Libor-Market-Model(LMM)利率衍生品定价研究

LiborMarketModel(LMM)Callablesnowballbondemail:[e-mail]del;callablesnowballbond;LeastsquareMontecarlo;BermudanoptionLibor(,)PtT()(,)TtrsdsPtTe−∫=(,)PtT(,)PtT11()(,,)()iiiiLtLtTTtTT−−=i]]1[,iiTT−()iLt1iT−1[,iiTT−()iiLtδiT1[,iiTT−]()iiLtδ1iT−1()()titirsdsiiLteδ−−∫=1(,)1()(,)iiiiPtTLtPtTδ−+=1(,)1()1(,)iiiiPtTLtPtTδ−⎡⎤=⎢⎣⎦−⎥(,)PtT(,)PtT()iLt()(,)iLtPtTii()(,)iLtPtT[11()(,)(,)(,)iiii]iLtPtTPtTPtTδ−=−()(,)iLtPtTiCapsFloors1iT−1(iiLT)−iT()iVT1iT−1(iiLT)−iT()iVT1()(())iiiiVTLTKδ+−=−1(iiLT)−,SRαβ1,,TTαβ+,1()(,)fixjjjVtSRPtTβαβαδ=+=∑1()()(,)floatjjjjVtLtPtTβαδ=+=∑()()fixfloatVtVt=,11(,)()(,)jjjjjjSRPtTLtPtTββαβααδ=+=+=∑∑jδ1,11()(,)()(,)jjjjjjjjjjLtPtTSRwLtPtTββααββααδδ=+=+=+==∑∑∑11(,),(,)jjjjjjjPtTwPtTββαα1jwδδ=+=+=∑∑=LiborMarketModel()(,)iLtPtTi(,)iPtT()()()()iiiidLtLttdWtσ=(,)iPtTiQkT(,)kPtTkQ1()()()()()()()()1()kjkjjjkkkkkkjijjtLtdLttLtdWttLtLtδρσσσδ=+=++∑12()()ln()ln()()()1()1(())()()(()())2kjkjjjkkkkjijjkkkktLtkLttLttLttLttttLtWttWtδρσσδσσ=++∆=+∆+−∆++∆−∑MonteCarloLSMC11maxPr,0NjjijijrpayoffEBCalliceBα−=+⎛⎞⎡⎤=−⎜⎟⎢⎥⎜⎟⎢⎥⎣⎦⎝⎠∑ijBjT01B=()11(),1jjjjjBBLtjNτ+=+≤≤−1j111(,),[,]tjjjBPtTBttt++=∈+iiCallpricei1max(,)iiirrsLiborf−=+−ii1i−isifi11NjjijijrBBα−=+∑01PrmkkmikkmrCallicePBBBα=⎛⎞=+⎜⎝⎠∑⎟1PrNiiPiceN==∑()()(())icttiiitkabttedσ−−⎡=+−+⎣⎤⎦211(1)ijttijeβρββ−−=+−0,0,0addc+0ijtt−=1ijρ=2βReferences[1]Brace,A.,Gatarek,D.,andMusiela,M.(1997),‘TheMarketModelofInterestRateDynamics’,MathematicalFinance,7,127-155.[2]Miltersen,K.R.,SandmannK.,SondermannD.(1997),“ClosedFormSolutionsforTermStructureDerivativeswithLog-NormalInterestRates,”JournalofFinance,52,409-430.[3]Brigo,D.andMercurio,F.(2006),InterestRateModels,TheoryandPractice,Berlin:Springer[4]Hull,J.(2003),Options,FuturesandOtherDerivatives,5thed.,UpperSaddleRiver:Prentice-Hall.[5]Jaeckel,P.(2002),MonteCarloMethodsinFinance,WestSussex:Wiley.[6]Longstaff,F.andSchwartz,E.(2001),‘ValuingAmericanOptionsbySimulation:ASimpleLeastSquaresApproach’,TheReviewofFinancialStudies,14,113-147.[7]Pedersen,M.(1999),‘BermudanSwaptionsintheLIBORMarketModel’,SimCorpFinancialResearchWorkingPaper.[8]Hagan,P.S.‘AccrualSwapsandRangeNotes’,Bloomberg(Unpublished).