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首页 利率模型理论与实践

利率模型理论与实践.pdf

利率模型理论与实践

amfong
2010-01-12 0人阅读 举报 0 0 暂无简介

简介:本文档为《利率模型理论与实践pdf》,可适用于人文社科领域

SpringerFinanceEditorialBoardMAvellanedaGBaroneAdesiMBroadieMHADavisEDermanCKlüppelbergEKoppWSchachermayerSpringerFinanceSpringerFinanceisaprogrammeofbooksaimedatstudents,academicsandpractitionersworkingonincreasinglytechnicalapproachestotheanalysisoffinancialmarketsItaimstocoveravarietyoftopics,notonlymathematicalfinancebutforeignexchanges,termstructure,riskmanagement,portfoliotheory,equityderivatives,andfinancialeconomicsAmmannM,CreditRiskValuation:Methods,Models,andApplication()BackK,ACourseinDerivativeSecurities:IntroductiontoTheoryandComputation()BarucciE,FinancialMarketsTheoryEquilibrium,EfficiencyandInformation()BieleckiTRandRutkowskiM,CreditRisk:Modeling,ValuationandHedging()BinghamNHandKieselR,RiskNeutralValuation:PricingandHedgingofFinancialDerivatives(,nded)BrigoDandMercurioF,InterestRateModels:TheoryandPractice(,nded)BuffR,UncertainVolatilityModelsTheoryandApplication()CarmonaRAandTehranchiMR,InterestRateModels:anInfiniteDimensionalStochasticAnalysisPerspective()DanaRAandJeanblancM,FinancialMarketsinContinuousTime()DeboeckGandKohonenT(Editors),VisualExplorationsinFinancewithSelfOrganizingMaps()DelbaenFandSchachermayerW,TheMathematicsofArbitrage()ElliottRJandKoppPE,MathematicsofFinancialMarkets(,nded)FenglerMR,SemiparametricModelingofImpliedVolatility()GemanH,MadanD,PliskaSRandVorstT(Editors),MathematicalFinance–BachelierCongress()GundlachM,LehrbassF(Editors),CreditRiskintheBankingIndustry()KellerhalsBP,AssetPricing()KülpmannM,IrrationalExuberanceReconsidered()KwokYK,MathematicalModelsofFinancialDerivatives()MalliavinPandThalmaierA,StochasticCalculusofVariationsinMathematicalFinance()MeucciA,RiskandAssetAllocation()PelsserA,EfficientMethodsforValuingInterestRateDerivatives()PrigentJL,WeakConvergenceofFinancialMarkets()SchmidB,CreditRiskPricingModels()ShreveSE,StochasticCalculusforFinanceI()ShreveSE,StochasticCalculusforFinanceII()YorM,ExponentialFunctionalsofBrownianMotionandRelatedProcesses()ZagstR,InterestRateManagement()ZhuYL,WuX,ChernIL,DerivativeSecuritiesandDifferenceMethods()ZieglerA,IncompleteInformationandHeterogeneousBeliefsinContinuoustimeFinance()ZieglerA,AGameTheoryAnalysisofOptions()DamianoBrigo·FabioMercurioInterestRateModels–TheoryandPracticeWithSmile,InflationandCreditWithFiguresandTablesDamianoBrigoHeadofCreditModelsBancaIMI,SanPaoloIMIGroupCorsoMatteottiMilano,ItalyandFixedIncomeProfessorBocconiUniversity,Milano,ItalyEmail:damianobrigogmailcomFabioMercurioHeadofFinancialModellingBancaIMI,SanPaoloIMIGroupCorsoMatteottiMilano,ItalyEmail:fabiomercuriobancaimiitMathematicsSubjectClassification():H,H,P,C,C,AJELClassification:G,G,ELibraryofCongressControlNumber:ISBNndedSpringerBerlinHeidelbergNewYorkISBNndedSpringerBerlinHeidelbergNewYorkISBNstedSpringerVerlagBerlinHeidelbergNewYorkThisworkissubjecttocopyrightAllrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanksDuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember,,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringerViolationsareliabletoprosecutionundertheGermanCopyrightLawSpringerisapartofSpringerScienceBusinessMediaspringercom©SpringerVerlagBerlinHeidelberg,PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etcinthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluseCoverdesign:designproduction,HeidelbergTypesetting:bytheauthorsusingaSpringerLATEXmacropackageProduction:LETEXJelonek,SchmidtVöcklerGbR,LeipzigPrintedonacidfreepaperYLToOurFamiliesPreface“ProfessorBrigo,willtherebeanynewquotesinthesecondedition”“Yesforexamplethisone!”AstudentataLondontrainingcourse,followingasimilarquestionbyaHongKongstudenttoMassimoMorini,“Iwouldhavewrittenyouashorterletter,butIdidn’thavethetime”BenjaminFranklinMOTIVATIONfiveyearslaterI’msurehe’sgotaperfectlygoodreasonfortakingsolongEmily,“CorpseBride”,TimBurton()Welcomeonboardthesecondeditionofthisbookoninterestratemodels,toalloldandnewreadersWeimmediatelysaythissecondeditionisactuallyalmostanewbook,withfourhundredfiftyandmorenewpagesonsmilemodeling,calibration,inflation,creditderivativesandcounterpartyriskAsexplainedintheprefaceofthefirstedition,theideaofwritingthisbookoninterestratemodelingcrossedourmindsinearlysummerWeboththoughtofdifferentversionsbefore,butitwasinBancaIMIthatthischallengingprojectbeganmaterially,ifnotspiritually(moredetailsaregiveninthetriviaAppendixG)Atthetimeweweregiventhetaskofstudyinganddevelopingfinancialmodelsforthepricingandhedgingofabroadrangeofderivatives,andwewereinvolvedinmediumlongtermprojectsThefirstyearsinBancaIMIsawuswritingalotofreportsandmaterialonouractivityinthebank,tothepointthatmuchofthosestudiesendedupinthefirsteditionofthebook,printedinInthefirsteditionprefacewedescribedmotivation,explainedwhatkindoftheoryandpracticeweweregoingtoaddress,illustratedtheaimandreadershipofthebook,togetherwithitsstructureandotherconsiderationsWedosoagainnow,clearlyupdatingwhatwewroteinWhyabookoninterestratemodels,andwhythisnewedition“SorryItooksolongtorespond,PlasticManI’dliketoformallydeclaremyreturntoactiveduty,myfriendsThisisJ’onnJ’onzzactivatingfulltelepathiclinkCounteroffensivehasbegun”JLA,DCComics()Inyearswhereeverymonthanewbookonfinancialmodelingoronmathematicalfinancecomesout,oneofthefirstquestionsinevitablyis:whyonemore,andwhyoneoninterestratemodelinginparticularVIIIPrefaceTheanswerspringsdirectlyfromourjobexperienceasmathematiciansworkingasquantitativeanalystsinfinancialinstitutionsIndeed,oneofthemajorchallengesanyfinancialengineerhastocopewithisthepracticalimplementationofmathematicalmodelsforpricingderivativesecuritiesWhenpricingmarketfinancialproducts,onehastoaddressanumberoftheoreticalandpracticalissuesthatareoftenneglectedintheclassical,generalbasictheory:thechoiceofasatisfactorymodel,thederivationofspecificanalyticalformulasandapproximations,thecalibrationoftheselectedmodeltoasetofmarketdata,theimplementationofefficientroutinesforspeedingupthewholecalibrationprocedure,andsoonInotherwords,thegeneralunderstandingofthetheoreticalparadigmsinwhichspecificmodelsoperatedoesnotleadtotheircompleteunderstandingandimmediateimplementationanduseforconcretepricingThisisanareathatisrarelycoveredbybooksonmathematicalfinanceUndoubtedly,thereexistexcellentbookscoveringthebasictheoreticalparadigms,buttheydonotprovideenoughinstructionsandinsightsfortacklingconcretepricingproblemsWethereforethoughtofwritingthisbookinordertocoverthisgapbetweentheoryandpracticeThefirstversionofthebookachievedthistaskinseveralrespectsHowever,themarketisrapidlyevolvingNewareassuchassmilemodeling,inflation,hybridproducts,counterpartyriskandcreditderivativeshavebecomefundamentalinrecentyearsNewbridgesarerequiredtocrossthegapbetweentheoryandpracticeintheserecentareasTheGapbetweenTheoryandPracticeButLo!SiddaˆrthaturnedEyesgleamingwithdivinetearstothesky,EyeslitwithheavenlypitytotheearthFromskytoearthhelooked,fromearthtosky,AsifhisspiritsoughtinlonelyflightSomefaroffvision,linkingthisandthat,Lostpastbutsearchable,butseen,butknownFrom“TheLightofAsia”,SirEdwinArnold()Agap,indeedAndafundamentaloneTheinterplaybetweentheoryandpracticehasprovedtobeanextremelyfruitfulingredientintheprogressofscienceandmodelinginparticularWebelievethatpracticecanhelptoappreciatetheory,thusgeneratingafeedbackthatisoneofthemostimportantandintriguingaspectsofmodelingandmoregenerallyofscientificinvestigationIftheorybecomesdeaftothefeedbackofpracticeorviceversa,greatopportunitiescanbemissedItmaybeapitytorestrictone’sinterestonlytoextremelyabstractproblemsthathavelittlerelevanceforthosescientistsorquantitativeanalystsworkingin“reallife”Now,itisobviousthateveryoneworkinginthefieldowesalottothebasicfundamentaltheoryfromwhichsuchextremelyabstractproblemsstemPrefaceIXItwouldbefoolishtodenytheimportanceofawelldevelopedandconsistenttheoryasafundamentalsupportforanypracticalworkinvolvingmathematicalmodelsIndeed,practicethatisdeaftotheoryorthatemploysasloppymathematicalapparatusisquitedangerousHowever,besidestheextremelyabstractrefinementofthebasicparadigms,whicharecertainlyworthstudyingbutthatinterestmostlyanacademicaudience,thereareotherfundamentalandmorespecificaspectsofthetheorythatareoftenneglectedinbooksandintheliterature,andthatinterestalargeraudienceIsThisBookaboutTheoryWhatkindofTheory“OurpaperbecameamonographWhenwehadcompletedthedetails,werewroteeverythingsothatnoonecouldtellhowwecameuponourideasorwhyThisisthestandardinmathematics”DavidBerlinski,“BlackMischief”()Inthebook,wearenotdealingwiththefundamentalnoarbitrageparadigmswithgreatdetailWeresumeandadoptthebasicwellestablishedtheoryofHarrisonandPliska,andavoidthedebateontheseveralpossibledefinitionsofnoarbitrageandontheirmutualrelationshipsIndeed,wewillraiseproblemsthatcanbefacedinthebasicframeworkaboveInsistingonthesubtleaspectsanddevelopmentsofnoarbitragetheorymorethanisnecessarywouldtakespacefromtheothertheoryweneedtoaddressinthebookandthatismoreimportantforourpurposesBesides,therealreadyexistseveralbooksdealingwiththemostabstracttheoryofnoarbitrageOnthetheorythatwedealwith,onthecontrary,thereexistonlyfewbooks,althoughinrecentyearsthetrendhasbeenimprovingWhatisthistheoryForaflavorofit,letusselectafewquestionsatrandom:•Howcanthemarketinterestratecurvesbedefinedinmathematicalterms•WhatkindofinterestratesdoesoneselectwhenwritingthedynamicsInstantaneousspotratesForwardratesForwardswaprates•Whatisasufficientlygeneralframeworkforexpressingnoarbitrageininterestratemodeling•AretherepayoffsthatdonotrequiretheinterestratecurvedynamicstobevaluedIfso,whatarethesepayoffs•Isthereadefinitionofvolatility(andofitstermstructures)intermsofinterestratedynamicsthatisconsistentwithmarketpractice•Whatkindsofdiffusioncoefficientsintheratedynamicsarecompatiblewithdifferentqualitativeevolutionsofthetermstructureofvolatilitiesovertime•Howis“humpedvolatilityshape”translatedinmathematicaltermsandwhatkindofmathematicalmodelsallowforitXPreface•Whatisthemostconvenientprobabilitymeasureunderwhichonecanpriceaspecificproduct,andhowcanonederiveconcretelytherelatedinterestratedynamics•Aredifferentmarketmodelsofinterestratedynamicscompatible•WhatdoesitmeantocalibrateamodeltothemarketintermsofthechosenmathematicalmodelIsthisalwayspossibleOristhereadegreeofapproximationinvolved•DoesterminalcorrelationamongratesdependoninstantaneousvolatilitiesoronlyoninstantaneouscorrelationsCanweanalyzethisdependence•Whatisthevolatilitysmile,howcanitbeexpressedintermsofmathematicalmodelsandofforwardratedynamicsinparticular•Isthereadiffusiondynamicsconsistentwiththequotingmechanismoftheswaptionsvolatilitysmileinthemarket•Whatisthelinkbetweendynamicsofratesandtheirdistributions•Whatkindofmodelismoreapttomodelcorrelatedinterestratecurvesofdifferentcurrencies,andhowdoesonecomputetherelateddynamicsundertherelevantprobabilitymeasures•WhendoesamodelimplytheMarkovpropertyfortheshortrateandwhyisthisimportant•Whatisinflationandwhatisitslinkwithclassicalinterestratemodeling•Howdoesonecalibrateaninflationmodel•Isthetimeofdefaultofacounterpartypredictableornot•Isitpossibletovaluepayoffsunderanequivalentpricingmeasureinpresenceofdefault•WhyarePoissonandCoxprocessessosuitedtodefaultmodeling•WhatarethemathematicalanalogiesbetweeninterestratemodelsandcreditderivativesmodelsForwhatkindofmathematicalmodelsdotheseanalogiesstand•Doescounterpartyriskrenderapayoffdynamicsdependentevenifwithoutcounterpartyriskthepayoffvaluationismodelindependent•Whatkindofmathematicalmodelsmayaccountforpossiblejumpfeaturesinthestochasticprocessesneededincreditspreadmodeling•Isthereageneralwaytomodeldependenceacrossdefaulttimes,andacrossmarketvariablesmoregenerally,goingbeyondlinearcorrelationWhatarethelimitsofthesegeneralizations,incase•WecouldgoonforawhilewithquestionsofthiskindOurpointis,however,thatthetheorydealtwithinabookoninterestratemodelsshouldconsiderthiskindofquestionWesympathizewithanyonewhohasgonetoabookstore(orperhapstoalibrary)lookingforanswerstosomeoftheabovequestionswithlittlesuccessWehavedonethesame,severaltimes,andwewereabletofindonlylimitedmaterialandfewreferenceworks,althoughinthelastfewyearsthePrefaceXIsituationhasimprovedWehopethesecondeditionofthisbookwillcementthestepsforwardtakenwiththefirsteditionWealsosympathizewiththereaderwhohasjustfinishedhisstudiesorwiththeacademicwhoistryingalifechangetoworkinindustryorwhoisconsideringsomeclosecooperationwithmarketparticipantsBeingusedtoprecisestatementsandrigoroustheory,thispersonmightfindanswerstotheabovequestionsexpressedincontradictoryorunclearmathematicallanguageThisissomethingelsewetoohavebeenthrough,andwearetryingnottodisappointinthisrespecteitherIsThisBookaboutPracticeWhatkindofPracticeIfwedon’tdothework,thewordsdon’tmeananythingReadingabookorlisteningtoatalkisn’tenoughbyitselfCharlotteJokoBeck,“NothingSpecial:LivingZen”,HarperCollins,Wetrytoanswersomequestionsonpracticethatareagainoverlookedinmostoftheexistingbooksinmathematicalfinance,andoninterestratemodelsinparticularAgain,herearesometypicalquestionsselectedatrandom:•Whatareaccrualconventionsandhowdotheyimpactonthedefinitionofrates•CanyougiveafewexamplesofhowtimeismeasuredinconnectionwithsomeaspectsofcontractsWhatare“daycountconventions”•WhatistheinterpretationofmostliquidmarketcontractssuchascapsandswaptionsWhatistheirmainpurpose•WhatkindofdatastructuresareobservedinthemarketArealldataequallysignificant•HowisaspecificmodelcalibratedtomarketdatainpracticeIsajointcalibrationtodifferentmarketstructuresalwayspossibleorevendesirable•Whatarethedangersofcalibratingamodeltodatathatarenotequallyimportant,orreliable,orupdatedwithpoorfrequency•Whataretherequirementsofatraderasfarasacalibrationresultsareconcerned•HowcanonehandlepathdependentorearlyexerciseproductsnumericallyAndproductswithbothfeaturessimultaneously•WhatnumericalmethodscanbeusedforimplementingamodelthatisnotanalyticallytractableHowaretreesbuiltforspecificmodelsCaninstantaneouscorrelationbeaproblemwhenbuildingatreeinpractice•WhatkindofproductsaresuitedtoevaluationthroughMonteCarlosimulationHowcanMonteCarlosimulationbeappliedinpracticeUnderwhichprobabilitymeasureisitconvenienttosimulateHowcanwereducethevarianceofthesimulation,especiallyinpresenceofdefaultindicatorsXIIPreface•Isthereamodelflexibleenoughtobecalibratedtothemarketsmileforcaps•HowistheswaptionssmilequotedIsitpossibleto“arbitrage”theswaptionsmileagainstthecapsmile•Whattypicalqualitativeshapesofthevolatilitytermstructureareobservedinthemarket•Whatistheimpactoftheparametersofachosenmodelonthemarketvolatilitystructuresthatarerelevanttothetrader•Whatistheaccuracyofanalyticalapproximationsderivedforswaptionsvolatilitiesandterminalcorrelations•IsitpossibletorelateCMSconvexityadjustmentstoswaptionsmiles•Doesthereexistaninterestratemodelthatcanbeconsidered“central”nowadays,inpracticeWhatdotradersthinkaboutit•Howcanweexpressmathematicallythepayoffsofsometypicalmarketproducts•Howdoyouhandleinpracticeproductsdependingonmorethanoneinterestratecurveatthesametime•Howdoyoucalibrateaninflationmodelinpractice,andtowhatquotes•Whatistheimportanceofstochasticvolatilityininflationmodeling•HowcanwehandlehybridstructuresWhatarethekeyaspectstotakeintoaccount•WhataretypicalvolatilitysizesinthecreditmarketArethesesizesmotivatingdifferentmodels•What’stheimpactofinterestratecreditspreadcorrelationonthevaluationofcreditderivatives•Iscounterpartyriskimpactinginterestratepayoffsinarelevantway•Aremodelswithjumpseasytocalibratetocreditspreaddata•IsthereawaytoimplycorrelationacrossdefaulttimesofdifferentnamesfrommarketquotesWhatmodelsaremoreaptatdoingso•Again,wecouldgoonforawhile,anditishardtofindasinglebookansweringthesequestionswitharigoroustheoreticalbackgroundAlso,answeringsomeofthesequestions(andothersthataresimilarinspirit)motivatesnewtheoreticaldevelopments,maintainingthefundamentalfeedbackbetweentheoryandpracticewehintedataboveAIMS,READERSHIPANDBOOKSTRUCTURE“Andthesepeoplearesittingupthereseriouslydiscussingintelligentstarsandtripsthroughtimetoyearsthatsoundliketelephonenumbers

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