《金融衍生品数学模型(第2版)》旨在运用金融工程方法讲述模型衍生品背后的理论，作为重点介绍了对大多数衍生证券很常用的鞅定价原理。书中还分析了固定收入市场中的大量金融衍生品，强调了定价、对冲及其风险策略。《金融衍生品数学模型(第2版)》从著名的期权定价模型的Black-Scholes-Merton公式开始，讲述衍生品定价模型和利率模型中的最新进展，解决各种形式衍生品定价问题的解析技巧和数值方法。目次：衍生品工具介绍；金融经济和随机计算；期权定价模型；路径依赖期权；美国期权；定价期权的数值方案；利率模型和债券计价；利率衍生品：债券期权、LIBOR和交换产品。 Preface1IntroductiontoDerivativeInstruments1.1FinancialOptionsandTheirTradingStrategies1.1.1TradingStrategiesInvolvingOptions1.2RationalBoundariesforOptionValues1.2.1EffectsofDividendPayments1.2.2Put-CallParityRelations1.2.3ForeignCurrencyOptions1.3ForwardandFuturesContracts1.3.1ValuesandPricesofForwardContracts1.3.2RelationbetweenForwardandFuturesPrices1.4SwapContracts1.4.1InterestRateSwaps1.4.2CurrencySwaps1.5Problems2FinancialEconomicsandStochasticCalculus2.1SinglePeriodSecuritiesModels2.1.1DominantTradingStrategiesandLinearPricingMeasures2.1.2ArbitrageOpportunitiesandRiskNeutralProbabilityMeasures2.1.3ValuationofContingentClaims2.1.4PrinciplesofBinomialOptionPricingModel2.2Filtrations，MartingalesandMultiperiodModels2.2.1InformationStructuresandFiltrations2.2.2ConditionalExpectationsandMartingales2.2.3StoppingTimesandStoppedProcesses2.2.4MultiperiodSecuritiesModels2.2.5MultiperiodBinomialModels2.3AssetPriceDynamicsandStochasticProcesses2.3.1RandomWalkModels2.3.2BrownianProcesses2.4StochasticCalculus：ItosLemmaandGirsanovsTheorem2.4.1StochasticIntegrals2.4.2ItosLemmaandStochasticDifferentials2.4.3ItosProcessesandFeynman-KacRepresentationFormula2.4.4ChangeofMeasure：Radon-NikodymDerivativeandGirsanovsTheorem.2.5Problems3OptionPricingModels：Blaek-Scholes-MertonFormulation3.1Black-Scholes-MertonFormulation3.1.1RisklessHedgingPrinciple3.1.2DynamicReplicationStrategy3.1.3RiskNeutralityArgument3.2MartingalePricingTheory3.2.1EquivalentMartingaleMeasureandRiskNeutralValuation3.2.2Black-ScholesModelRevisited3.3Black-ScholesPricingFormulasandTheirProperties3.3.1PricingFormulasforEuropeanOptions3.3.2ComparativeStatics3.4ExtendedOptionPricingModels3.4.1OptionsonaDividend-PayingAsset3.4.2FuturesOptions3.4.3ChooserOptions3.4.4CompoundOptions3.4.5MertonsModelofRiskyDebts3.4.6ExchangeOptions3.4.7EquityOptionswithExchangeRateRiskExposure3.5BeyondtheBlack-ScholesPricingFramework3.5.1TransactionCostsModels3.5.2Jump-DiffusionModels3.5.3ImpliedandLocalVolatilities3.5.4StochasticVolatilityModels3.6Problems4PathDependentOptions4.1BarrierOptions4.1.1EuropeanDown-and-OutCallOptions4.1.2TransitionDensityFunctionandFirstPassageTimeDensity4.1.3OptionswithDoubleBarriers4.1.4DiscretelyMonitoredBarrierOptions4.2LookbackOptions4.2.1EuropeanFixedStrikeLookbackOptions4.2.2EuropeanFloatingStrikeLookbackOptions4.2.3MoreExoticFormsofEuropeanLookbackOptions4.2.4DifferentialEquationFormulation4.2.5DiscretelyMonitoredLookbackOptions4.3AsianOptions.4.3.1PartialDifferentialEquationFormulation4.3.2ContinuouslyMonitoredGeometricAveragingOptions4.3.3ContinuouslyMonitoredArithmeticAveragingOptions4.3.4Put-CallParityandFixed-FloatingSymmetryRelati