內容簡介
讀者對象：數學專業研究生、老師和經濟、金融的相關人員。目錄
PrefaceMotivation
Aims，readershipandBookStructure
FinalWordandAcknowledgments
DescriptionofContentsbyChapter
AbbreviationsandNotation
PartI.BASICDEFINITIONSANDNOARBITRAGE
1.DefinitionsandNotation
1.1TheBankAccountandtheShortRate
1.2Zero-CouponBondsandSpotInterestRates
1.3FundamentalInterest-RateCurves
1.4ForwardRates
1.5Interest-RateswapsandForwardSwapRates
1.6Interest-RateCaps/FloorsandSwaptions
2.No-ArbitragePricingandNumeraireChange
2.1No-ArbitrageinContinuousTime
2.2TheChange-of-NumeraireTechnique
2.3AChangeofNumeraireToolkit(Brigo&Mercurio2001c)
2.3.1Ahelpfulnotation:"DC"
2.4TheChoiceofaConvenientNumeraire
2.5TheForwardMeasure
2.6TheFundamentalPricingFormulas
2.6.1ThePricingofCapsandFloors
2.7PricingClaimswithDeferredpayoffs
2.8PricingClaimswithMultiplePayoffs
2.9ForeignMarketsandNumeraireChange
PartII.FROMSHORTRATEMODELSTOHJM
3.One-factorshort-ratemodels
3.1IntroductionandGuidedTour
3.2ClassicalTime-HomogeneousShort-RateModels
3.2.1TheVasicekModel
3.2.2TheDothanModel
3.2.3TheCox，IngersollandRoss(CIR)Model
3.2.4AffineTerm-StructureModels
3.2.5TheExponential-Vasicek(EV)Model
3.3TheHull-WhiteExtendedVasicekModel
3.3.1TheShort-RateDynamics
3.3.2BondandOptionPricing
3.3.3TheConstructionofaTrinomialTree
3.4PossibleExtensionsoftheCIRModel
3.5TheBlack-KarasinskiModel
3.5.1TheShort-RateDynamics
3.5.2TheConstructionofaTrinomialTree
3.6VolatilityStructuresinOne-FactorShort-RateModels
3.7Humped-VolatilityShort-RateModels
3.8AGeneralDeterministic-ShiftExtension
3.8.1TheBasicAssumptions
3.8.2FittingtheInitialTermStructureofInterestRates
3.8.3ExplicitFormulasforEuropeanOptions
3.8.4TheVasicekCase
3.9TheCIR++Model
3.9.1 TheConstructionofaTrinomialTree
3.9.2EarlyExercisePricingviaDynamicProgramming
3.9.3ThePositivityofRatesandFittingQuality
3.9.4MonteCarloSimulation
3.9.5JumpDiffusionCIRandCIR++models(JCIR，JCIR++)
3.10Deterministic-ShiftExtensionofLognormalModels
3.11SomeFurtherRemarksonDerivativesPricing
3.11.1PricingEuropeanOptionsonaCoupon-BearingBond
3.11.2TheMonteCarloSimulation
3.11.3PricingEarly-ExerciseDerivativeswithaTree
3.11.4AFundamentalCaseofEarlyExercise:BermudanStyleSwaptions.
3.12ImpliedCapVolatilityCurves
3.12.1TheBlackandKarasinskiModel
3.12.2TheCIR++Model
3.12.3TheExtendedExponential-VasicekModel
3.13ImpliedSwaptionVolatilitySurfaces
3.13.1TheBlackandKarasinskiModel
3.13.2TheExtendedExponential-VasicekModel
3.14AnExampleofCalibrationtoReal-MarketDataTwo-FactorShort-RateModels
4.1IntroductionandMotivation
4.2TheTwo-Additive-FactorGaussianModelG2++
4.2.1TheShort-RateDynamics
4.2.2ThePricingofaZero-CouponBond
4.2.3VolatilityandCorrelationStructuresinTwo-FactorModels
4.2.4ThePricingofaEuropeanOptiononaZero-CouponBond
4.2.5TheanalogywiththeHull-WhiteTwo-FactorModel
4.2.6TheConstructionofanApproximatingbinomialTree
4.2.7ExamplesofCalibrationtoReal-MarketData
4.3TheTwo-Additive-FactorExtendedCIR/LSModelCIR2++
4.3.1TheBasicTwo-FactorCIR2Model
432RelationshipwiththeLongstaffandSchwartzModel(LS)
4.3.3Forward-MeasureDynamicsandOptionPricingforCIR2
4.3.4TheCIR2++ModelandOptionPricing
5.TheHeath-Jarrow-Morton(HJM)Framework
5.1TheHJMForward-RateDynamics
5.2MarkovianityoftheShort-RateProcess
5.3TheRitchkenandSankarasubramanianFramework
5.4TheMercurioandMoraledaModel
PartIII.MARKETMODELS
6.TheLIBORandSwapMarketModels(LFMandLSM)
6.1Introduction
6.2MarketModels:aGuidedTour.
6.3TheLognormalForward-LIBORModel(LFM)
6.3.1SomeSpecificationsoftheinstantaneousVolatilityofForwardRates
6.3.2Forward-RateDynamicsunderDifferentNumeraires
6.4CalibrationoftheLFMtoCapsandFloorsPrices
6.4.1Piecewise-ConstantInstantaneous-VolatilityStructures
6.4.2ParametricVolatilityStructures
6.4.3CapQuotesintheMarket
6.5TheTermStructureofVolatility
6.5.1Piecewise-ConstantInstantaneousVolatilityStructures
6.5.2ParametricVolatilityStructures
6.6InstantaneousCorrelationandTerminalCorrelation
6.7SwaptiousandtheLognormalForward-SwapModel(LSM)
6.7.1SwaptionsHedging
6.7.2Cash-SettledSwaptions
6.8IncompatibilitybetweentheLFMandtheLSM
6.9TheStructureofInstantaneousCorrelations
6.9.1Someconvenientfullrankparameterizations
6.9.2Reduced-rankformulations:Rebonato'sanglesandeigen-valueszeroing
6.9.3Reducingtheangles
6.10MonteCarloPricingofSwaptionswiththeLFM
6.11MonteCarloStandardError
6.12MonteCarloVarianceReduction:ControlVariateEstimator
6.13Rank-OneAnalyticalSwaptionPrices
6.14Rank-rAnalyticalSwaptionPrices
6.15ASimplerLFMFormulaforSwaptionsVolatilities
6.16AFormulaforTerminalCorrelationsofForwardRates
6.17CalibrationtoSwaptionsPrices
6.18InstantaneousCorrelations:Inputs(HistoricalEstimation)orOutputs(FittingParameters)?
6.19Theexogenouscorrelationmatrix
6.19.1HistoricalEstimation
6.19.2Pivotmatrices
6.20ConnectingCapletandSx1-SwaptionVolatilities
6.21ForwardandSpotRatesoverNon-StandardPeriods
6.21.1DriftInterpolation
6.21.2TheBridgingTechnique
7.CasesofCalibrationoftheLIBORMarketModel
7.1InputsfortheFirstCases
7.2JointCalibrationwithPiecewise-ConstantVolatilitiesasinTABLE5
7.3JointCalibrationwithParameterizedVolatilitiesasinFormulation7
7.4ExactSwaptions"Cascade"CalibrationwithVolatilitiesasinTABLE1
7.4.1SomeNumericalResults
7.5APauseforThought
7.5.1Firstsummary
7.5.2AnautomaticfastanalyticalcalibrationofLFMtoswaptions.Motivationsandplan
7.6FurtherNumericalStudiesontheCascadeCalibrationAlgorithm
……
8.MonteCarloTestsforLFMAnalyticalApproximations
PartⅣ.THEVOLATILITYSMILF
9.IncludingtheSmileintheLFM
10.Local-VolatilityModels
11.Stochasti-VolatilityModels
12.Uncertain-ParameterModels
PartⅤ.EXAMPLESOFMARKETPAYOFFS
13.PricingDerivativesonaSingleInterest-RateCurve
14.PricingDerivativesonTwoInterest-RateCurves
PartⅥ.INFLATION
15.PricingofInflation-IndexedDerivatives
16.InflationIndexedSwaps
17.Inflation-IndexedCaplets/Floorlets
18.Calibrationtomarketdata
19.IntroducingStochasticVolatility
20.PricingHybridswithanInflationComponent
PartⅦ.CREDIT
21.IntroductionandPricingundercounterpartyRisk
22.IntensityModels
23.CDSOptionsMarketModels
PartⅧ.APPENDICES
A.OtherInterest-RateModels
B.PricingEquityDerivativesunderStochasticRates
C.ACrashIntrotoStochasticDifferentialEquationsandPoissonProcesses
D.AUsefulCalculation
E.ASecondUsefulCalculation
F.ApproximatingDiffusionswithTrees
G.TriviaandFrequentlyAskedQuestions
H.TalkingtotheTraders
References
前言
Welcomeonboardthesecondeditionofthisbookoninterestratemodels，toalloldandnewreaders.Weimmediatelysaythissecondeditionisactuallyalmostanewbook，withfourhundredfiftyandmorenewpagesonsmilemodeling，calibration，inflation，creditderivativesandcounterpartyrisk.Asexplainedintheprefaceofthefirstedition，theideaofwritingthisbookoninterest-ratemodelingcrossedourmindsinearlysummer1999.Weboththoughtofdifferentversionsbefore，butitwasinBancaIMIthatthischallengingprojectbeganmaterially，ifnotspiritually(moredetailsaregiveninthetriviaAppendixG).Atthetimeweweregiventhetaskofstudying
anddevelopingfinancialmodelsforthepricingandhedgingofabroadrangeofderivatives，andwewereinvolvedinmedium/long-termprojects.
ThefirstyearsinBancaIMIsawuswritingalotofreportsandmaterialonouractivityinthebank，tothepointthatmuchofthosestudiesendedupinthefirsteditionofthebook，printedin2001.
Inthefirsteditionprefacewedescribedmotivation，explainedwhatkindoftheoryandpracticeweweregoingtoaddress，illustratedtheaimandreadershipofthebook，togetherwithitsstructureandotherconsiderations.Wedosoagainnow，clearlyupdatingwhatwewrotein2001.
