金融建模中的鞅方法

　　The origin of this book can be traced to courses on financial mathematics taught by us at the University of New South Wales in Sydney， Technical University of Warsaw （Politechnika Watszawska） and Institut National Polytechnique de Grenoble. Our initial aim was to write a short text around the material used in two one-semester graduate courses attended by students with diverse disciplinary backgrounds （mathematics， physics， computer science， engineering， economics and commerce）. The anticipated diversity of potential readers explains the somewhat unusual way in which the book is written. It starts at a very elementary mathematical level and does not assume any prior knowledge of financial markets. Later， it develops into a text which requires some familiarity with concepts of stochastic calculus （the basic relevant notions and results are collected in the appendix）. Over time， what was meant to be a short text acquired a life of its own and started to grow. The final version can be used as a textbook for three one-semester courses one at undergraduate level， the other two as graduate courses.本书为英文版。

暂缺《金融建模中的鞅方法》作者简介

Preface
NoteontheSecondPrinting
PartI.SpotandFuturesMarkets
1.AnIntroductiontoFinancialDerivatives
1.1Options
1.2FuturesContractsandOptions
1.3ForwardContracts
1.4CallandPutSpotOptions
1.4.1One-periodSpotMarket
1.4.2ReplicatingPortfolios
1.4.3MartingaleMeasureforaSpotMarket
1.4.4AbsenceofArbitrage
1.4.5OptimalityofReplication
1.4.6PutOption
1.5FuturesCallandPutOptions
1.5.1FuturesContractsandFuturesPrices
1.5.2One-periodFuturesMarket
1.5.3MartingaleMeasureforaFuturesMarket
1.5.4AbsenceofArbitrage
1.5.5One-periodSpot/FuturesMarket
1.6ForwardContracts
1.6.1ForwardPrice
1.7OptionsofAmericanStyle
2.TheCox-Ross-RubinsteinModel
2.1TheCRRModelofaStockPrice
2.1.1TheCRROptionPricingFormula
2.1.2TheBlack-ScholesOptionPricingFormula
2.2ProbabilisticApproach
2.2.1MartingaleMeasure
2.2.2Risk-neutralValuationFormula
2.3ValuationofAmericanOptions
2.3.1AmericanCallOptions
2.3.2AmericanPutOptions
2.4OptionsonaDividend-payingStock
2.5TransactionCosts
2.5.1ReplicationofOptions
2.5.2PerfectHedgingofOptions
3.FiniteSecurityMarkets
3.1FiniteSpotMarkets
3.1.1ArbitrageOpportunities
3.1.2ArbitragePrice
3.1.3Risk-neutralValuationFormula
3.1.4PriceSystems
3.1.5CompletenessofaFiniteMarket
3.2FiniteFuturesMarkets
3.2.1Self-financingFuturesStrategies
3.2.2MartingaleMeasuresforaFuturesMarket
3.2.3Risk-neutralValuationFormula
3.3FuturesPricesVersusForwardPrices
4.MarketImperfections
4.1PerfectHedging
4.1.1IncompleteMarkets
4.1.2ConstraintsonShort-sellingandBorrowingofCash
4.1.3DifferentLendingandBorrowingRates
4.2Mean-varianceHedging
4.2.1Variance-minimizingHedging
4.2.2Risk-minimizingHedging
5.TheBlack-ScholesModel
5.1SpotMarket
5.1.1Self-financingStrategies
5.1.2MartingaleMeasurefortheSpotMarket
5.1.3TheBlack-ScholesOptionValuationFormula
5.1.4ThePut-CallParityforSpotOptions
5.1.5TheBlack-ScholesPDE
5.2ARisklessPortfolioMethod
5.3SensitivityAnalysis
6.ModificationsoftheBlack-ScholesModel
6.1FuturesMarket
6.1.1Self-financingStrategies
6.1.2MartingaleMeasurefortheFuturesMarket
6.1.3TheBlackFuturesOptionFormula
6.1.4OptionsonForwardContracts
6.2OptiononaDividend-payingStock
6.2.1CaseofaConstantDividendYield
6.2.2CaseofKnownDividends
6.3StockPriceVolatility
6.3.1HistoricalVolatility
6.3.2ImpliedVolatility
6.3.3VolatilityMisspecification
6.3.4StochasticVolatilityModels
6.3.5NumericalMethods
7.ForeignMarketDerivatives
7.1Cross-currencyMarketModel
7.1.1DomesticMartingaleMeasure
7.1.2ForeignMartingaleMeasure
7.1.3ForeignStockPriceDynamics
7.2CurrencyForwardContractsandOptions
7.2.1ForwardExchangeRate
7.2.2CurrencyOptionValuationFormula
7.3ForeignEquityForwardContracts
7.3.1ForwardPriceofaForeignStock
7.3.2QuantoForwardContracts
7.4ForeignMarketFuturesContracts
7.5ForeignEquityOptions
7.5.1OptionsStruckinaForeignCurrency
7.5.2OptionsStruckinDomesticCurrency
7.5.3QuantoOptions
7.5.4Equity-linkedForeignExchangeOptions
8.AmericanOptions
8.1ValuationofAmericanClaims
8.2AmericanCallandPutOptions
8.3EarlyExerciseRepresentationofanAmericanPut
8.4AnalyticalApproach
8.5ApproximationsoftheAmericanPutPrice
8.6OptiononaDividend-payingStock
9.ExoticOptions
9.1Packages
9.2Forward-startOptions
9.3ChooserOptions
9.4CompoundOptions
9.5DigitalOptions
9.6BarrierOptions
9.7LookbackOptions
9.8AsianOptions
9.9BasketOptions
9.10QuantileOptions
9.11CombinedOptions
9.12RussianOption
10.Continuous-timeSecurityMarkets
10.1StandardMarketModels
10.1.1StandardSpotMarket
10.1.2FuturesMarket
10.1.3ChoiceofaNumeraire
10.1.4ExistenceofaMartingaleMeasure
10.1.5FundamentalTheoremofAssetPricing
10.2MultidimensionalBlack-ScholesModel
10.2.1MarketCompleteness
10.2.2Variance-minimizingHedging
10.2.3Risk-minimizingHedging
10.2.4MarketImperfections
PartII.Fixed-incomeMarkets
11.InterestRatesandRelatedContracts
11.1Zero-couponBonds
11.1.1TermStructureofInterestRates
11.1.2ForwardInterestRates
11.1.3Short-termInterestRate
11.2Coupon-bearingBonds
11.2.1Yield-to-Maturity
11.2.2MarketConventions
11.3InterestRateFutures
11.3.1TreasuryBondFutures
11.3.2BondOptions
11.3.3TreasuryBillFutures
11.3.4EurodollarFutures
11.4InterestRateSwaps
11.4.1ForwardRateAgreements
12.ModelsoftheShort-termRate
12.1Arbitrage-freeFamilyofBondPrices
12.1.1ExpectationsHypotheses
12.2CaseofItoProcesses
12.3Single-factorModels
12.3.1Time-homogeneousModels
12.3.2Time-inhomogeneousModels
12.3.3ModelChoice
12.3.4AmericanBondOptions
12.3.5OptionsonCoupon-bearingBonds
12.4Multi-factorModels
12.4.1ConsolYieldModel
12.5DefaultableBonds
13.ModelsofInstantaneousForwardRates
13.1Heath-Jarrow-MortonMethodology
i3.1.1Ho-LeeModel
13.1.2Heath-Jaxrow-MortonModel
13.1.3AbsenceofArbitrage
13.1.4Short-termInterestRate
13.2ForwardMeasureApproach
13.2.1ForwardPrice
13.2.2ForwardMartingaleMeasure
13.3GaussianHJMModel
13.3.1MarkovianCase
14.ModelsofBondPricesandLIBORRates
14.1BondPriceModels
14.1.1FamilyofBondPrices
14.1.2SpotandForwardMartingaleMeasures
14.1.3Arbitrage-freeProperties
14.1.4ImpliedSavingsAccount
14.1.5BondPriceVolatility
14.2ForwardProcesses
14.3ModelsofForwardLIBORRates
14.3.1Discrete-tenorCase
14.3.2Continuous-tenorCase
14.3.3SpotLIBORMeasure
14.4ModelofForwardSwapRates
15.OptionValuationinGaussianModels
15.1EuropeanSpotOptions
15.1.1BondOptions
15.1.2StockOptions
15.1.3OptiononaCoupon-bearingBond
15.1.4PricingofGeneralContingentClaims
15.1.5ReplicationofOptions
15.2FuturesPrices
15.2.1FuturesOptions
15.3PDEApproachtoInterestRateDerivatives
15.3.1PDEsforSpotDerivatives
15.3.2PDEsforFuturesDerivatives
16.SwapDerivatives
16.1InterestRateSwaps
16.2GaussianModel
16.2.1ForwardCapsandFloors
16.2.2Captions
16.2.3Swaptions
16.2.4OptionsonaSwapRateSpread
16.2.5YieldCurveSwaps
16.2.6ExoticCaps
16.3ModelofForwardLIBORRates
16.3.1Caps
16.3.2Swaptions
16.4ModelofForwardSwapRates
16.5Flesaker-HughstonModel
16.5.1AbsenceofArbitrage
16.5.2ValuationofCapsandSwaptions
16.6EmpiricalStudies
17.Cross-currencyDerivatives
17.1Arbitrage-freeCross-currencyMarkets
17.1.1ForwardPriceofaForeignAsset
17.1.2ValuationofForeignContingentClaims
17.1.3Cross-currencyRates
17.2GaussianHJMModel
17.2.1CurrencyOptions
17.2.2ForeignEquityOptions
17.2.3Cross-currencySwaps
17.2.4Cross-currencySwaptions
17.2.5BasketCaps
17.3ModelofForwardLIBORRates
PartIII.APPENDICES
A.ConditionalExpectations
B.It6StochasticCalculus
B.1TheItoIntegral
B.2Girsanov'sTheorem
B.3LawsofCertainFunctionalsofaBrownianMotion
References
Index