interest-rate modeling without probabilities

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1、CHAPTER68interest-ratemodelingwithoutprobabilitiesInthisChapter...•theEpstein–Wilmottmodel,anon-Brownianmotionmodelforinterestrates:•howtovalueinterest-rateproductsinaworst-casescenario•theYieldEnvelope•optimalstatichedging68.1INTRODUCTIONThetwomainclassicalapproachestopr

2、icingandhedgingfixedincomeproductsmaybetermed‘yield-based’and‘stochastic.’Theformer(seeChapter13)assumesthatinterestratesareconstantforeachproduct,which,ofcourse,isinconsistentacrossproducts.Theseideasareusedagreatdealforthesimpler,‘linear’products.Thelatterapproach(seeCha

3、pters30and35)assumesthatinterestratesaredrivenbyanumberofrandomfactors.Itisusedfor‘non-linear’contracts,contractshavingsomeformofoptionality.Inthestochasticmodelsanequationfortheshort-termratewillgiveasanoutputthewholeyieldcurve.Bothoftheseapproachescanbecriticized.Theyie

4、ld-basedideasarenotsuitedtocomplexproductsandthepopularstochasticmodelsareinaccurate.Forthelatter,itisextremelydifficulttoestimateparameters,andafterestimatingthem,theyarepronetochange,makingamockeryoftheunderlyingtheory.Oneofthemainproblemsistheassumptionofafinitenumberoff

5、actors.Fromsuchanassumptionitfollowsthatyoucandeltahedgeanycontractwiththissamenumberofsimplercontracts.Forexample,inaone-factorworldyoucanhedgeonepartoftheyieldcurvewithanyotherpart,somethingwhichisclearlynotpossibleinpractice.Isitacceptabletohedgeasix-monthoptiononaone-

6、yearbondwithaten-yearbond?Althoughpractitionersusecommonsensetogetaroundthis(theywouldhedgetheoptionwiththeone-yearbond),thiscommonsenseisnotreflectedinthemodeling.InthischapterIaddresstheproblemfromanewperspective,byassumingaslittleaspossibleabouttheprocessunderlyingthemo

7、vementofinterestrates.Iwillmodelashort-terminterestrateandpriceaportfolioofcashflowsinaworst-casescenario,usingtheshortrateasthe1078PartFiveadvancedtopicsratefordiscounting.Oneofthekeyfeaturesofthemodelinthischapteristhatdeltahedgingplaysnoimportantrole.Theresultingproblem

8、isnonlinearandthusthevalueofacontractthendependsonwhatitishedgedwith.Thisapproachnecessarilycorr