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1、KING'SCOLLEGELONDONDEPARTMENTOFMATHEMATICSFinancialMathematicsAnIntroductiontoDerivativesPricingLaneP.HughstonChristopherJ.HunterSharePrice$200$150$100$50$0DateJulyAug.Sept.Oct.Nov.FinancialMathematicsAnIntroductoryGuideLaneP.Hughston1DepartmentofMathem
2、aticsKing'sCollegeLondonTheStrand,LondonWC2R2LS,UKChristopherJ.Hunter2NatWestGroup135Bishopsgate,LondonPostalCode,UKandDepartmentofMathematicsKing'sCollegeLondonTheStrand,LondonWC2R2LS,UKcopyright°c2000L.P.HughstonandC.J.Hunter1email:lanehughston@yahoo.
3、com2email:ChristopherJHunter@yahoo.comiPrefaceThisbookisintendedasaguidetosomeelementsofthemathematicsof¯nance.Hadwebeenabitbolderitwouldhavebeenentitled`MathematicsforMoneyMakers'sinceitdealswithderivatives,oneofthemostnotoriouswaystomake(orlose)alotof
4、money.Ourmaingoalinthebookistodevelopthebasicsofthetheoryofderivativepricing,asderivedfromtheso-called`noarbitragecondition'.Indoingso,wealsointroduceanumberofmathematicaltoolsthatareofinterestintheirownright.Attheendofitall,whileyoumaynotbeamillionaire
5、,youshouldunderstandhowtoavoid`breakingthebank'withafewbadtrades.Inordertomotivatethestudyofderivatives,webeginthebookwithadiscussionofthe¯nancialmarkets,theinstrumentsthataretradedonthemandhowarbitrageopportunitiescanoccurifderivativesaremispriced.Weth
6、enarriveataproblemthatinevitablyariseswhendealingwithphysicalsystemssuchasthe¯nancialmarkets:howtodealwiththe`°owoftime'.Therearetwoprimarymeansofparametrizingtime
7、thediscretetimepa-rameterization,wheretimeadvancesin¯nitesteps;andthecontinuoustimeparame
8、terization,wheretimevariessmoothly.Weinitiallychoosetheformermethod,anddevelopasimplediscretetimemodelforthemovementsofassetpricesandtheirassociatedderivatives.ItisbasedonanidealisedCasino,wherebettingontherandomoutcomeofacointossreplacesthebuyingandsel
9、lingofanasset.Oncewehaveseenthebasicideasinthiscontext,wethenexpandthemodelandinterpretitinalanguagethatbringsouttheanalogywithastockmarket.Thisisthebinomialmodelforastockmarket,wheretimeisdiscreteandstockpricesmoveinarandomfashi
