Pricing European and American Options with Extrapolation

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1、PricingEuropeanandAmericanOptionswithExtrapolationChao-JungChenGraduateInstituteofFinanceNationalTaiwanUniversityContents1Introduction11.1SettingtheGround............................11.2SurveyofLiterature...........................31.3StructuresoftheThesis.........

2、................42Methodologies52.1PayoffsofOptions.............................52.2PricingModels..............................72.2.1Log-normalModelforStockPrice................72.2.2TheBlack-ScholesModel.....................92.2.3TreeMethods........................

3、...122.3Extrapolation...............................163NumericalResults173.1TheCRRMethod.............................173.1.1EvenNumberofPeriods.....................183.1.2ModifiedCRRMethod......................183.2Extrapolation...............................184Conc

4、lusionsandFutureWork324.1Conclusions................................324.2FutureWork................................32Bibliography341ListofFigures1.1SawtoothEffect..............................32.1Profit/LossofOptions...........................62.2Binomialmodelfortwop

5、eriods......................122.3Pegthestrikepricefortwoperiods....................153.1Europeancallandput...........................203.2Americanputandcall...........................213.3Europeancallandputunderevennumberofperiods..........223.4Americanputandcallun

6、derevennumberofperiods..........233.5Europeancallandput(peggingthestrikeprice)............243.6Americanputandcall(peggingthestrikeprice)............253.7RelativeerrorofEuropeancall(outofmoney).............263.8RelativeerrorofEuropeancall(atthemoney).............263

7、.9RelativeerrorofEuropeancall(inthemoney).............273.10RelativeerrorofEuropeanput(outofthemoney)...........273.11RelativeerrorofEuropeanput(atthemoney).............283.12RelativeerrorofEuropeanput(inthemoney).............283.13RelativeerrorofAmericancall(outof

8、themoney)...........293.14RelativeerrorofAmericancall(atthemoney).............293.15RelativeerrorofAmericancall(inthemoney).............303.16Rel