extensions to the non-probabilistic interest-rate model

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1、CHAPTER70extensionstothenon-probabilisticinterest-ratemodelInthisChapter...•moreontheEWmodel70.1INTRODUCTIONThereisnoendtothenumberofbellsandwhistlesthatcanbeattachedtofinancialmodels.Wecanincorporatemanyofthefeaturesthatwehaveseeninotherchaptersintothepresentmodel.Theobviousim

2、provement,whichwillnottakemuchmorecomputationaleffort,istoincludejumpsofsomeform.Itiscommonexperiencethatratesdojump.Insomecountriesthesejumpsareorchestratedbygovernments.ThecrashmodelsofChapter58areaniceadditiontothemodelsincetheyarealsobasedonaworst-casescenarioanalysis.Weal

3、soconsiderotherextensionstothenon-probabilisticmodel.Forexample,weexplorethepossibilityofmodelingeconomiccycles.Thenweintroducetheuncertaintyband.Thisallowsustomodelmoreaccuratelyrealinterestratemovements.Wethenexaminepastdatatochooseasensiblewidthfortheband.Finally,weconsider

4、theimpactofliquidity.70.2FITTINGFORWARDRATESAsafirstthought,considertakingtheEpstein–Wilmottmodelexplainedinthepreviouschaptersandmakingitcloserinspirittoboththeclassicalstochasticmodelsandthedurationtypeofmodels.Supposethatwebelieveinterestratestobecompletelydeterministicandgo

5、vernedbytheequationdr=a(b(t)−r).(70.1)dtThatis,theratesaremeanrevertingtosomelevelb(t)ataratea.ThisissimilartoafittedVasicek,butwithouttherandomelement.Ifthisistrueandmarketspriceaccordingtothis1118PartFiveadvancedtopicsmodel,thentheforwardratecurvetodayF(t∗;T)mustsatisfyd∗∗F(t

6、;t)=a(b(t)−F(t;t)).dtItfollowsthat∗1d∗b(t)=F(t;t)+F(t;t).(70.2)adtSoourinterestratemodelisjust(70.1)withb(t)givenby(70.2).Nowadda‘marginoferror’tothismodelsothatitbecomesdra(b(t)−r)−c<

7、fallpossiblemodelworlds.Themarginoferrorccanbefoundby‘fitting’thefunctionb(t)many,manytimesusinghistoricalforward-ratedata,andthendeterminingbyhowmuchthisfunctionisinerror.70.3ECONOMICCYCLESThereisevidencethatinterestratesfolloweconomiccycleswithaperiodofaroundfivetotenyears.Can

8、weincorporatethisobservationintoourmodelfortheshort-terminter