Table Of Content

JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm Pricing and Hedging Financial Derivatives A Guide for Practitioners Leonardo Marroni and Irene Perdomo JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm Thiseditionfirstpublished2014 ©2014JohnWiley&Sons,Ltd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyfor permissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inany formorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUK Copyright,DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileypublishesinavarietyofprintandelectronicformatsandbyprint-on-demand.Somematerialincludedwith standardprintversionsofthisbookmaynotbeincludedine-booksorinprint-on-demand.Ifthisbookrefersto mediasuchasaCDorDVDthatisnotincludedintheversionyoupurchased,youmaydownloadthismaterialat http://booksupport.wiley.com.FormoreinformationaboutWileyproducts,visitwww.wiley.com. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnamesand productnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheir respectiveowners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparing thisbook,theymakenorepresentationsorwarrantieswiththerespecttotheaccuracyorcompletenessofthe contentsofthisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessforaparticular purpose.Itissoldontheunderstandingthatthepublisherisnotengagedinrenderingprofessionalservicesand neitherthepublishernortheauthorshallbeliablefordamagesarisingherefrom.Ifprofessionaladviceorother expertassistanceisrequired,theservicesofacompetentprofessionalshouldbesought. LibraryofCongressCataloging-in-PublicationData Marroni,Leonardo Pricingandhedgingfinancialderivatives:aguideforpractitioners/LeonardoMarroni,IrenePerdomo. pagescm.—(TheWileyfinanceseries) Includesbibliographicalreferencesandindex. ISBN978-1-119-95371-5(hardback) 1.Derivativesecurities—Prices. 2.Hedging(Finance) I.Perdomo,Irene II.Title. HG6024.A3M3672013 332.64′57–dc23 2013021914 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN978-1-119-95371-5(hardback)ISBN978-1-119-95457-6(ebk) ISBN978-1-119-95458-3(ebk)ISBN978-1-118-77321-5(ebk) Coverimage:Shutterstock Setin10/12ptTimesbyAptaraInc.,NewDelhi,India PrintedinGreatBritainbyCPIGroup(UK)Ltd,Croydon,CR04YY JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm Contents Preface ix Acknowledgements xi 1 AnIntroductiontotheMajorAssetClasses 1 1.1 Equities 1 1.1.1 Introduction 1 1.1.2 Pricingequities 2 1.1.3 Fundamentalanalysis 2 1.1.4 Technicalanalysis 3 1.1.5 Quantitativeanalysis 3 1.1.6 Theequityriskpremiumandthepre-FOMCannouncementdrift 5 1.2 Commodities 5 1.2.1 Introduction 5 1.2.2 Hedging 6 1.2.3 Backwardationandcontango 7 1.2.4 Investmentincommodities 9 1.2.5 Commodityfundamentals 10 1.2.6 Super-cyclesincommodityprices 11 1.2.7 Futureregulation 12 1.3 FixedIncome 12 1.3.1 Introduction 12 1.3.2 Creditrisk 13 1.3.3 Theempiricalpatternofyieldcurvemoves 13 1.3.4 Modellinginterestratemovements 14 1.3.5 Modellingtherisksofdefault 14 1.4 ForeignExchange 15 1.4.1 Introduction 15 1.4.2 Howforeignexchangeratesarequoted 16 Summary 17 2 Derivatives:Forwards,FuturesandSwaps 19 2.1 Derivatives 19 JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm iv Contents 2.2 ForwardContracts 20 2.2.1 Definition 20 2.2.2 Payoffsofforwardcontracts 21 2.2.3 Forwardpriceversusdeliveryprice 23 2.3 FuturesContracts 24 2.4 CalculatingImpliedForwardPricesandValuingExistingForwardContracts 26 2.4.1 Calculatingimpliedforwardpricesonequities 26 2.4.2 Calculatingimpliedforwardpricesonforeignexchangerates 29 2.4.3 Calculatingimpliedforwardpricesoncommodities 31 2.4.4 Valuingexistingforwardcontracts 34 2.5 PricingFuturesContracts 34 2.6 Swaps 35 2.6.1 Introduction 35 2.6.2 Interestrateswaps 36 2.6.3 Commodityswaps 41 2.6.4 Commodityswapvaluation 44 2.6.5 Commodityswapswithvariablenotionalandprice 46 2.6.6 Currencyswaps 46 2.6.7 Equityswaps 48 Summary 49 3 Derivatives:OptionsandRelatedStrategies 51 3.1 CallOptions 51 3.1.1 Definition 51 3.1.2 Examples 52 3.1.3 ScenarioanalysisfortheS&P500Indexcalloption 53 3.2 PutOptions 55 3.2.1 Definition 55 3.2.2 Examples 55 3.2.3 Scenarioanalysisforputoptions 56 3.3 BoundaryConditionsforCallandPutOptionsPrices 58 3.3.1 Introductionandbasicnotation 58 3.3.2 Acalloptioncannotbeworthmorethanthepriceofthe underlyingasset 59 3.3.3 Thepriceofaputoptioncannotbehigherthanthepresentvalue ofthestrikeprice,K 60 3.3.4 Lowerboundariesforcalloptionsonnon-dividendpayingstocks 60 3.3.5 Lowerboundariesforputoptionsonnon-dividendpayingstocks 61 3.4 Put–CallParity 61 3.5 Swaptions 63 3.6 OptionsStrategies 64 3.6.1 Introductiontooptionstrategies 64 3.6.2 Optionspreads 65 3.6.3 Directionalstrategiesusingverticalspreads 65 3.6.4 Riskreversalandcollars 69 3.6.5 Volatilitystrategieswithputsandcalls 70 Summary 76 JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm Contents v 4 BinomialOptionPricing 77 4.1 One-PeriodBinomialTree:ReplicationApproach 77 4.2 Risk-NeutralValuation 83 4.2.1 Introductiontorisk-neutralvaluation 83 4.2.2 Analternativewaytothinkoftheoptionprice 84 4.2.3 Risk-neutralprobabilities 85 4.3 Two-PeriodBinomialTree:ValuingBackDowntheTree 85 4.4 TheBinomialTree:AGeneralization 89 4.5 EarlyExerciseandAmericanOptions 90 4.6 VolatilityCalibration 90 Summary 92 5 TheFundamentalsofOptionPricing 93 5.1 IntrinsicValueandTimeValueofanOption 93 5.1.1 Introductionanddefinitions 93 5.1.2 Jensen’sinequality 94 5.1.3 Timevalueofanoption 95 5.2 WhatisVolatilityandWhyDoesitMatter? 95 5.3 MeasurementofRealizedVolatilityandCorrelation 97 5.4 OptionPricingintheBlack–ScholesFramework 99 5.5 TheOptionDeltaandtheReplicationoftheOptionPayoff 100 5.6 OptionReplication 102 5.7 OptionReplication,Risk-NeutralValuationandDeltaHedgingRevisited 104 5.8 OptionsonDividendPayingAssets 106 5.9 OptionsonFutures:TheBlackModel 107 5.10 MonteCarloPricing 108 5.10.1 IntroductiontotheMonteCarlotechnique 108 5.10.2 GenerationofaMonteCarlopath 110 5.11 OtherPricingTechniques 112 5.11.1 Partialdifferentialequation 112 5.11.2 Binomial/trinomialtreepricing 113 5.12 PricingTechniquesSummary 113 5.13 TheExcelSpreadsheet“OptionReplication” 114 5.13.1 Introductionanddescriptionofthespreadsheet 114 5.13.2 Whythereplicationisnotperfect 117 Summary 117 6 ImpliedVolatilityandtheGreeks 121 6.1 ImpliedVolatility 121 6.2 TheGreeks 123 6.3 DeltaanditsDynamics 123 6.3.1 Definitionandcalculation 123 6.3.2 Thedynamicsofdelta 125 6.4 GammaanditsDynamics 127 6.5 VegaanditsDynamics 132 6.6 ThetaanditsDynamics 136 6.6.1 Definitionandcalculation 136 JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm vi Contents 6.6.2 Gammaversustheta:Anequilibriumattheheartofoptionpricing 138 6.6.3 Dynamicsoftheta 140 6.7 Rho 142 6.8 OptionTrading 143 6.8.1 Takingapositiononimpliedvolatilityoronimpliedversus realizedvolatility 143 6.8.2 Takingapositionontheterminalpayofforre-hedgingwitha certainfrequency 144 6.9 SomeAdditionalRemarks(inQ&AFormat) 146 6.10 AnExampleoftheBehaviourofImpliedVolatility:EUR/USDRateand S&P500in2010–2012 147 Summary 148 7 VolatilitySmileandtheGreeksofOptionStrategies 151 7.1 TheVolatilitySmile–WhyistheImpliedVolatilityNotFlatAcross DifferentStrikes? 151 7.2 The“StickyDelta”and“StickyStrike”ApproachestoDescribing VolatilitySmile 153 7.3 TheVolatilityTermStructure–WhyistheImpliedVolatilityNotFlat AcrossDifferentExpiries? 155 7.4 TheVolatilitySurface–CombiningSmileandTermStructure 156 7.5 AnalysingtheGreeksofCommonOptionStrategies 158 7.5.1 Verticalcallorputspreads 158 7.5.2 Straddlesandstrangles 162 7.5.3 Riskreversals 163 7.5.4 Butterflies 165 7.5.5 Butterfliesandvolatilityconvexity 168 7.6 SomeAdditionalRemarksonStraddles,RiskReversalsandButterflies 170 7.7 VegaHedgingisNotJustSimplyOffsettingOverallVegaExposure 171 7.8 HedgingVolatilityRisk:ABriefIntroductionoftheVanna–Volga Approach 172 7.9 TheVolatilitySmile–OneStepFurther 173 7.9.1 Introduction 173 7.9.2 Whyandhowtobuildasmile 173 7.9.3 Smilearbitrage 175 7.9.4 Volatilitysurface 176 7.9.5 Volatilitytimedependenceinforward-basedassets 176 7.9.6 Modelsofforward-basedassetvolatilities 178 7.9.7 Calibratingamodelofforward-basedassetvolatilities 178 7.10 PricingExoticOptions 178 7.11 DifferentTypesofVolatility 179 7.11.1 Volatilitiesdiscussedsofar 179 7.11.2 Forward-startingvolatility 179 7.11.3 Localvolatility 181 7.11.4 Thelimitsoflocalvolatility 181 7.11.5 Stochasticvolatilitymodels 182 7.11.6 Local-stochasticvolatilitymodels 183 Summary 184 JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm Contents vii 8 ExoticDerivatives 185 8.1 ExoticDerivativeswithFixedPayoffs 185 8.1.1 Europeandigitaloptions 185 8.1.2 Onetouchandnotouchoptions 185 8.1.3 Combinationsoffixedpayoffoptions 187 8.2 OtherCommonExoticDerivatives 188 8.2.1 Barrieroptions 188 8.2.2 Asianoptions 190 8.3 EuropeanDigitalOptions:PricingandGreeks 191 8.3.1 PricingEuropeandigitaloptions 191 8.3.2 TheGreeksofadigitaloption 194 8.3.3 Incorporatingvolatilityskewintothepriceofa digitaloption 196 8.4 OtherExoticOptions:PricingandGreeks 200 8.4.1 Pricingcommonbarrieroptions 200 8.4.2 Greeksofcommonbarrieroptions 202 8.4.3 GreeksofAsianoptions 208 Summary 208 9 Multi-AssetDerivatives 209 9.1 BasketOptions 209 9.1.1 BasketoptiondefinitionandGreeks 209 9.1.2 Cross-gammaandcorrelationrevisited 210 9.2 Best-ofandWorst-ofOptions 211 9.2.1 Best-ofandworst-ofdefinitions 211 9.2.2 ThepriceandtheGreeksofbest-ofandworst-ofoptions 214 9.2.3 Best-ofcall 214 9.2.4 Best-ofput 215 9.2.5 Worst-ofcall 218 9.2.6 Worst-ofput 219 9.2.7 Cross-gammaandcorrelationrevisited(again...) 221 9.3 QuantoDerivatives 222 9.4 “Compo”Derivatives 225 Summary 227 10 StructuredProducts 229 10.1 Definition 229 10.2 CommonFeatures 229 10.3 PrincipalProtection 230 10.4 TheBenefittotheIssuer 231 10.5 RedemptionAmountsandParticipation 232 10.6 PrincipalatRisk:EmbeddingaShortOption 234 10.7 MoreComplicatedPayoffs 235 10.7.1 “Sharkfin”notes 235 10.7.2 Reverseconvertiblenotes 236 10.7.3 Rangeaccrualnotes 236 10.7.4 Auto-callablenotes 237 JWBK593-fm JWBK593-Marroni Printer:YettoCome October1,2013 6:53 Trim:244mm×170mm viii Contents 10.8 Auto-CallableNote:PricingandRiskProfile 238 10.8.1 Pricing 238 10.8.2 Riskprofile 239 10.9 OneStepForward:TheWorst-ofDigitalNote 240 10.10 AReal-LifeExampleofStructuredProduct 241 10.11 LiquidityandExchange-TradedNotes(ETNs) 242 Summary 243 Index 245