paul wilmott on quantitative finance mortgage-backed securities

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1、CHAPTER34mortgage-backedsecuritiesInthisChapter...•typesofmortgages•whatmakesmortgage-backedsecuritiesspecial•modelingprepayment34.1INTRODUCTIONMosthomeownersknowaboutmortgages.Andmortgage-backedsecuritiesaresimplymanymortgageslumpedtogetherforonwardsale.Themostinterestingaspectofmortgage-bac

2、kedsecuritiesisthatyoumustmodelthebehaviorofhomeowners,whetherornottheypayofftheirmortgagesearly,refinanceetc.Becausetherearesomanyindividualmortgagesineachsecurityitisonlynecessarytomodeltheaveragebehaviorofthehomeowners.34.2INDIVIDUALMORTGAGESAmortgageisaloan,usuallytoprivateindividuals,tohe

3、lpthemwiththepurchaseofahome.Theycomeinavarietyofforms.Therateofinterestcouldbefixed,orfloating,orfixedforawhileandthenlefttofloat.Sometimesthemonthlypaymenttothelendercoversbothinterestandgradualrepaymentoftheprincipal.Sometimesonlytheinterestiscoveredandtheprincipalmustberepaidattheendoftheloan

4、viasomeotherformoffunding.Thelifetimeofmostmortgagesislong,typically20,25or30years.Thesizeoftheloanthatanindividualcanborrowwilldependontheirincomeandestimatedcredit-worthiness.Theloanitselfisbackedbytheproperty.Thereisrisktothelenderabovenor-malinterestriskbecauseofthepossibilityofdefaultcom

5、binedwiththepossibilityoffallingpropertyvalues.•Fixedratemortgageshavearateofinterestthatisfixedforthelifeofthemortgage.Monthlypaymentsremainatthesamelevelandincludepaymentofinterestandagradualrepaymentofprincipal.ThesearethemostcommonformofmortgageintheUS.572PartThreefixed-incomemodelingandder

6、ivatives•Floatingratemortgageshaveinterestpaymentslinkedtoavariableinterestrate.Thisvari-ablerateissetbythemortgagee,thelender,andvariesdiscretelyandislooselyassociatedwiththeinterestratesofthecurrency.ThesearethemostcommonmortgagesintheUK.34.2.1MonthlyPaymentsintheFixedRateMortgageSincethemo

7、nthlypaymentsareconstant,theyrepresentbothpaymentofinterestandgradualrepaymentofprincipal.Tostartwiththeinterestformsthebulkofthepaymentlaterinthelifeofthemortgageitistherepaymentofprincipalthatmakesupthemajorpartofeachpayment.Iftheinterestra