摘要
在我国，银行在金融系统中占据核心地位，而抵押贷款则是银行最主要的资产项目，不动产又是其中最重要的抵押物。美国的次贷危机告诉我们，当银行的抵押贷款资产出现严重问题的时候，会对金融系统乃至整个经济造成巨大影响。因此，我们以抵押贷款，特别是住房抵押贷款作为我们研究的标的。
以往对于住房抵押贷款的研究多集中在两个方面：第一，是对贷款违约率的研究，这些研究大都采取简单的理论模型附加大量微观数据为基础的实证检验；第二，是出于考虑抵押贷款证券化过程中定价问题的研究，这些研究大都把抵押贷款看成期权合约，采用现代金融定价理论，在对关键变量进行设定以后计算定价。两类研究都具有很强的现实意义。然而，两类研究都有一个基本的假定，就是个体之间不存在差异性。违约率的研究考虑的个体虽然有可能有差异性，但是这种差异性是把个体看成具有相同分布的随机变量而产生的差异；在定价领域如果考虑到个体差异性的存在的话，定价的研究会变得非常复杂，在这里所付出的努力不如代表性变量的合理估计更加务实。
本文在前人研究的基础上引入了贷款人的差异性，来探讨三个问题：第一，对于某些影响违约率的因素来说，由于差异性的存在其对违约率的影响方式将可能会改变，换言之，如果经济中只有一类个体，那么一个因素的变化导致一件事情发生就好像是一个人的行为一样，但是当经济中有多种个体的时候，一个因素的变化会导致对于不同的个体发生不同的事情，个体内部的微观结构发生了变化，而我们所研究的违约率就是这个微观结构的一种表现；第二，差异性的存在导致了不同的个体会选择不同的贷款，银行必须对于不同的贷款品种设定不同的贷款价格，而这个价格序列的排列问题，我们称之为贷款菜单问题；第三，差异性的存在导致了不同的贷款申请人会选择不同的贷款，那么他们会如何选择，以及这种选择对于整个金融系统有什么意义，都是值得我们关注的。第一个问题的回答给出了我们的研究和现实银行管理之间的密切关系；第二个问题的回答给出了在各种市场结构下银行的决策过程以及结果；第三个问题的回答给出了在银行做出决策以后，个人的最优化行为导致的市场结构的选择性分离。通过回答这三个问题，我们寻找了一条探索住房抵押贷款微观市场结构的路径。
我们以个人购买住房的投资动机作为建模的个人行为标准，根据文章研究的目的合理剪裁了无摩擦期权模型的部分特征，放弃了期限长度的现实近似，使用了0-1期的简单环境，舍弃了随机布朗运动假设而引入了变量服从一般分布作为讨论的基础。而后，我们在第二章中进行违约率加总的时候选择了更加合理的手段，得到了更符合现实经济的结论；在第三章、第四章中，我们引入了甄别的研究思路，探讨了住房抵押贷款市场的微观结构在不同市场结构下的表现。
研究发现，差异性的存在会导致抵押贷款的违约率对于例如抵押物的价格变化、利率以及房屋租金等通过投资收益来影响违约行为的影响因素会产生分段响应。以住房抵押贷款违约率对于房屋价格增长率的响应为例，存在一个住房价格增长率数值会使得当住房价格增长率高于该数值的时候，违约率与住房价格增长率不相关；当住房价格增长率低于该数值的时候，违约率与住房价格增长率负相关。断点的高低和贷款房价比率有关系，贷款房价比率越高的贷款种类，断点就越高。
在竞争性的市场当中，对于未来住房价格走势比较悲观的个体会选择存款，而对于未来住房价格走势比较乐观的个体会选择贷款。银行最终形成了贷款房价比率和贷款利率正相关的贷款菜单，较为乐观的个体更可能会选择贷款房价比率比较高的贷款。在垄断市场当中，最悲观的个体会选择存款；其它乐观的个体则依据自己的保留贷款条件是否可以对银行更有利而有所区分，银行会把贷款发放给对自己而言，保留贷款条件最有利的那一部分个人，其余的则会选择独立买房。贷款菜单是个人保留贷款条件的包络的一部分，贷款房价比率和利率依然正相关。选择贷款的个人越乐观，选择的贷款房价比率越低。竞争性条件下的个人选择体现了个人的意愿，而垄断市场条件下的个人选择体现了银行的利益诉求。
文章对于一个在危机刚刚发生不久备受关注的题目选择了一个全新的视角来考察，文中大胆的修改了一般无摩擦期权模型的建模方法，成功地在住房抵押贷款市场的微观结构的研究中引入了异质性个体，开创新的将甄别理论的研究思想引入到了银行贷款的问题中来，在克服了一系列的技术困难之后得到了一些基本的结论。
抵押贷款所引起的金融危机即使在美国历史上已经不止一次，对于抵押贷款市场微观结构的研究有助于帮助我们银行更加合理的设计抵押贷款产品，也有助于我们的金融监管部门对于银行风险管理更加有针对性。我们的研究只是粗浅的，众多影响因素的差异性对于抵押贷款市场微观结构的影响尚待考察。但是，我们以个人预期的差异性作为一个范本，为将来更加全面的研究提供一个研究的思路和标尺。同时我们对于住房抵押贷款市场微观结构的考察也带给了我们许多启示。
Banks are the most important part in the financial system in China, and of theirassets, mortgages, especially residential mortgages are the most important. The USSubprime Crisis told us that if there is some trouble in banks’ mortgages, the wholefinancial system as well as the whole economy may suffer. Therefore, we make thisstudy on home mortgages.
Two problems have being concerned in past research on mortgages. One is theforeclosure rate and its possible reasons to change. These researches may use simplemodels going with empirical research carrying great amount of data on micro activity.The other is the valuation of mortgages if banks are willing to sell them to others.These researches usually deal with mortgages like options, using newly developedfinancial pricing theory to calculate the mortgage value. Both kinds are important.However, there is one assumption in both of them that applicants are homogeneous.There might be heterogeneity in the empirical research on foreclosure rate, but thisheterogeneity is caused by the same distribution of some mortgage applicants’ quality.Moreover, if we consider heterogeneity in mortgage pricing, the solution might bealmost impossible, hard work on which is worse than a better estimation of thevariables on homogeneity model.
Importing heterogeneity, three aspects are studied in this article. First, if thereare some factors influencing the foreclosure rate, how the influence is affected byheterogeneity. In other words, if there is only one kind of individuals, a factorchanges and something happens, it behaves as if there is only one man. But if thereare various kinds of individuals, a factor changes and different things happen fordifferent people. The inner structure of the individual might change. The foreclosurerate we study is a piece of it. Second, if the mortgage applicants are different, theydeserve different mortgages and banks may provide them with different ones. How dothese mortgages value? We call this the mortgage-menu problem. Third, if theapplicants are different, they may apply for different mortgages. How do they select? What does this mean to the financial system? The answer for the first question givesus the relationship between our research and the banking management. The answerfor the second tells us how banks make decisions in different market structures. Theanswer for the third shows us that how do individuals’ self-decisions split the market.By answering these questions, a research path to the micro structure of the mortgagemarket is found.
Basically we assume that people buy house for investment, not for consumption.And then we changed some characteristics of the Frictionless Option Model. We use a2-period economy instead of the long time assumption of traditional model whichseems more close to reality. We assume the stochastic variables are distributedanyway, which replaces the Brownian motion assumption. In chapter2, moreadequate way to aggregate is used when studying the foreclosure rate. With its help,more realistic result is found. In chapter3and4, the idea of screening is introducedinto our research. The micro structure of the mortgage market is studied in differentcircumstances.
The following results are found. For the factors like the house price appreciation,interest rate or house rent cost that influence the investment decision of the mortgageapplicants, there is one point in them. Take the house price for example. If the houseprice appreciation is higher than that point, it is unrelated to the mortgage foreclosurerate. If the house price appreciation is lower than that point, it is negatively related tothe mortgage foreclosure rate. That point holds a positive relationship with theloan-to-value ratio.
If banks are in perfect competition, optimists on future house price would like toapply for mortgages. On the other hand, pessimists on future house price would liketo save. The mortgage menu can be formed at last and the mortgage interest rate ispositively related to the mortgage loan-to-value ratio. There is more possibility thatthe optimists may choose higher loan-to-value ratio. If there is only one bank inmonopoly, the most pessimists on future house price would like to save as well as theperfect competition case. But for other people, things are different. Their choicesdepend on the reservation loan condition. If a person’s condition is preferred buy thebank, the person is chosen to be a mortgage applier. Other people buy house all by themselves. The loan menu is a part of the envelope of the reservation loan conditions.The loan interest rate is positively related to the loan-to-value ratio. Optimists chooselower loan-to-value ratios, while pessimists choose higher ones. In the perfectcompetition market, people’s choices reflect their willing, but in the monopoly case,the choices are only the result of bank’s profit pursue.
Shortly after the crisis began, the mortgage related problem has been a hot point.The article makes a whole new study by modeling the problem with self-reformedfrictionless option model, successfully introducing heterogeneity into the homemortgage study and using the idea of screening in the mortgage study for the firsttime. After conquering a lot of technical difficulties, some basic results are given.
Financial crisis caused by mortgage defaults is not for the first time even inAmerican history. The research on micro structure of mortgage market helps banks tomake better mortgages and helps the central banks to manage the banking systembetter. This research is still unsatisfying, and more heterogeneous factors might beconsidered. We take the different expectation as an example and benchmark for moredetailed and complete research in the future. At the same time, great deals of usefulrevelations come out after the research of the mortgage market micro structure.
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