comparisonofdefaultprobabilityestimates.. ..........................................583

24.6Usingequitypricestoestimatedefaultprobabilities..... ............................586

24.7Creditriskinderivativestransactions.. ..................................................588

24.8Defaultcorrelation.. ...........................................................................594

24.9CreditVaR. ......................................................................................597 Summary.... ......................................................................................600 Furtherreading... ...............................................................................601 Practicequestions ...............................................................................601 Furtherquestions ...............................................................................603

Chapter25.Creditderivatives... ......................................................................................605

25.1Creditdefaultswaps ...........................................................................606

25.2Valuationofcreditdefaultswaps.... ......................................................610

25.3Creditindices..... ...............................................................................613

25.4Theuseofﬁxedcoupons. ....................................................................614

25.5CDSforwardsandoptions..... .............................................................615

25.6Basketcreditdefaultswaps..... .............................................................616

25.7Totalreturnswaps.. ...........................................................................616

25.8Collateralizeddebtobligations. .............................................................617

25.9RoleofcorrelationinabasketCDSandCDO... ....................................619

25.10ValuationofasyntheticCDO. .............................................................620

25.11Alternativestothestandardmarketmodel..

Chapter26.Exoticoptions

26.1Packages.....

26.2PerpetualAmericancallandputoptions....

26.3NonstandardAmericanoptions...... ......................................................635

26.4Gapoptions

26.5Forwardstartoptions.....

26.6Cliquetoptions...

26.7Compoundoptions.. ...........................................................................637

26.8Chooseroptions.. ...............................................................................638

26.9Barrieroptions...

26.10Binaryoptions....

26.11Lookbackoptions...

26.12Shoutoptions.....

26.13Asianoptions.....

26.14Optionstoexchangeoneassetforanother..

26.15Optionsinvolvingseveralassets......

26.16Volatilityandvarianceswaps..

26.17Staticoptionsreplication.

Chapter27.Moreonmodelsandnumericalprocedures..

27.1AlternativestoBlack–Scholes–Merton.

27.2Stochasticvolatilitymodels.....

27.3TheIVFmodel... ...............................................................................668

27.4Convertiblebonds...

27.5Path-dependentderivatives......

27.6Barrieroptions..... ..............................................................................675

27.7Optionsontwocorrelatedassets...... .....................................................678

27.8MonteCarlosimulationandAmericanoptions.... ...................................680

Chapter28.Martingalesandmeasures ..............................................................................690

28.1Themarketpriceofrisk... ...................................................................691

28.2Severalstatevariables... .......................................................................694

28.3Martingales... .....................................................................................695

28.4Alternativechoicesforthenumeraire .....................................................696

28.5Extensiontoseveralfactors...... ............................................................699

28.6Black’smodelrevisited. .......................................................................700

28.7Optiontoexchangeoneassetforanother. ..............................................701

28.8Changeofnumeraire.... .......................................................................702

Chapter29.Interestratederivatives:Thestandardmarketmodels ..........................................708

29.1Bondoptions .....................................................................................708

29.2Interestratecapsandﬂoors...... ............................................................713

29.3Europeanswapoptions. .......................................................................719

29.4Hedginginterestratederivatives ............................................................723

Chapter30.Convexity,timing,andquantoadjustments... .....................................................728

30.1Convexityadjustments.. .......................................................................728

30.2Timingadjustments...... .......................................................................732

30.3Quantos ............................................................................................734

Chapter31.Equilibriummodelsoftheshortrate..... ............................................................741

31.1Background.. .....................................................................................741

31.2One-factormodels. ..............................................................................743

31.3Real-worldvs.risk-neutralprocesses. .....................................................748

31.4Estimatingparameters.. .......................................................................749

31.5Moresophisticatedmodels ...................................................................750

Chapter32.No-arbitragemodelsoftheshortrate... ............................................................754

32.1Extensionsofequilibriummodels..... .....................................................754

32.2Optionsonbonds. ..............................................................................758

32.3Volatilitystructures.. ...........................................................................759

32.4Interestratetrees. ...............................................................................760

32.5Ageneraltree-buildingprocedure... ......................................................762

32.6Calibration.. ......................................................................................771

32.7Hedgingusingaone-factormodel.. ......................................................773

Chapter33.HJM,LMM,andmultiplezerocurves...... ......................................................777

33.1TheHeath,Jarrow,andMortonmodel...... ...........................................777

33.2TheLIBORmarketmodel..... .............................................................780

33.3Handlingmultiplezerocurves. .............................................................790

33.4Agencymortgage-backedsecurities. ......................................................791

Chapter34.SwapsRevisited..... ......................................................................................796

34.1Variationsonthevanilladeal. .............................................................796

34.2Compoundingswaps ...........................................................................798

34.3Currencyswaps... ...............................................................................799

34.4Morecomplexswaps......

34.5Equityswaps...... ...............................................................................803

34.6Swapswithembeddedoptions. .............................................................804 34.7Otherswaps ......................................................................................807

Chapter35.Energyandcommodityderivatives...... .............................................................811

35.1Agriculturalcommodities ....................................................................812

35.2Metals. .............................................................................................812

35.3Energyproducts.. ...............................................................................813

35.4Modelingcommodityprices.... .............................................................815

35.5Weatherderivatives.. ...........................................................................821

35.6Insurancederivatives ...........................................................................822

35.7Pricingweatherandinsurancederivatives.... ...........................................824

35.8Howanenergyproducercanhedgerisks....

Chapter36.Realoptions... .............................................................................................829

36.1Capitalinvestmentappraisal... .............................................................829

36.2Extensionoftherisk-neutralvaluationframework..... .............................830

36.3Estimatingthemarketpriceofrisk. ......................................................832

36.4Applicationtothevaluationofabusiness.. ...........................................833

36.5Evaluatingoptionsinaninvestmentopportunity

37.1Lessonsforallusersofderivatives....

37.2Lessonsforﬁnancialinstitutions......

37.3Lessonsfornonﬁnancialcorporations......

BUSINESSSNAPSHOTS

1.1TheLehmanBankruptcy. ...............................................................................4

1.2SystemicRisk..... ..........................................................................................5

1.3HedgeFunds...... ........................................................................................12

1.4TheHarshadMehtaScam...... ......................................................................19

1.5SocGen’sBigLossin2008......

2.1TheUnanticipatedDeliveryofaFuturesContract......

2.2Long-TermCapitalManagement’sBigLoss.

3.1HedgingbyGoldMiningCompanies......

3.2Metallgesellschaft:HedgingGoneAwry..

4.1CharacteristicsoftheIndianInterestRateRegime......

4.2OrangeCounty’sYieldCurvePlays. ..............................................................112

4.3ATypicalForwardRateAgreement(FRA).

4.4Liquidityandthe2007–2009FinancialCrisis......

5.1KidderPeabody’sEmbarrassingMistake.

5.2ASystemsError? .......................................................................................138

5.3TheCMENikkei225FuturesContract...

5.4IndexArbitrageinOctober1987.....

6.1DayCountsCanBeDeceptive.

6.2TheWildCardPlay.... ................................................................................166

6.3Asset–LiabilityManagementbyBanks....

7.1ExampleofatypicalOvernightIndexedSwap(OIS)deal....

7.2ExtractfromHypotheticalSwapConﬁrmation....

7.3TheHammersmithandFulhamStory.....

8.1TheBaselCommittee.. ................................................................................223 10.1GucciGroup’sLargeDividend .....................................................................246 10.2TaxPlanningUsingOptions...

11.1Put–CallParityandCapitalStructure.....

12.1LosingMoneywithBoxSpreads.....

12.2HowtoMakeMoneyfromTradingStraddles.....

15.1MutualFundReturnsCanbeMisleading

15.2WhatCausesVolatility?... ............................................................................357 15.3Warrants,EmployeeStockOptions,andDilution

17.1CanWeGuaranteethatStocksWillBeatBondsintheLongRun?..

19.1DynamicHedginginPractice.. .....................................................................449 19.2WasPortfolioInsurancetoBlamefortheCrashof1987?....

20.1MakingMoneyfromForeignCurrencyOptions..

20.2Crashophobia..... .......................................................................................469 21.1CalculatingPiwithMonteCarloSimulation ...................................................500 21.2CheckingBlack–Scholes–MertoninExcel

22.1HowBankRegulatorsUseVaR...... ..............................................................526 24.1DowngradeTriggersandAIG. .....................................................................592 25.1WhoBearstheCreditRisk?.... .....................................................................606 25.2CurrentregulatorypositionontradingincreditderivativesinIndia. ...................607 25.3TheCDSMarket .......................................................................................608

26.1IsDeltaHedgingEasierorMoreDiﬃcultforExotics? .....................................652

29.1Put–CallParityforCapsandFloors.......

29.2SwaptionsandBondOptions.. .....................................................................720

30.1Siegel’sParadox.. .......................................................................................736

33.1IOsandPOs ..............................................................................................793

34.1HypotheticalConﬁrmationforNonstandardSwap......

34.2HypotheticalConﬁrmationforCompoundingSwap....

34.3HypotheticalConﬁrmationforanEquitySwap...

34.4ProcterandGamble’sBizarreDeal.. ..............................................................808

36.1ValuingAmazon.com.. ................................................................................834

37.1BigLossesbyFinancialInstitutions. ..............................................................844

37.2BigLossesbyNonﬁnancialOrganizations...

37.3SundaramMultipaper. ................................................................................853

TECHNICALNOTES

AvailableontheAuthor’sWebsite http://www-2.rotman.utoronto.ca/ hull/TechnicalNotes/index.html

1.ConvexityAdjustmentstoEurodollarFutures

2.PropertiesoftheLognormalDistribution

3.WarrantValuationWhenValueofEquityplusWarrantsIsLognormal

4.ExactProcedureforValuingAmericanCallsonStocksPayingaSingleDividend

5.CalculationoftheCumulativeProbabilityinaBivariateNormalDistribution

6.DiﬀerentialEquationforPriceofaDerivativeonaStockPayingaKnownDividend Yield

7.DiﬀerentialEquationforPriceofaDerivativeonaFuturesPrice

8.AnalyticApproximationforValuingAmericanOptions

9.GeneralizedTree-BuildingProcedure

10.TheCornish–FisherExpansiontoEstimateVaR

11.ManipulationofCreditTransitionMatrices

12.CalculationofCumulativeNoncentralChi-SquareDistribution

13.EﬃcientProcedureforValuingAmerican-StyleLookbackOptions

14.TheHull–WhiteTwo-FactorModel

15.ValuingOptionsonCoupon-BearingBondsinaOne-FactorInterestRateModel

16.ConstructionofanInterestRateTreewithNonconstantTimeStepsandNonconstant Parameters

17.TheProcessfortheShortRateinanHJMTermStructureModel

18.ValuationofaCompoundingSwap

19.ValuationofanEquitySwap

20.ChangingtheMarketPriceofRiskforVariablesThatAreNotthePricesofTraded Securities

21.HermitePolynomialsandTheirUseforIntegration

22.ValuationofaVarianceSwap

23.TheBlack,Derman,ToyModel

24.ProofthatForwardandFuturesPricesareEqualWhenInterestRatesAreConstant

25.ACash-FlowMappingProcedure

26.ABinomialMeasureofCreditCorrelation

27.CalculationofMomentsforValuingAsianOptions

28.CalculationofMomentsforValuingBasketOptions

29.ProofofExtensionstoIto’sLemma

30.TheReturnofaSecurityDependentonMultipleSourcesofUncertainty

31.PropertiesofHo–LeeandHull–WhiteInterestRateModels

Preface

Itissometimeshardtobelievethattheﬁrsteditionofthisbookwasonly330pagesand 13chapterslong!Thebookhasgrownandbeenadaptedtokeepupwiththefastpace ofchangeinderivativesmarkets.

Likeearliereditions,thebookservesseveralmarkets.Itisappropriateforgraduate coursesinbusiness,economics,financialmathematics,andfinancialengineering.Itcan beusedonadvancedundergraduatecourseswhenstudentshavegoodquantitative skills.Also,manypractitionerswhoareinvolvedinderivativesmarketsfindthebook useful.Wearedelightedthathalfthepurchasersofthebookareanalysts,traders,and otherderivativesprofessionals.

Oneofthekeydecisionsthatmustbemadebyanauthorwhoiswritingintheareaof derivativesconcernstheuseofmathematics.Ifthelevelofmathematicalsophistication istoohigh,thematerialislikelytobeinaccessibletomanystudentsandpractitioners.If itistoolow,someimportantissueswillinevitablybetreatedinarathersuperﬁcialway. Wehavetriedtobeparticularlycarefulaboutthewaybothmathematicsandnotation havebeenusedinthebook.Nonessentialmathematicalmaterialhasbeeneither eliminatedorincludedinend-of-chapterappendicesorintechnicalnotesonthewebsite www.rotman.utoronto.ca/ hull .Conceptsthatarelikelytobenewtomanyreaders havebeenexplainedcarefully,andmanynumericalexampleshavebeenincluded.

Thebookassumesthatthereaderhastakenanintroductorycourseinﬁnanceandan introductorycourseinprobabilityandstatistics.Nopriorknowledgeofoptions, futurescontracts,swaps,andsoon,isassumed.Itisnotthereforenecessaryfor studentstotakeanelectivecourseininvestmentspriortotakingacoursebasedon thisbook.

Options,FuturesandOtherDerivatives canbeusedforafirstcourseinderivativesor foramoreadvancedcourse.Therearemanydifferentwaysitcanbeusedinthe classroom.Instructorsteachingafirstcourseinderivativesarelikelytowanttospend mostclassroomtimeonthefirsthalfofthebook.Instructorsteachingamoreadvanced coursewillfindthatmanydifferentcombinationsofchaptersinthesecondhalfofthe bookcanbeused.ThematerialinChapter37workswellattheendofeitheran introductoryoranadvancedcourse.

What ’sNewintheTenthEdition?

Materialhasbeenupdatedandimproved.OISdiscountingisnowusedthroughoutthe book.Thismakesthepresentationofthematerialmorestraightforwardandmore theoreticallyappealing.Thevaluationofinstrumentssuchasswapsandforwardrate agreementsrequires(a)forwardratesfortherateusedtocalculatepayments(usually LIBOR)and(b)therisk-freezerocurveusedfordiscounting(usuallytheOISzero

curve).Themethodspresentedcanbeextendedtosituationswherepaymentsare dependentonanyriskyrate.

Thechangesinthetentheditionincludethefollowing:

1. Arewriteofthechapteronswaps(Chapter7)toimprovepresentationand reﬂectchangingmarketpractices.

2. Anewchapter(Chapter9)onvaluationadjustments(CVA,DVA,FVA,MVA, andKVA).FinancialeconomistshavereservationsaboutFVA,MVA,andKVA (andtheseareexplained),butXVAshavebecomesuchanimportantpartof derivativesvaluationthatitisimportanttocoverthem.

3. Materialatvariouspointsinthebookonhownegativeinterestratescanbe handledinpricingmodels.Intheno-arbitrageworldthatweassumewhenvaluing derivatives,negativeratesmakenosense.Buttheyareafeatureofﬁnancial marketsinanumberofEuropeancountriesandJapanandcannotbeignored.

4. Anewchapteronequilibriummodelsofthetermstructure(Chapter31).These modelsareimportantpedagogicallyandarewidelyusedinlong-termscenario analyses.Idecidedthattheydeservedtheirownchapter.

5. MoredetailsonthecalculationofGreeklettersandsmiledynamics.

6. Morediscussionoftheexpectedshortfallmeasureandstressedriskmeasures, reﬂectingtheirincreasinguseinregulationandriskmanagement.

7. CoverageoftheSABRmodel.

8. UpdatedmaterialonCCPsandtheregulationofOTCderivatives.

9. Improvedmaterialonmartingalesandmeasures,tailingthehedge,bootstrap methods,andconvertiblebonds.

10. Updatingofexamplestoreﬂectcurrentmarketconditions.

11. Newend-ofchapterproblemsandrevisionstomanyoldend-of-chapterproblems.

12. NewversionofthesoftwareDerivaGem.

Software

DerivaGem4.00isincludedwiththisbook.Asbefore,thisconsistsoftwoExcel applications:the OptionsCalculator andthe ApplicationsBuilder.TheOptionsCalculator consistsofeasy-to-usesoftwareforvaluingawiderangeofoptions.TheApplications BuilderconsistsofanumberofExcelfunctionsfromwhichuserscanbuildtheirown applications.Itincludesanumberofsampleapplicationsandenablesstudentstoexplore thepropertiesofoptionsandnumericalproceduresmoreeasily.Italsoallowsmore interestingassignmentstobedesigned.

DerivaGem4.00allowsanumberofnewmodels(Heston,SABR,Bacheliernormal, anddisplacedlognormal)tobeusedforvaluation.Thesoftwareisdescribedmorefully attheendofthebook.Youcandownloadthesoftwarefrom: www.pearsoned.co.in/hull10e.

Acknowledgments

Manypeoplehaveplayedapartinthedevelopmentofsuccessiveeditionsofthisbook. Indeed,thelistofpeoplewhohaveprovidedmewithfeedbackonthebookisnowso longthatitisnotpossibletomentioneveryone.Wehavebeneﬁtedfromtheadviceof manyacademicswhohavetaughtfromthebookandfromthecommentsofmany derivativespractitioners.Inparticular,wewouldliketothankthestudentsonour coursesattheUniversityofTorontoandattheIndianInstituteofManagement Bangalorewhohavemademanysuggestionsonhowthematerialcanbeimproved. EddieMizzifromTheGeometricPressdidanexcellentjobeditingtheﬁnalmanuscript andhandlingpagecomposition.EmilioBaronefromLuissGuidoCarliUniversityin Rome,PrakashApteandMRRaofromIndianInstituteofManagementBangalore andIndianSchoolofBusinessHyderabadprovidedmanydetailedcomments.

AlanWhite,acolleagueattheUniversityofToronto,deservesaspecialacknowledgment.AlanandJohnhasbeencarryingoutjointresearchandconsultingintheareasof derivativesandriskmanagementforover30years,spendingalotoftimediscussingkey issues;alotusandme(Sankarshan)includedhavestartedlearningaboutDerivatives fromworksofAlanandJohn.Manyofthenewideasinthisbook,andmanyofthenew waysusedtoexplainoldideas,areasmuchAlan’sasours.Alanhasdonemostofthe developmentworkontheDerivaGemsoftware.

SpecialthanksareduetomanypeopleatPearson,particularlyDonnaBattista, NeerajBhalla,NicoleSuddeth,AlisonKalil,PradeepKumarBhattacharjee,and Purushothaman,C.fortheirenthusiasm,adviceandencouragement.

Wewelcomecommentsonthebookfromreaders.Oure-mailaddressare:

hull@rotman.utoronto.ca Sankarshan.basu@iimb.ac.in

JohnHull SankarshanBasu

AbouttheAuthor

JohnHull istheMapleFinancialProfessorofDerivativesandRiskManagementatthe JosephL.RotmanSchoolofManagement,UniversityofToronto.Heisaninternationallyrecognizedauthorityonderivativesandriskmanagementwithmanypublicationsin thisarea.Hisworkhasanappliedfocus.In1999,hewasvotedFinancialEngineerofthe YearbytheInternationalAssociationofFinancialEngineers.Hehasactedasconsultant tomanyNorthAmerican,Japanese,andEuropeanﬁnancialinstitutions.Hehaswon manyteachingawards,includingUniversityofToronto’sprestigiousNorthropFrye award.

AbouttheAdapter

SankarshanBasu isaProfessorintheFinanceandAccountingAreaattheIndian InstituteofManagementBangalore(IIMB).Currently,heisalsotheChairpersonof thePostGraduateProgrammeinPublicPolicyandManagement.Hehasearlierbeen theChairpersonofCareerDevelopmentServicesandAlumniRelationsatIIMB.

SankarshanhasaB.Sc.withhonoursinStatisticsfromPresidencyCollege,Calcutta, M.Sc.inStatisticsfromtheIndianInstituteofTechnology,KanpurMadras,aPh.D. fromtheLondonSchoolofEconomicsandPoliticalScience,UK.Hisprimaryresearch andteachinginterestsareinfinancialmarketsandquantitativefinance,particularly derivativesandfixedincomesecuritiesandinsuranceandpensionissues.

PriortojoiningIIMB,SankarshanhasalsoworkedwithICICILtd.(nowICICI BankLtd.),aswellasbeenateachingfacultyatLondonSchoolofEconomicsand PoliticalScienceandHeriotWattUniversity,Edinburgh,UK.Sankarshanhasalso beenavisitingprofessoratUniversityofTwente,Netherlands,GothenburgUniversity, Sweden,ESCP,Paris,CFVG,HoChiMinCityandHanoi,VietnamandAsian InstituteofTechnology,Bangkok.

Sankarshanisactiveinteaching,consultingaswellaswellasresearch.Hehas publishedanumberofpapers,bookchaptersaswellastwobooks.Healsoserves ontheboardsofacoupleofcompanies.

Introduction

Inthelast40years,derivativeshavebecomeincreasinglyimportantinfinance.Futures andoptionsareactivelytradedonmanyexchangesthroughouttheworld.Many differenttypesofforwardcontracts,swaps,options,andotherderivativesareentered intobyfinancialinstitutions,fundmanagers,andcorporatetreasurersintheover-thecountermarket.Derivativesareaddedtobondissues,usedinexecutivecompensation plans,embeddedincapitalinvestmentopportunities,usedtotransferrisksinmortgages fromtheoriginallenderstoinvestors,andsoon.Wehavenowreachedthestagewhere thosewhoworkinfinance,andmanywhoworkoutsidefinance,needtounderstand howderivativeswork,howtheyareused,andhowtheyarepriced.

Whetheryoulovederivativesorhatethem,youcannotignorethem!Thederivatives marketishuge—muchbiggerthanthestockmarketwhenmeasuredintermsof underlyingassets.Thevalueoftheassetsunderlyingoutstandingderivativestransactionsisseveraltimestheworldgrossdomesticproduct.Asweshallseeinthischapter, derivativescanbeusedforhedgingorspeculationorarbitrage.Theycanbeusedto transferawiderangeofrisksintheeconomyfromoneentitytoanother.

A derivative canbedeﬁnedasaﬁnancialinstrumentwhosevaluedependson(or derivesfrom)thevaluesofother,morebasic,underlyingvariables.Veryoftenthe variablesunderlyingderivativesarethepricesoftradedassets.Astockoption,for example,isaderivativewhosevalueisdependentonthepriceofastock.However, derivativescanbedependentonalmostanyvariable,fromthepriceofhogstothe amountofsnowfallingatacertainskiresort.

Sincetheﬁrsteditionofthisbookwaspublishedin1988therehavebeenmany developmentsinderivativesmarkets.Thereisnowactivetradingincreditderivatives, electricityderivatives,weatherderivatives,andinsurancederivatives.Manynewtypes ofinterestrate,foreignexchange,andequityderivativeproductshavebeencreated. Therehavebeenmanynewideasinriskmanagementandriskmeasurement.Capital investmentappraisalnowofteninvolvestheevaluationofwhatareknownas real options.Manynewregulationshavebeenintroducedcoveringover-the-counterderivativesmarkets.Thebookhaskeptupwithallthesedevelopments.

Derivativesmarketshavecomeunderagreatdealofcriticismbecauseoftheirrolein thecreditcrisisthatstartedin2007.Derivativeproductswerecreatedfromportfoliosof riskymortgagesintheUnitedStatesusingaprocedureknownassecuritization.Manyof theproductsthatwerecreatedbecameworthlesswhenhousepricesdeclined.Financial