mathematical methods for financial engineering

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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.ThePartialDifferentialEquationApproach204.1.TheDiffusionEquation204.2.FiniteDifferenceMethodsfortheDiffusionEquation224.3.TheFourierTransformandthevonNeumannStabilityTes

3、t294.4.StabilityandtheFourierTransform314.5.OptionPricingviatheFouriertransform334.6.FourierTransformConventions355.MathematicalBackgroundMaterial375.1.ProbabilityTheory375.2.DifferentialEquations395.3.RecurrenceRelations405.4.Mortgages–aonceexoticinstrume

4、nt435.5.PricingMortgagesvialackofarbitrage445.6.ExponentialGrowthandPopulationRhetoric456.NumericalLinearAlgebra466.1.OrthogonalMatrices4612BRADBAXTER1.IntroductionYoucanaccessthesenotes,andothermaterial,onmyofficemachine:http://econ109.econ.bbk.ac.uk/brad/

5、Methods/Thesenotesareupdatedfairlyregularly,sopleasecheckfornewerversionsfromtimetotime.Pastexamscanbedownloadedfromhttp://econ109.econ.bbk.ac.uk/brad/FinEngExams/However,inmyexperience,studentswillbenefitenormouslyfromtheold-fashionedmethodoftakingnotesas

6、Ilecture.Ishallpostfurthermaterialonmyofficemachinethroughouttheyear.Thisisnotacourseinpricing,butIhavetriedtoillustratetopicsbyexamplesdrawnfrommathematicalfinance.1.1.ReadingList.Therearemanybooksonmathematicalfinance,butveryfewgoodones.Mystrongestrecommend

7、ationsareforthebooksbyHighamandKwok.However,thefollowingbooksarealluseful.(i)M.BaxterandA.Rennie,FinancialCalculus,CambridgeUniversityPress.Thisgivesafairlyinformaldescriptionofthemathematicsofpricing,concentratingonmartingales.It’snotasourceofinformation

8、forefficientnumericalmethods.(ii)A.Etheridge,ACourseinFinancialCalculus,CambridgeUniversityPress.Thisdoesnotfocusonthealgorithmicsidebutisverylucid.(iii)D.Higham,AnIntroductiontoFinancialOptionValuation,CambridgeUnive