Modelling Financial Derivatives with Mathematica

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1、1.AdvancedToolsforRocketScience-(i)separationofvariables,(ii)similaritymethods,(iii)Green'sfunctionsandimages,(iv)finite-differencenumerics,(v)treenumerics,(vi)MonteCarlosimulationassolutiontechniques.allwithintheMatlirtn~ticaenvironmenl.Acomparisonoftheseapproachesandtheiroutcomesismorethanjustan

2、interestingacademicexercise,asweshallconsidernext.1.2TheConceptofModelRiskandtheNeedforVerificationInformalDefinitionsofModelandAlgorithmRiskModelriskcanariseinavarietyofways.Givenafinancialinstrument.wegenerallyformulateathree-stagevaluationprocess:(a)conceptualdescription;(b)mathematicalformulat

3、ionoftheconceptualdescription;(c)solutionofthemathematicalmodelthroughananalyticalandlornumericalprocess.Itispossibletomakemistakes,orperhapsunreasonablesimplifyingassumptions,atanyoneofthesethreestages.Eachofthesegivesrisetoaformofmodelrisk-theriskthattheprocessfromreadingaconlracltorespondingwit

4、hasetofanswers(fairvalue,Delta,Gamma,...,impliedvolatility)hasledtothewronganswerbeingsupplied.ThisbookusesMcrthetn~rticlrtolookintelligentlyatthethirdpoint,whichwemightcallcrlgot-ithtnrisk.Onemightthinkthatthiscanbeeliminatedjustbybeingcareful-therealstoryisthatderivativesecuritiesarecapableofexh

5、ibitingsomediverseformsofmalhematicalpathologythatconfoundourintuitionandplayhavocwithstandardorevenstate-of-thc-artalgorithms.Thisbookwillpresentsomefamiliarandratherlessfamiliarexamplesoftrouble.Iwishtoemphasizethatthisisnotjustamatterofworryingaboutalevelofaccuracythatisbelowthe"noiselevel"oftr

6、aders.Itispossibletogethorriblywronganswersevenwhenonethinksthatoneisbeingrathercareful.IalsotendtothinkthatitisthejobofaQuantsteamtosupplyasaccurateanansweraspossibletotradingandsalesteams.Iftheywanttomodifyyouranswerby50basispoints,forwhateverreasons,thatistheirresponsibility!VerificationandReso

7、lvingDisagreementamongstExpertsAgoodruleofthumbisthatingeneralyoucangivewhatyouthinkisthesameproblemtosixdifferentgroupsandobtainatleastthreemateriallydifferentanswers.Inderivativesmodellingyoucanusuallygetfourdi