Mathematical Finance-Fries

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1、MathematicalFinanceTheory,ModelingandImplementationChristianP.FriesStochasticProcesses•InterestRateStructures•HybridModelsNumericalMethods•ObjectOrientedImplementationZxX(t1,")dP(")!X(t,!)ZT!1X(t)dW(t)[!1]00t1TtT0T1T2T3T4StockOptionBermudanStockOptionmaturiyexerciseDatesstrikenotionalsstrikes

2、dLj(t)=Lj(t)·µj(t)dt+Lj(t)·σj(t)dWjgetPrice(monteCarloStockProcessModel)getPrice(monteCarloStockProcessModel)dFX(t)=FX(t)·µFX(t)dt+FX·σFX(t)dWFXdL˜j(t)=L˜j(t)·µ˜j(t)dt+L˜j(t)·σ˜j(t)dW˜jBlackScholesModel«interface»MonteCarloStockProcessModelgetInitialValue(component)getDrift(timeIndex,componen

3、t)getProcessValue()getVolatility(timeIndex,component)getNumeraireValue()!Llδlµj(t)=·σj(t)σl(t)ρj,l(1+Llδl)β(t)≤l≤j"#$Ti+11+Li(Ti)δiLogNormalProcessµFX(t)dt=logBrownianMotionTi1+L˜i(Ti)δigetProcessValue(timeIndex,component)!L˜lδlFXgetInitialValue(component)getBrownianIncrement(timeIndex,path,f

4、actor)µ˜j(t)=·σ˜j(t)σ˜l(t)ρj,l−σ˜j(t)σ(t)ρ˜(t)(1+L˜lδl)j,FXgetDrift(timeIndex,component)β(t)≤l≤jgetVolatility(timeIndex,component)MathematicalFinanceTheory,ModelingandImplementationStochasticProcesses,InterestRateModels,HybridModels,NumericalMethods,ObjectOrientedImplementationChristianP.Frie

5、s1stMay2007preliminary,uncorrectedandincompleteversion(publicbeta)Nowadayspeopleknowthepriceofeverythingandthevalueofnothing.OscarWildeThePictureofDorianGray,[38].TypesetbytheauthorusingTeXShopforMacOSX™.DrawingsbytheauthorusingOm-niGraffleforMacOSX™.ChartscreatedusingJava™Codebytheauthor.2Comm

6、entswelcome.Thisworkislicensedundera©2004,2005,2006,2007ChristianFriesCreativeCommonsLicense.Version1.4.18[build20070403]-1stMay2007http://creativecommons.org/licenses/by-nc-nd/2.5/deed.enhttp://www.christian-fries.de/finmath/bookLicenceThisworkislicensedunderCreativeCommonsLicense.Suggestedc

7、itationF,CP.:MathematicalFinance:Theory,Modeling,Implementation.FrankfurtamMain,2007.http://www.christian-fries.de/finmath/book.FeedbackPleasehelptoimprovethiswork!PleasesenderrorreportsandsuggestionstoChristianFries