欢迎来到天天文库
浏览记录
ID:7270471
大小:189.90 KB
页数:12页
时间:2018-02-09
《extensions to the non-probabilistic interest-rate model》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
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.Can8、weincorporatethisobservationintoourmodelfortheshort-terminter
7、fallpossiblemodelworlds.Themarginoferrorccanbefoundby‘fitting’thefunctionb(t)many,manytimesusinghistoricalforward-ratedata,andthendeterminingbyhowmuchthisfunctionisinerror.70.3ECONOMICCYCLESThereisevidencethatinterestratesfolloweconomiccycleswithaperiodofaroundfivetotenyears.Can
8、weincorporatethisobservationintoourmodelfortheshort-terminter
此文档下载收益归作者所有