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1、MATHEMATICALMETHODSFORFINANCIALENGINEERINGBRADBAXTERVersion:20130926Contents1.Introduction21.1.ReadingList22.TheGeometricBrownianMotionUniverse42.1.AnalyticValuesofEuropeanPutsandCalls72.2.TheBlack–ScholesEquationinlog-space92.3.AsianOptions102.4.Multivar
2、iateGeometricBrownianMotion112.5.GaussianIntegralsonawedge133.TheBinomialModelUniverse144.ThePartialDi?erentialEquationApproach204.1.TheDi?usionEquation204.2.FiniteDi?erenceMethodsfortheDi?usionEquation224.3.TheFourierTransformandthevonNeumannStabilityTes
3、t294.4.StabilityandtheFourierTransform314.5.OptionPricingviatheFouriertransform334.6.FourierTransformConventions355.MathematicalBackgroundMaterial375.1.ProbabilityTheory375.2.Di?erentialEquations395.3.RecurrenceRelations405.4.Mortgages–aonceexoticinstrume
4、nt435.5.PricingMortgagesvialackofarbitrage445.6.ExponentialGrowthandPopulationRhetoric456.NumericalLinearAlgebra466.1.OrthogonalMatrices4612BRADBAXTER1.IntroductionYoucanaccessthesenotes,andothermaterial,onmyo?cemachine:http://econ109.econ.bbk.ac.uk/brad/
5、Methods/Thesenotesareupdatedfairlyregularly,sopleasecheckfornewerversionsfromtimetotime.Pastexamscanbedownloadedfromhttp://econ109.econ.bbk.ac.uk/brad/FinEngExams/However,inmyexperience,studentswillbene?tenormouslyfromtheold-fashionedmethodoftakingnotesas
6、Ilecture.Ishallpostfurthermaterialonmyo?cemachinethroughouttheyear.Thisisnotacourseinpricing,butIhavetriedtoillustratetopicsbyexamplesdrawnfrommathematical?nance.1.1.ReadingList.Therearemanybooksonmathematical?nance,butveryfewgoodones.Mystrongestrecommend
7、ationsareforthebooksbyHighamandKwok.However,thefollowingbooksarealluseful.(i)M.BaxterandA.Rennie,FinancialCalculus,CambridgeUniversityPress.Thisgivesafairlyinformaldescriptionofthemathematicsofpricing,concentratingonmartingales.It’snotasourceofinformation
8、fore?cientnumericalmethods.(ii)A.Etheridge,ACourseinFinancialCalculus,CambridgeUniversityPress.Thisdoesnotfocusonthealgorithmicsidebutisverylucid.(iii)D.Higham,AnIntroductiontoFinancialOptionValuation,CambridgeUnive
