Pricing and Hedging Financial Derivatives: A Guide for Practitioners

266 Pages·2013·2.54 MB·English

by  Leonardo Marroni, Irene Perdomo

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
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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
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PrintedinGreatBritainbyCPIGroup(UK)Ltd,Croydon,CR04YY
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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
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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
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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
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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
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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
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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