1、外文题目CATASTROPHICDEFAULTANDCREDITRISKFORLENDINGINSTITUTIONS出处JOURNALOFFINANCIALSERVICESRESEARCH作者JAMESBKAUANDDONALDCKEENAN原文CATASTROPHICDEFAULTANDCREDITRISKFORLENDINGINSTITUTIONSIINTRODUCTIONCREDITRISKFORAMORTGAGELENDERCOMESINTOPLAYONLYWHENMORTGAGEINSURANCEISABSENTORINADEQUATEMORTGAGEINSURANCE,INFACT
2、,INSURESLENDERSAGAINSTMOSTORDINARYDEFAULTTHATIS,DEFAULTINDUCEDBYMOVEMENTSINTHEOVERALLMARKETFORHOUSINGALTHOUGH,ASWILLBESEEN,FORENTIRELYEXPLICABLEREASONS,LESSOFTHISORDINARYDEFAULTISINSUREDTHANMIGHTBESUPPOSEDHOWEVER,PRIVATEMORTGAGEINSURANCETYPICALLYEXCLUDESCOVERAGEOFTHETRULYCATASTROPHICDEFAULTRESULTING
3、FROMSUCHACTSOFGODASTHEFIRES,FLOODS,EARTHQUAKES,ANDHURRICANES,INCREASINGLYFAMILIARINTHEUNITEDSTATESINRECENTYEARSOFTEN,THESEEVENTSAFFECTASUBSTANTIALPORTIONOFTHEHOUSESWITHINAPARTICULARNEIGHBORHOODORREGIONANDIFDISASTERINSURANCEORGOVERNMENTAIDISINADEQUATEORNONEXISTENT,DEFAULTISLIABLETOOCCURTHEMOSTPROMINE
4、NTEXAMPLEOFANATURALDISASTERLEADINGTOSUBSTANTIALDEFAULTHASBEENTHE1994NORTHRIDGECALIFORNIAEARTHQUAKE,ALTHOUGHTHE1971SANFERNANDOEARTHQUAKEALSOISOFNOTEMANYEXPERTSFORESEEANEARTHQUAKESIMILARINMAGNITUDETOTHE1906SANFRANCISCOEARTHQUAKEOCCURRINGINCALIFORNIAWITHINTHENEXT20TO30YEARS,WHICHMAYBEEXPECTEDTORESULTIN
5、TENSOFTHOUSANDSOFDEFAULTSEXACTLYTHISSORTOFEVENT,RAREBUTOFGREATMAGNITUDE,MOSTLENDERSWOULDWANTTOINSUREAGAINSTBUTCANNOTANARGUMENTCANBEMADETHAT,IFMORTGAGESWERERESOLDANDSUFFICIENTLYREDISTRIBUTED,CATASTROPHICDEFAULTWOULDBEOFCONSEQUENCEONLYTOTHEEXTENTTHATITCONTRIBUTEDTOTHEEXPECTEDCOSTOFDEFAULTHOWEVER,THESA
6、MEREASONINGMIGHTBEAPPLIEDTOORDINARYDEFAULTANDSO,WITHSUCHDIVERSIFICATION,THEENTIRERATIONALEFORMORTGAGEINSURANCEOFANYKINDWOULDDISAPPEARTHEREFORE,THECONTINUALEXPANSIONOFTHEPRIVATEMORTGAGEINSURANCEINDUSTRYSPEAKSAGAINSTTHISARGUMENTINDEED,THESADEXPERIENCEOFTHE1980STEXASREALESTATEBUSTANDTHESUBSEQUENTSCOXAN
7、DROSS,1976JONES,1984BATES,1991THISYIELDSAJUMPDIFFUSIONPROCESSOFTHEFORMBMORTGAGEVALUATIONWITHCATASTROPHESASINDICATED,THECOSTOFAMORTGAGETOTHEBORROWERCANBECONSIDEREDTHESUMOFANAMORTIZINGLOANACALLOPTIONTOPREPAY,ANDADEFAULTOPTIONTHEYAREINFLUENCEDONLYBYCHANGESINTHETERMSTRUCTUREANDTHEHOUSEPRICE,ANYDERIVATIV
8、EASSETSUCHASTHEMORTGAGEANDITSCOMPONENTS,CANBEVALUEDBYSOLVINGTHISPARTIALDIFFERENTIALEQUATIONWITHOUTTHETERMSCONTAININGTHEPOISSONPARAMETER,WEHAVETHEUSUALVALUATIONEQUATIONFORADERIVATIVEASSETBEINGDRIVENBYREGULARDIFFUSIONPROCESSESINADDITION,HOWEVER,OVERANYSMALLMOMENTOFTIME,THEASSETCEASESTOBEOFVALUEANDJUMP
9、SDOWNTOVALUETHECATASTROPHICPAYOFFVARIESFROMASSETTOASSET,BUTCANBEFIGUREDOUTEASILYFORANYOFTHEMORTGAGESCOMPONENTSFROMTHEOBSERVATIONTHAT,FORTHEENTIREMORTGAGEVARIESFROMASSETTOASSET,BUTCANBEFIGUREDOUTEASILYFORANYOFTHEMORTGAGESCOMPONENTSFROMTHEOBSERVATION。THATIS,WEIMPOSETHECONDITIONTHAT,IFTHECATASTROPHEHAP
10、PENS,THENTHEMORTGAGEISTERMINATED,SOTHATTHELENDERRECEIVESBACKTHEDISTRESSEDPROPERTYOFVALUE,INTHEEVENTTHATDEFAULTISNOTINTHEBORROWERSINTEREST,THELOANISPREPAID,PRESUMABLYBECAUSETHEBORROWERPULLSUPSTAKESANDSELLSTHEUNINHABITABLEHOUSEORREBUILDSTHEHOUSEANDMUSTREFINANCETHELOANCINSURANCECOVERAGEANDPATHDEPENDENC
11、EINADDITIONTOSOLVINGFORTHEMORTGAGE,ONEMAYSOLVEFORTHEVALUEOFINSURANCEIFINSURANCEWEREPAIDUPFRONT,THISWOULDBEANENTIRELYPASSIVEASSET,INTHESENSETHATTHEVALUEOFTHEMORTGAGEDICTATESWHETHERINSURANCEISTOBEPAIDBUTTHEVALUEOFINSURANCEWOULDHAVENOINFLUENCEONTHEVALUEOFTHEMORTGAGEHOWEVER,WEAREINTERESTEDINTHEFEATURETH
12、ATPRIVATEINSURANCETYPICALLYCEASESONCETHEEQUITYINTHEHOUSEREACHES20OFTHEHOUSESORIGINALVALUEITTHENSEEMSAPPROPRIATETOADDTHECORRESPONDINGFEATURETHATPRIVATEMORTGAGEINSURANCEISNOTACTUALLYPAIDUPFRONTBUTOVERTIME,INTHEFORMOFMONTHLYINSTALLMENTSTHISMEANSTHATTHEDEFINITIONMUSTBEEXPANDEDTOINCLUDETHEEXPECTEDCOSTOFI
13、NSURANCEPAYMENTSINADDITIONTOTHECOSTOFAMORTIZINGTHELOANANDTHAT,NEXTTOTHEMORTGAGEPAYMENT,AMONTHLYINSURANCEPREMIUMMUSTBEADDEDTHEREISTHENANEVERSOSLIGHTLYINCREASEDINCENTIVETOPREPAYORDEFAULT,SINCEDOINGSOAVOIDSFURTHERINSURANCEPAYMENTSWHATISMORE,THEPROBLEMBECOMESPATHDEPENDENT,SINCETHEINSURANCEPREMIUMISNOTPR
14、ESENTIFTHE20RULEHASBEENTRIGGEREDATSOMEPASTDATETHISEFFECTOFINSURANCEPAYMENTSISQUITESMALLANDMIGHTWELLBEIGNOREDINTHEVALUATIONOFTHEMORTGAGE,BUTASNOTED,THEREISSIMULTANEOUSLYTHEISSUEOFINSURANCECOVERAGE,WHICHISCONSIDERABLYMOREIMPORTANTFORTHISPAPER,SINCETHELENDERBEARSWHATEVERLOSSESARENOTINSUREDGIVENTHATONEW
15、ANTSTOSOLVETHEPATHDEPENDENCYPROBLEMFORINSURANCECOVERAGE,ONEMIGHTASWELLDOSOFORINSURANCEPAYMENTSASWELLTHISISDONEBYRUNNINGTWOVERSIONSOFTHEMORTGAGEVALUATIONPROCESS,ONEUNDERTHEASSUMPTIONTHATINSURANCEHASCEASEDINSOMEPREVIOUSMONTH,ANDONEUNDERTHEASSUMPTIONTHATITHASNOTATEACHMONTHSEND,THELATTERSOLUTIONISALTERE
16、DBYSUBSTITUTINGINTHEFORMERSVALUESFORCOMBINATIONSUNDERWHICHTHETHENCURRENTHOUSEPRICEFULFILLSTHE20RULETHEVALUATIONPROCEDUREPROCEEDSASBEFOREBACKWARDINTIMEAND,INTHEEND,ATTHEORIGINOFTHECONTRACT,ONLYTHELATTEROFTHETWOSOLUTIONS。THEREAREONLYTWOOTHERSMALLREMAININGCOMPLICATIONSTOTHEVALUATIONOFTHEMORTGAGEFIRST,I
17、NTHENAMEOFREALISM,WEHAVEADDED“SUBOPTIMAL”TERMINATIONATTHEENDOFEACHMONTH,APPLIEDACCORDINGTOAFIXEDPSAPUBLICSECURITIESASSOCIATIONSCHEDULETHISACCOUNTSFORTERMINATIONOCCURRINGFORREASONS,SUCHASJOBRELOCATION,THATDONOTINVOLVEMINIMIZINGTHEVALUEOFTHEMORTGAGEWHETHERTHISTAKESTHEFORMOFPREPAYMENTORDEFAULTISDECIDED
18、ENDOGENOUSLYINTHESAMEMANNERASISCATASTROPHICTERMINATION,BUTOFCOURSE,ITMOSTLIKELYTAKESTHEFORMOF“SUBOPTIMAL”PREPAYMENTSECOND,WEHAVEPERMITTEDTHETRANSACTIONCOSTSOFTERMINATION,WHICHVARYDEPENDINGONWHETHERTHETERMINATIONISDONEBYPREPAYMENTORDEFAULTANDWHETHERTHETERMINATIONISORDINARY,RATIONALTERMINATION,“SUBOPT
19、IMAL”TERMINATION,ORCATASTROPHICALLYINDUCEDTERMINATIONHEREAGAIN,ITISANADVANTAGEOFOURCHOSENTECHNIQUETHATONECANDISTINGUISHTHETRANSACTIONCOSTSOFORDINARYANDCATASTROPHICDEFAULTDPROBABILITYOFLOSSTOTHELENDERNOW,INSURANCEPAYSOUTTHEDIFFERENCEBETWEENTHEACCRUEDUNPAIDPRINCIPALANDINTEREST,ANDTHEHOUSEVALUE,UPTOTHE
20、MAXIMUMCOVERAGE,USUALLYBEING25OFTHEORIGINALHOUSEVALUEWHENEVERTHISMAXIMUMCOVERAGEBINDSORTHEDEFAULTHASCEASEDTOBEINSURED,THEUNCOVEREDPORTIONBECOMESALOSSTOTHELENDERWESEEKTODETERMINETHISDISTRIBUTIONOFLOSSESITMIGHTBEARGUEDTHAT,ECONOMICALLY,THEUNINSUREDPORTIONISABETTERMEASUREOFTHELENDERSLOSS,BUTITSEEMSFAIR
21、TOSAYTHATMOSTLENDERSWOULDCOUNTTHEIRLOSSINTERMSOFTHEUNPAIDPRINCIPALNOTRETURNED,RATHERTHANTHEMORTGAGEPAYMENTSTHATMIGHTHAVEBEENPAIDFINALLY,WENOTETHAT,TOOVERCOMETHEPATHDEPENDENCYPROBLEMDUETOWHETHERINSURANCEISINFORCEORNOT,JUSTASWITHTHEVALUATIONCALCULATIONSDISCUSSEDPREVIOUSLY,WEMUSTRUNTWOPARALLELVERSIONSO
22、FTHEPROBABILITYCALCULATIONS,ONEUNDERTHEASSUMPTIONTHATINSURANCEISINFORCE,ONEUNDERASSUMPTIONTHATITISNOTASPREVIOUSLYDESCRIBEDFORTHEVALUATIONCALCULATIONS,THESETWOSETSOFANSWERSAREMERGEDATTHEENDOFEACHMONTH,ANDBYTHISPROCESS,WEARRIVEATTHEBEGINNINGOFTHECONTRACTWITHAPROBABILITYCALCULATIONTHATTAKESINTOACCOUNTT
23、HEFACTTHEINSURANCEWILLCEASETOAPPLYAFTEROWNEREQUITYREACHES20OFTHEORIGINALHOUSEVALUEIIICONCLUSIONTHEPOINTOFMORTGAGEINSURANCEISTOPROTECTTHELENDERAGAINSTDEFAULTHOWEVER,PRIVATEMORTGAGEINSURANCETYPICALLYHASAMAXIMUMCOVERAGEOF25OFTHEUNPAIDPRINCIPALANDCEASESTOBEREQUIREDONCEBORROWEREQUITYHASREACHED20OFTHEHOUS
24、ESORIGINALVALUETHE25MAXIMUMMEANSTHATINSURANCECANBEINADEQUATETOCOVERLOSSES,EVENATTHEMODEST10HOUSEPRICEVOLATILITIESTAKENASTHEBASECASEOFTHISPAPERTHEREASON,OFCOURSE,ISTHAT,GIVENTHEOPPORTUNITYTOTERMINATEINTHEFUTURE,BORROWERSRATIONALLYDELAYCURRENTDEFAULTUNTILTHEIRPAYOFFISWELLINTHEMONEYANDTHEHOUSEHASSUBSTA
25、NTIALLYDROPPEDINPRICEBEYONDTHISCASEWHEREDEFAULTISINSUREDBUTINADEQUATELYSO,THELENDERALSOMUSTWORRYABOUTDEFAULTTHATOCCURSAFTERINSURANCEHASCEASEDFORINSURANCECOVERAGETOCEASE,THEHOUSEPRICEMUSTHAVERISENBUTJUSTASTHEREISUPWARDVOLATILITY,SOTHEREISDOWNWARDVOLATILITY,ANDIFTHISSUBSEQUENTLYRESULTSINDEFAULT,ALLLIA
26、BILITYGOESTOTHELENDERFINALLY,PRIVATEMORTGAGEINSURANCEREFUSESTOCOVERTHECATASTROPHICFALLSINPROPERTYVALUESASSOCIATEDWITHMAJORNATURALDISASTERSALLTHESEPOSSIBILITIESOFLOSSAREOFCONSEQUENCETOTHELENDERANDNEEDTOBEEVALUATEDTHEPOINTOFTHISPAPERISTHATTHEOPTIONPRICINGMETHODOLOGYPROVIDESTHEMEANSFORCALCULATINGSUCHPR
27、OBABILITYDISTRIBUTIONS,ANDTHETECHNIQUESTRADITIONALROLEINPRICINGMORTGAGESISBUTONEASPECTOFITSUSEFULNESSTOLENDINGINSTITUTIONS外文题目CATASTROPHICDEFAULTANDCREDITRISKFORLENDINGINSTITUTIONS出处JOURNALOFFINANCIALSERVICESRESEARCH作者JAMESBKAUANDDONALDCKEENAN译文灾难性的违约和贷款机构的信用风险1引言只有当按揭保险缺席或不足时，才会出现抵押贷款人的信用风险。抵押保险事实上
28、确保最普通的贷款人违约也就是说，总体市场住房波动引起的违约。（虽然，从全面评估，这种普通违约比被保险的预计值要小）。然而，私人抵押贷款的保险范围通常不包括最近几年在美国越来越常见的由于天灾，如火灾，水灾、地震、飓风造成的灾难违约行为。通常,这些事件影响一大块在特定的街道或地区的房屋；如果灾难保险或政府援助是不够的,甚至是不存在的,违约就可能发生。最突出的因为自然灾害导致的大量违约行为的例子是1994年加州的北岭地震，1971年圣费尔南多地震也是值得注意的。许多专家预见未来20到30年中发生与1906年加州旧金山地震相似震级的地震，可能会引起成千上万的违约。这类大震级但比较罕见的事件，大多数银行
29、想投保，但不能。可以得出结论，如果抵押贷款被转手并有足够的再分配性，灾难性的违约后果价值仅仅在于它导致了预期违约成本（对于这些稀有事件，这一贡献非常小）因此，同样的逻辑也可用于普通的违约，如此多样化使各种抵押保险的整体理由消失。因此,不断扩大的私人抵押保险行业反对这个争论说。事实上,20世纪80年代德州房地产泡沫的破灭以及随后的S琼斯,1984年贝茨,1991年）增量就是服从跳跃扩散过程。B对灾难的抵押工程量清单计价成本抵押贷款借款人可以被认为是借方金额贷款提升的看涨期权,清缴默认选项假设他们只受改变期限结构、房价影响,任何衍生资产如抵押贷款和它的部件,通过求解价值偏微分方程可得结论没有条款包
30、含泊松参数,我们通常在推动通过有规律的扩散过程衍生资产评估方程,此外,在一些小的时间段,资产是一种价值或一种下跳的价值。灾难性回报不同于资产的回报,但通过观察却可以轻易找到各种抵押贷款成分。那就是,我们设定情况,如果灾难发生,那麽抵押终止。那么贷款人收回痛苦经历后的价值，在这种情况下，违约不是借款人的意愿，贷款是预付的，大概因为借款人抬升股本和销售不适宜居住的房子又或者重建房子，这都必须融资贷款。C保险和路径依赖除了计算抵押,一个人也可计算保险的价值。假如保险已经付清,这将是一种完全被动的资产,在这种意义上的抵押贷款的价值决定是否支付保险，但是保险的价值就没有影响按揭的价值吗我们会关注一个现象
31、，当抵押资产的净值达到房子本身价值的20，私人保险公司将会停止接保。然后在相应的地方适当添加拨款，私人抵押保险不实行预先缴付，而是随着时间的推移,实行分期付款。这意味着必须扩展除摊销贷款成本以外的保险预期成本的支付，之后就是抵押贷款的支付还有每月的保险费用。接着还有轻微加大刺激预付和违约增加,因为这样做,免除进一步的保险费。更甚的是，当在过去的时日20的规则被激发，保险费已不存在，这个问题成为依赖的原因。这种效果的保险支付太小而很可能在评估的抵押会被忽略，但值得注意，有同时出版的保险,这是相当重要的,因为此篇文章的第一步便是贷款人承担任何损失是不可保险。考虑到一个人想通过投保项目解决这个途径依
32、存关系，他不防支付保险。这是在由两个版本的抵押价值运行的过程中,一个人假设保险已经在以前的一些月停止,以下的人假设也不会改变。在每个月的最后,后者解决方案改变了替代在前的价值观部件组合下实现了当前房价达到20的规则。评估程序获得过后退的时间,最后,在起源的合同,只有后者的一个解决方案。对于评估的抵押，只有其他的两种剩下的小而复杂的因素。首先,在这个名字的现实主义、我们增加了“不适合的”在每个月结束时终止,应用根据一个固定的PSA公众证券协会计划。这就说明了为什么终止发生的原因,如工作安置,那不涉及最小化价值的按揭吗。这是否需要提前还款或是违约，决定于与灾难性终止相同方式的内因。当然,它很可能需
33、要形成“不适合“提前还款。其次,我们已允许终止的交易成本,这取决于终止是否通过预付费或违约终止,是否会普通的、理性的终止、“不适合“终止、或造成灾难性影响的终止。在这里,这是一个利用我们所选择的技术,你可以区分普通的交易费用和灾难性的违约。D损失可能性的第一步现在,保险支付通常都是用25的屋子原有价值区别无偿积累的本金，利息，房子价值和最大范围。每当这个最大范围联结或是违约已经被被保险人停止,这揭露的部分就成为了债主的损失。我们要去确定该分布的损失。它可能认为,从经济上来看,没有保险的部分是出租人减少损失的一个更好的措施,但公平地说,大多数银行方面将他们未付的不还的损失，可能已经发生支付,而不
34、是抵押贷款。最后,我们注意到,克服了由于是否途径依存关系产生的问题，保险是有效的,就像在此之前的评估计算,我们讨论一定要用两条平行版本的概率的计算,一个假设保险有影响力、一个假设保险没影响。先前形容为评估计算,这两套答案都合并到月底,这一过程,我们用开始的合同概率计算，考虑事实保险停止后股权达到屋子原有的价值的20。3结论抵押保险的观点是保护贷款人防止违约。然而,私人抵押保险公司一般有支付25本金的最大范围和一旦借款人资产达到房子原有价值的20保险要求被停止。最大的25意味着保险可能会不足以弥补亏损,甚至在本文提出的基准10会影响住房价格的波动。原因当然存在,给予借款人终止在未来的机会,借款人合理拖延当前的违约,直到他们得到有利的回报或是这座房子的价格已经持续下降。在这情况下,违约是保险但不充分是,作为改革的第一步也要担心发生在保险违约上的停止。保险项目被终止，房子价格必须上涨。但就如波动，有上就有下，如果随后导致违约，一切责任归于贷方。最后,发生了2次大型自然灾害，私人抵押保险拒绝支付灾难产生的相关房产价值下跌。债主这一切损失的可能性需要评估。这篇文章的观点，期权价格方法提供工具来计算这样的概率分布，该技术一个方面作用在传统的抵押贷款定价上，另一方面作用在其有用性贷款机构上。
