Table Of ContentFinancial Engineering and Arbitrage
in the Financial Markets
ToBritt,Elsa,Ethan,andilly
Financial Engineering and Arbitrage
in the Financial Markets
Robert Dubil
A John Wiley & Sons, Ltd., Publication
Thiseditionfirstpublished2011
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LibraryofCongressCataloging-in-PublicationData
Dubil,Robert.
Financialengineeringandarbitrageinthefinancialmarkets/RobertDubil.
p.cm.—(TheWileyfinanceseries)
Includesbibliographicalreferencesandindex.
ISBN978-0-470-74601-1(cloth:alk.paper)
1.Financialengineering.2.Arbitrage.3.Capitalmarket.4.Investments—Mathematics.I.Title.
HG4523.D832011
332’.041—dc23
2011017543
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN978-0-470-74601-1(hardback) ISBN978-1-119-95062-2(ebk)
ISBN978-1-119-95063-9(ebk) ISBN978-1-119-95064-6(ebk)
Setin10/12ptTimesbyAptaraInc.,NewDelhi,India
PrintedandboundbyCPIGroup(UK)Ltd,Croydon,CRO4YY
Contents
Introduction xi
1 PurposeandStructureofFinancialMarkets 1
1.1 OverviewofFinancialMarkets 1
1.2 RiskSharing 2
1.3 TransactionalStructureofFinancialMarkets 6
1.4 Arbitrage:PureVersusRelativeValue 8
1.5 FinancialInstitutions:TransformingIntermediariesvsBroker-Dealers 12
1.6 Primary(Issuance)andSecondary(Resale)Markets 13
1.7 MarketPlayers:HedgersvsSpeculators 15
1.8 PreviewoftheBook 18
PARTI RELATIVEVALUEBUILDINGBLOCKS
2 SpotMarkets 23
2.1 BondsandAnnualBondMath 23
2.1.1 Zero-CouponBond 23
2.1.2 CouponBond 25
2.1.3 AmortizingBond 27
2.1.4 FloatingRateBond 28
2.2 Intra-YearCompoundingandDay-Count 30
2.2.1 Intra-YearCompounding 30
2.2.2 Day-Count 31
2.2.3 AccruedInterest 33
2.3 TermStructureofInterestRatesandtheDiscountFactorBootstrap 34
2.3.1 TermStructure 34
2.3.2 DiscountFactorBootstrap 36
2.3.3 ValuationofanArbitraryBond 36
2.4 InterestRateRisk:DurationandConvexity 39
2.4.1 Duration 41
2.4.2 PortfolioDuration 44
2.4.3 Convexity 45
2.4.4 OtherRiskMeasures 46
vi Contents
2.5 Equity,Commodity,andCurrencyMath 47
2.5.1 Equities 48
2.5.2 Currencies 49
2.6 ShortSelling 51
2.6.1 BuyingonMargin 52
2.6.2 ShortSellinginaMarginAccount 53
2.6.3 ShortSellingofBonds 54
3 FuturesMarkets 57
3.1 FundamentalsofFuturesandForwards 57
3.2 FuturesMechanics 59
3.2.1 PhysicalCommodityFutures 59
3.2.2 InterestRateFutures 62
3.2.3 StockIndexFutures 69
3.2.4 CurrencyFuturesandForwards 70
3.3 Cash-and-CarryArbitrage 73
3.3.1 Commodities 74
3.3.2 StockIndexes 76
3.3.3 Currencies 79
3.4 FuturesNotSubjecttoCash-and-Carry 81
3.5 YieldCurveConstructionwithInterestRateFutures 84
3.5.1 CertaintyEquivalenceofEurodollarFutures 85
3.5.2 ForwardRateAgreements 86
3.5.3 BuildingSpotZeros 88
3.5.4 RecoveringtheForwards 91
3.5.5 IncludingRepoRatesintheCalculationoftheForwards 93
4 SwapMarkets 95
4.1 FundamentalsofSwaps 95
4.1.1 TheDualNatureofSwaps 96
4.1.2 ImplicationforPricingandHedging 96
4.2 InterestRateSwaps 97
4.2.1 DefinitionofanInterestRateSwap 97
4.2.2 ValuationofInterestRateSwaps 99
4.2.3 HedgingofInterestRateSwaps 101
4.3 Cross-CurrencySwaps 105
4.3.1 DefinitionofaFixed-for-FixedCross-CurrencySwap 105
4.3.2 ValuationandSettlementofCross-CurrencySwaps 107
4.3.3 Cross-CurrencySwapsasPackagesofOff-MarketFXForwards 109
4.3.4 MulticurrencyandCombinationCross-CurrencySwaps 110
4.4 Equity,Commodity,andExoticSwaps 112
4.4.1 EquitySwaps 112
4.4.2 CommoditySwaps 114
4.4.3 VolatilitySwaps 115
4.4.4 IndexPrincipalSwaps 116
Contents vii
5 OptionsonPricesandHedge-BasedValuation 119
5.1 CallandPutPayoffsatExpiry 120
5.2 CompositePayoffsatExpiry 122
5.2.1 StraddlesandStrangles 122
5.2.2 SpreadsandCombinations 123
5.3 OptionValuesPriortoExpiry 126
5.4 OptionsandForwards,RiskSharingandPut–CallParity 127
5.5 CurrencyOptions 128
5.6 BinomialOptionPricing 129
5.6.1 One-StepExamples 129
5.7 Black–ScholesModelandExtensions 141
5.7.1 Black–ScholeswithNoDividends 141
5.7.2 Dividends 142
5.7.3 OptionsonCurrencyRates 143
5.7.4 Black–ScholesDelta,Gamma,andVega 144
5.8 ResidualRiskofOptions:Gamma,Vega,andVolatility 145
5.8.1 ImpliedVolatility 147
5.8.2 VolatilitySmilesandSkews 148
5.9 AReal-LifeOptionPricingExercise 150
5.9.1 ConsistencyChecks:Put–CallParity,Black–Scholes,andBinomial 150
6 OptionsonNon-PriceVariables 155
6.1 BlackModelsForBondPriceOptions,Caps/Floors,andEuropean
Swaptions 156
6.1.1 OptionsonBondPrices 156
6.1.2 CapandFloorDefinitions 158
6.1.3 RelationshipofCapsandFloorstoFRAsandSwaps 159
6.1.4 ACapApplication 160
6.1.5 PricingofCapsandFloors 163
6.1.6 EuropeanSwaptionDefinitions 164
6.1.7 OptionstoCancelSwaps 165
6.1.8 RelationshipofSwaptionstoForwardSwaps 165
6.1.9 PricingofEuropeanSwaptions 167
6.1.10 LimitationsoftheBlackModel 168
6.2 Convexity-AdjustedModelsForLiborForwards,Quantos,andConstant
MaturitySwaps 168
6.2.1 ConvexityAdjustmentforEurodollarFutures 169
6.2.2 ConvexityAdjustmentforCMSOptions 170
6.2.3 QuantoAdjustments 171
6.3 Arbitrage-FreeInterestRateModels 172
6.3.1 ShortRateModels 173
6.3.2 TrinomialTreesandCalibration 174
6.3.3 TheHeath–Jarrow–MortonModelandtheLIBORMarketModel 176
6.3.4 BermudanSwaptionsandMultifactorModels 180
6.4 ExoticInterestRateOptions 181
viii Contents
6.4.1 PeriodicCaps 181
6.4.2 DigitalsandRanges 181
7 DefaultRiskandCreditDerivatives 183
7.1 CreditDefaultSwaps 184
7.1.1 CreditDefaultSwap 184
7.1.2 NoArbitrage:CDSvsCorporateBondSpread 185
7.1.3 BundledSingle-NameCreditDerivatives 186
7.2 AConstantDefaultProbabilityModel 190
7.3 ADeterministicCreditMigrationModel 193
7.4 APoissonModelofSingleIssuerDefault 195
7.4.1 PoissonDistribution 195
7.4.2 ASingleIssuerDefaultModel 196
7.4.3 PricingaCreditDefaultSwapinaSingleIssuerDefaultModel 198
7.5 TheDefaultCorrelationoftheReferenceIssuerandtheProtectionSeller 199
PARTII CASHFLOWENGINEERING
8 StructuredFinance 203
8.1 ASimpleClassificationofStructuredNotes 204
8.2 InterestRateandYieldCurve-BasedStructuredProducts 206
8.2.1 AnInverseFloater 206
8.2.2 ALeveragedInverseFloater 209
8.2.3 ACappedFloater 211
8.2.4 ACallable 211
8.2.5 ARangeFloater 212
8.2.6 AnIndexPrincipalSwap 212
8.3 AssetClass-LinkedNotes 213
8.3.1 Principal-ProtectedEquity-LinkedNotes 213
8.3.2 A(Rainbow)Multi-Asset-LinkedNote 216
8.3.3 Principal-At-RiskNotesandCommodity-TrackingETNs 216
8.4 InsuranceRiskStructuredProducts 219
9 Mortgage-BackedSecurities 223
9.1 MortgageFinancingBasics 224
9.2 PrepaymentRisk 226
9.3 MortgagePass-ThroughSecurities 227
9.4 CollateralizedMortgageObligations 232
9.4.1 Sequential-PayCMO 232
9.4.2 PlannedAmortizationClassCMO 233
9.4.3 Interest-only(IO)andPrincipal-only(PO)Classes 237
9.5 MulticlassandNon-VanillaCMOs 241
9.5.1 AMulticlassPACStructurewithaPACI/OandaFloater/Inverse
CouponSplit 241
9.5.2 Non-AcceleratingSeniorandAccrualTranchesinSequential
CMOs 242
Contents ix
10 CollateralizedDebtObligationsandBasketCreditDerivatives 243
10.1 CollateralizedDebtObligations 243
10.1.1 CashCDO 244
10.1.2 SyntheticCDO 246
10.2 BasketCreditDerivatives 249
10.2.1 First-to-DefaultBasket 249
10.2.2 Nth-to-DefaultBasket,ArbitrageConditions,andHedging 251
10.2.3 HedgingofBasketDerivatives 252
10.3 CopulasandtheModelingofDefaultCorrelation 252
10.3.1 AGaussianCopula 254
10.3.2 GeneralCopulaModels 255
10.4 SyntheticCDOTranchePricingandLossAnalysis 256
10.4.1 SyntheticCDORevisited 256
10.4.2 SyntheticCDOPricingandExpectedLoss 257
10.4.3 SyntheticCDO–LossRates,RatingsandtheCrisisof2008 259
10.5 CreditDerivativeIndexes 260
PARTIII THEPLAYERS
11 IndividualInvestors:ASurveyofModernInvestmentTheory 265
11.1 ABriefHistoryofInvestmentThought 266
11.2 FreeCashFlowValuationofCompanies 269
11.2.1 FreeCashFlowDefinitions 270
11.2.2 GrowthandtheDiscountingoftheCashFlows 273
11.2.3 TerminalMultipleModelsofCashFlowDiscounting 274
11.3 TheModernPortfolioTheoryandtheCAPM 276
11.3.1 DiversificationandtheEfficientFrontier 276
11.3.2 Two-FundSeparation 278
11.3.3 SystematicRiskandtheCAPM 279
11.3.4 UsingtheCAPMasaStockScreentoDiscoverAlpha 280
11.4 MultifactorIndexModels 282
11.4.1 TheFama–FrenchThree-FactorModel 283
11.4.2 TheCarhartFourthFactor:theMomentum 283
11.4.3 InternationalIndexFactors 284
11.5 FundamentalIndexing 284
11.5.1 ABriefHistoryofFundamentalIndexing 285
11.5.2 FundamentalIndexingandRebalancing 285
11.5.3 TacticalAssetAllocation 286
11.5.4 FundamentallyIndexedUSFunds 286
12 HedgeFunds:Alpha,Beta,andStrategyIndexes 287
12.1 HedgeFundStrategies 289
12.1.1 RelativeAssetValueFunds 289
12.1.2 RelativeCorporate/CreditStructure 292
12.1.3 TheoreticalRelativeValue 294
12.1.4 StatisticalRelativeValueArbitrage 296
x Contents
12.2 PortableAlphaandMarket-NeutralPlays 298
12.3 HedgeFundReplicationandStrategyIndexes 299
13 Banks:Asset-LiabilityManagement 303
13.1 BankBalanceSheetsandIncomeStatements 305
13.2 Interest-SensitiveGapManagement 313
13.3 DurationGapManagement 320
13.4 ValueatRisk 322
14 PrivateEquity,Pension,andSovereignFunds 329
14.1 PrivateEquity 329
14.1.1 InvestmentinPrivateEquity–LimitedPartnershipFunds 330
14.1.2 LeverageBuyouts 331
14.1.3 PrivateEquityLending–MezzanineCapitalandDistressedLoans 332
14.1.4 OtherFormsofPrivateEquity–PIPEs 333
14.1.5 VentureCapital 333
14.1.6 ExitStrategies–IPOsandSecondarySales 334
14.2 RiskAllocationforPensionFundsandSovereignFunds 335
14.2.1 DefinedBenefitPensionFundsandEndowments 335
14.2.2 TheRiskBudgetAllocationProcess 336
Acknowledgment 338
References 339
Index 343
Description:A whole is worth the sum of its parts. Even the most complex structured bond, credit arbitrage strategy or hedge trade can be broken down into its component parts, and if we understand the elemental components, we can then value the whole as the sum of its parts. We can quantify the risk that is hed
