《金融衍生品數學模型》

《金融衍生品數學模型(第2版)》旨在運用金融工程方法講述模型衍生品背後的理論，作為重點介紹了對大多數衍生證券很常用的鞅定價原理。書中還分析了固定收入市場中的大量金融衍生品，強調了定價、對沖及其風險策略。《金融衍生品數學模型(第2版)》從著名的期權定價模型的Black-Scholes-Merton公式開始，講述衍生品定價模型和利率模型中的最新進展，解決各種形式衍生品定價問題的解析技巧和數值方法。目次：衍生品工具介紹；金融經濟和隨機計算；期權定價模型；路徑依賴期權；美國期權；定價期權的數值方案；利率模型和債券計價；利率衍生品：債券期權、LIBOR和交換產品。

基本信息

• 名稱：《金融衍生品數學模型》
• 作者：郭宇權 著
• 類別：圖書 > 金融與投資 > 金融理論
• 價格：49.00
• 語種：中文
• ISBN：9787510005503
• 出版社：世界圖書出版公司
• 頁數：530頁
• 開本：16開
• 出版時間：2010年4月1日
• 裝幀：平裝

目錄

Preface
1IntroductiontoDerivativeInstruments
1.1FinancialOptionsandTheirTradingStrategies
1.1.1TradingStrategiesInvolvingOptions
1.2RationalBoundariesforOptionValues
1.2.1EffectsofDividendPayments
1.2.2Put-CallParityRelations
1.2.3ForeignCurrencyOptions
1.3ForwardandFuturesContracts
1.3.1ValuesandPricesofForwardContracts
1.3.2RelationbetweenForwardandFuturesPrices
1.4SwapContracts
1.4.1InterestRateswaps
1.4.2CurrencySwaps
1.5Problems
2FinancialEconomicsandStochasticCalculus
2.1SinglePeriodSecuritiesModels
2.1.1DominantTradingStrategiesandLinearPricingMeasures
2.1.2arbitrageOpportunitiesandRiskNeutralProbabilityMeasures
2.1.3ValuationofContingentClaims
2.1.4PrinciplesofbinomialOptionPricingModel
2.2Filtrations，martingalesandMultiperiodModels
2.2.1InformationStructuresandFiltrations
2.2.2ConditionalExpectationsandMartingales
2.2.3StoppingTimesandStoppedProcesses
2.2.4MultiperiodSecuritiesModels
2.2.5MultiperiodBinomialModels
2.3AssetPriceDynamicsandStochasticProcesses
2.3.1RandomWalkModels
2.3.2BrownianProcesses
2.4StochasticCalculus：ItosLemmaandGirsanovsTheorem
2.4.1StochasticIntegrals
2.4.2ItosLemmaandStochasticDifferentials
2.4.3ItosProcessesandFeynman-kacRepresentationFormula
2.4.4ChangeofMeasure：Radon-NikodymDerivativeandGirsanovsTheorem.
2.5Problems
3OptionPricingModels：Blaek-Scholes-MertonFormulation
3.1Black-Scholes-MertonFormulation
3.1.1RisklessHedgingPrinciple
3.1.2DynamicReplicationStrategy
3.1.3RiskneutralityArgument
3.2MartingalePricingTheory
3.2.1EquivalentMartingaleMeasureandRiskNeutralValuation
3.2.2Black-ScholesModelRevisited
3.3Black-ScholesPricingFormulasandTheirProperties
3.3.1PricingFormulasforEuropeanOptions
3.3.2ComparativeStatics
3.4ExtendedOptionPricingModels
3.4.1OptionsonaDividend-PayingAsset
3.4.2FuturesOptions
3.4.3ChooserOptions
3.4.4CompoundOptions
3.4.5MertonsModelofRiskyDebts
3.4.6ExchangeOptions
3.4.7EquityOptionswithExchangeRateRiskExposure
3.5BeyondtheBlack-ScholesPricingFramework
3.5.1TransactionCostsModels
3.5.2Jump-DiffusionModels
3.5.3ImpliedandLocalVolatilities
3.5.4StochasticVolatilityModels
3.6Problems
4PathDependentOptions
4.1BarrierOptions
4.1.1EuropeanDown-and-OutCallOptions
4.1.2TransitionDensityFunctionandFirstPassageTimeDensity
4.1.3OptionswithDoubleBarriers
4.1.4DiscretelyMonitoredBarrierOptions
4.2lookbackOptions
4.2.1EuropeanFixedStrikeLookbackOptions
4.2.2EuropeanFloatingStrikeLookbackOptions
4.2.3MoreExoticFormsofEuropeanLookbackOptions
4.2.4DifferentialEquationFormulation
4.2.5DiscretelyMonitoredLookbackOptions
4.3AsianOptions.
4.3.1PartialDifferentialEquationFormulation
4.3.2ContinuouslyMonitoredGeometricAveragingOptions
4.3.3ContinuouslyMonitoredArithmeticAveragingOptions
4.3.4Put-CallParityandFixed-FloatingSymmetryRelations
4.3.5FixedStrikeOptionswithDiscreteGeometricAveraging
4.3.6FixedStrikeOptionswithDiscreteArithmeticAveraging
4.4Problems
5AmericanOptions
5.1CharacterizationoftheOptimalExerciseBoundaries
5.1.1AmericanOptionsonanAssetPayingDividendYield
5.1.2SmoothPastingCondition.
5.1.3OptimalExerciseBoundaryforanAmericanCall
5.1.4Put-CallSymmetryRelations.
5.1.5AmericanCallOptionsonanAssetPayingSingleDividend
5.1.6One-DividendandMultidividendAmericanPutOptions
5.2PricingFormulationsofAmericanOptionPricingModels
5.2.1LinearComplementarityFormulation
5.2.2OptimalStoppingProblem
5.2.3IntegralRepresentationoftheEarlyExercisePremium
5.2.4AmericanBarrierOptions
5.2.5AmericanLookbackOptions
5.3AnalyticApproximationMethods
5.3.1CompoundOptionApproximationMethod
5.3.2NumericalSolutionoftheIntegralEquation
5.3.3QuadraticApproximationMethod
5.4OptionswithVoluntaryResetRights
5.4.1ValuationoftheShoutFloor
5.4.2Reset-StrikePutOptions
5.5Problems
6NumericalSchemesforPricingOptions
6.1LatticeTreeMethods
6.1.1BinomialModelRevisited
6.1.2ContinuousLimitsoftheBinomialModel
6.1.3DiscreteDividendModels
6.1.4EarlyExerciseFeatureandCallableFeature
6.1.5TrinomialSchemes
6.1.6ForwardShootingGridMethods
6.2FiniteDifferenceAlgorithms
6.2.1ConstructionofExplicitSchemes
6.2.2ImplicitSchemesandTheirImplementationIssues
6.2.3FrontFixingMethodandPointRelaxationTechnique
6.2.4TruncationErrorsandOrderofConvergence
6.2.5NumericalStabilityandOscillationPhenomena
6.2.6NumericalApproximationofAuxiliaryConditions
6.3MonteCarloSimulation
6.3.1VarianceReductionTechniques
6.3.2LowdiscrepancySequences
6.3.3ValuationofAmericanOptions
6.4Problems
7InterestRateModelsandBondPricing
7.1BondPricesandInterestRates
7.1.1BondPricesandYieldCurves
7.1.2ForwardRateAgreement，BondForwardandVanillaSwap
7.1.3ForwardRatesandShortRates
7.1.4BondPricesunderDeterministicInterestRates
7.2One-FactorShortRateModels
7.2.1ShortRateModelsandBondPrices
7.2.2VasicekMeanReversionModel
7.2.3Cox-Ingersoll-RossSquareRootDiffusionModel
7.2.4GeneralizedOne-FactorShortRateModels
7.2.5CalibrationtoCurrentTermStructuresofBondPrices
7.3MultifactorInterestRateModels
7.3.1ShortRate/LongRateModels
7.3.2StochasticVolatilityModels
7.3.3AffineTermStructureModels
7.4Heath-Jarrow-MortonFramework
7.4.1ForwardRateDriftCondition
7.4.2ShortRateProcessesandTheftMarkovianCharacterization
7.4.3ForwardLIBORProcessesunderGanssianHIMFramework
7.5Problems
8InterestRateDerivatives：BondOptions，LIBORandSwapProducts
8.1ForwardMeasureandDynamicsofForwardPrices
8.1.1ForwardMeasure
8.1.2PricingofEquityOptionsunderStochasticInterestRates
8.1.3FuturesProcessandFutures-ForwardPriceSpreadi
8.2BondOptionsandRangeNotes
8.2.1OptionsonDiscountBondsandCoupon-BearingBonds
8.2.2RangeNotes
8.3CapsandLIBORMarketModels
8.3.1PricingofCapsundergaussianHJMFramework
8.3.2BlackFormulasandLIBORMarketModels
8.4SwapProductsandSwaptions
8.4.1ForwardSwapRatesandSwapMeasure
8.4.2ApproximatePricingofSwaptionunderLognormalLIBORMarketModel
8.4.3Cross-CurrencySwaps
8.5Problems
References
AuthorIndex
SubjectIndex

前言

Inthepastthreedecades，wehavewitnessedthephenomenalgrowthinthetradingoffinancialderivativesandstructuredproductsinthefinancialmarketsaroundtheglobeandthesurgeinresearchonderivativepricingtheory，cadingfinancialinstitutionsarehiringgraduateswithasciencebackgroundwhocanuseadvancedanalyricalandnumericaltechniquestopricefinancialderivativesandmanageportfoliorisks，aphenomenoncoinedasRocketScienceonWallStreet.TherearenowmorethanahundredMasterleveldegreedprogramsinFinancialEngineering/QuantitativeFinance/ComputationalFinanceindifferentcontinents.Thisbookiswrittenasanintroductorytextbookonderivativepricingtheoryforstudentsenrolledinthesedegreeprograms.Anotheraudienceofthebookmayincludepractitionersinquantitativeteamsinfinancialinstitutionswhowouldliketoacquiretheknowledgeofoptionpricingtechniquesandexplorethenewdevelopmentinpricingmodelsofexoticstructuredderivatives.Thelevelofmathematicsinthisbookistailoredtoreaderswithpreparationattheadvancedundergraduatelevelofscienceandengineeringmajors，inparticular，basicproficienciesinprobabilityandstatistics，differentialequations，numericalmethods，andmathematicalanalysis.Advanceknowledgeinstochasticprocessesthatarerelevanttothemartingalepricingtheory，likestochasticdifferentialcalculusandtheoryofmartingale，areintroducedinthisbook.
ThecornerstonesofderivativepricingtheoryaretheBlack-Scholes-Mertonpricingmodelandthemartingalepricingtheoryoffinancialderivatives.Therenownedriskneutralvaluationprinciplestatesthatthepriceofaderivativeisgivenbytheexpectationofthediscountedterminalpayoffundertheriskneutralmeasure，inaccordancewiththepropertythatdiscountedsecuritypricesaremartingalesunderthismeasureinthefinancialworldofabsenceofarbitrageopportunities.Thissecondeditionpresentsasubstantialrevisionofthefirstedition.Theneweditionpresentsthetheorybehindmodelingderivatives，withastrongfocusonthemartingalepricingprinciple.Thecontinuoustimemartingalepricingtheoryismotivatedthroughtheanalysisoftheunderlyingfinancialeconomicsprincipleswithinadiscretetimeframework.Awiderangeoffinancialderivativescommonlytradedintheequityandfixedincomemarketsareanalyzed，emphasizingontheaspectsofpricing，hedging，andtheirriskmanagement.StartingfromtheBlack-Scholes-Mertonformulationoftheoptionpricingmodel，readersareguidedthroughthebookonthenewadvancesinthestate-of-the-artderivativepricingmodelsandinterestratemodels.Bothanalytictechniquesandnumericalmethodsforsolvingvarioustypesofderivativepricingmodelsareemphasized.Alargecollectionofclosedformpriceformulasofvariousexoticpathdependentequityoptions（likebarrieroptions，lookbackoptions，Asianoptions，andAmericanoptions）andfixedincomederivativesaredocumented.