灾难性的违约和贷款机构的信用风险外文翻译

1、灾难性的违约和贷款机构的信用风险外文翻译 外文题目: Catastrophic Default and Credit Risk for Lending Institutions出 处:Journal of Financial Services Research作 者: JAMES B. KAU and DONALD C. KEENAN原文:Catastrophic Default and Credit Risk for Lending InstitutionsIIntroduction Credit risk for a mortgage lender comes into play only

2、 when mortgage insurance is absent or inadequate. Mortgage insurance, in fact, insures lenders against most ordinary default: that is, default induced by movements in the overall market for housing although, as will be seen, for entirely explicable reasons, less of this ordinary default is insured t

3、han might be supposed. However, private mortgage insurance typically excludes coverage of the truly catastrophic default resulting from such acts of God as the fires, floods, earthquakes, and hurricanes, increasingly familiar in the United States in recent yearsOften, these events affect a substanti

4、al portion of the houses within a particular neighborhood or region; and if disaster insurance or government aid is inadequate or nonexistent, default is liable to occur. The most prominent example of a natural disaster leading to substantial default has been the 1994 Northridge California earthquak

5、e, although the 1971 San Fernando earthquake also is of note. Many experts foresee an earthquake similar in magnitude to the 1906 San Francisco earthquake occurring in California within the next 20 to 30 years, which may be expected to result in tens of thousands of defaults. Exactly this sort of ev

6、ent, rare but of great magnitude, most lenders would want to insure against but cannot An argument can be made that, if mortgages were resold and sufficiently redistributed, catastrophic default would be of consequence only to the extent that it contributed to the expected cost of defaultHowever, th

7、e same reasoning might be applied to ordinary default and so, with such diversification, the entire rationale for mortgage insurance of any kind would disappear. Therefore, the continual expansion of the private mortgage insurance industry speaks against this argument. Indeed, the sad experience of

8、the 1980s Texas real estate bust and the subsequent S&L crisis has amply demonstrated that numerous lending institutions continue to be significantly exposed to catastrophic events of a local character. Given the apparent inability or unwillingness of lenders to correctly value and diversify away th

9、eir credit risk, there should remain an interest on their part, as well as on the part of researchers, in gaining a firm understanding not only of the expected costs of a mortgage lenders liability but of the entire distribution of these possible liabilities This paper takes the now widely accepted

10、view that mortgages are just another financial contract and, so, can be valued by aoptions-pricing methodology. The decision to default is an option available to the borrower and occurs exactly when it is in the borrowers financial interests. Since valuation drives such models, we necessarily obtain

11、 the market values of default, mortgage insurance, and the lenders liability that any research adopting the option pricing methodology naturally would report. However,for the reasons just indicated, more insight is to be gained by going beyond these aggregate market valuations and, in a novel manner

12、, generating the distributions of events that average up to the market cost of the lenders liability. This involves doing probability calculations not present in the usual valuation calculations of options pricing, although since the correct valuation of a mortgages value involves endogenously deter

13、mining the precise circumstances under which a borrower will or wont default, this information necessarily is available and needs only to be extracted in the course of valuing the mortgage. The procedure for doing so is explained in section II, followed in section III by an analysis of numerical res

14、ults obtained for a sample mortgage subject to a small chance of a major catastrophic event.II. The model AThe economic environment with catastrophes While we mention all key aspects of the model, considerations of space require that we spend less time on features of a mortgage, such as, for example

15、, prepayment, that bear only indirectly on our central concern, catastrophic default. For a more leisurely discussion of the more .The key elements of any fixed rate mortgage FRM are amortization of the loan, together with the options to prepay or default. The first two features are particularly sen

16、sitive to the term structure, while the decision to default is particularly dependent on the value of the house, so that we choose the evolving spot interest rate and the house price to represent the uncertain economic environment. In the most conventional of fashions Cox, Ingersoll, and Ross, 1985,

17、the evolution of interest rates is assumed to obey a mean-reverting stochastic process. The regular diffusion portion of the house price also is assumed to be of the most standard of forms, mainly a proportional-growth log normal process Merton, 1973.However, to represent the arrival of catastrophic

18、 events, ones that occur beyond typical movements in house prices, we also append on a Poisson process Merton, 1976; Cox and Ross, 1976; Jones, 1984; Bates, 1991. This yields a jump-diffusion process of the form.BMortgage valuation with catastrophes As indicated, the cost of a mortgage to the borrow

19、er can be considered the sum of an amortizing loan a call option to prepay, and a default option .they are influenced only by changes in the term structure and the house price, any derivative asset such as the mortgage and its components, can be valued by solving this partial differential equation.

20、without the terms containing the Poisson parameter, we have the usual valuation equation for a derivative asset being driven by regular diffusion processes. In addition, however, over any small moment of time, the asset ceases to be of value and jumps down to value; The catastrophic payoff varies fr

21、om asset to asset, but can be figured out easily for any of the mortgages components from the observation that, for the entire mortgage varies from asset to asset, but can be figured out easily for any of the mortgages components from the observation。That is, weimpose the condition that, if the cata

22、strophe happens, then the mortgage is terminated, so that the lender receives back the distressed property of value , in the event that default is not in the borrowers interest, the loan is prepaid, presumably because the borrower pulls up stakes and sells the uninhabitable house or rebuilds the hou

23、se and must refinance the loan.CInsurance coverage and path dependence In addition to solving for the mortgage, one may solve for the value of insurance. If insurance were paid up front, this would be an entirely passive asset, in the sense that the value of the mortgage dictates whether insurance i

24、s to be paid but the value of insurance would have no influence on the value of the mortgage. However, we are interested in the feature that private insurance typically ceases once the equity in the house reaches 20% of the houses original value. It then seems appropriate to add the corresponding fe

25、ature that private mortgage insurance is not actually paid up front but over time, in the form of monthly installments. This means that the definition must be expanded to include the expected cost of insurance payments in addition to the cost of amortizing the loan and that, next to the mortgage pay

26、ment, a monthly insurance premium must be added. There is then an ever so slightly increased incentive to prepay or default, since doing so avoids further insurance payments. What is more, the problem becomes path dependent, since the insurance premium is not present if the 20% rule has been trigger

27、ed at some past date. This effect of insurance payments is quite small and might well be ignored in the valuation of the mortgage, but as noted, there is simultaneously the issue of insurance coverage, which is considerably more important for this paper, since the lender bears whatever losses are no

28、t insured. Given that one wants to solve the path-dependency problem for insurance coverage, one might as well do so for insurance payments as well. This is done by running two versions of the mortgage valuation process, one under the assumption that insurance has ceased in some previous month, and

29、one underthe assumption that it has not. At each months end, the latter solution is altered by substituting in the formers values for combinations under which the then current house price fulfills the 20% rule. The valuation procedure proceeds as before backward in time and, in the end, at the origi

30、n of the contract, only the latter of the two solutions。 There are only two other small remaining complications to the valuation of the mortgage. First, in the name of realism, we have added “suboptimal” termination at the end of each month, applied according to a fixed PSA Public Securities Associa

31、tion schedule.This accounts for termination occurring for reasons, such as job relocation,that do not involve minimizing the value of the mortgage. Whether this takes the form of prepayment or default is decided endogenously in the same manner as is catastrophic termination, but of course, it most l

32、ikely takes the form of “suboptimal” prepayment. Second, we have permitted the transaction costs of termination, which vary depending on whether the termination is done by prepayment or default and whether the termination is ordinary, rational termination,“suboptimal” termination, or catastrophicall

33、y induced termination. Here again, it is an advantage of our chosen technique that one can distinguish the transaction costs of ordinary and catastrophic default.DProbability of loss to the lender Now, insurance pays out the difference between the accrued unpaid principal and interest, and the house

34、 value, up to the imum coverage, usually being 25% of the original house value. Whenever this imum coverage binds or the default has ceased to be insured, the uncovered portion becomes a loss to the lender. We seek to determine this distribution of losses. It might be argued that, economically ,the

35、uninsured portion is a better measure of the lenders loss, but it seems fair to say that most lenders would count their loss in terms of the unpaid principal not returned, rather than the mortgage payments that might have been paid. Finally, we note that, to overcome the path-dependency problem due

36、to whether insurance is in force or not, just as with the valuation calculations discussed previously, we must run two parallel versions of the probability calculations, one under the assumption that insurance is in force, one under assumption that it is not. As previously described for the valuatio

37、n calculations, these two sets of answers are merged at the end of each month, and by this process, we arrive at the beginning of the contract with a probability calculation that takes into account the fact the insurance will cease to apply after owner equity reaches 20% of the original house value.

38、III.Conclusion The point of mortgage insurance is to protect the lender against default. However, private mortgage insurance typically has a imum coverage of 25% of the unpaid principal and ceases to be required once borrower equity has reached 20% of the houses original value. The 25% imum means th

39、at insurance can be inadequate to cover losses, even at the modest 10% house price volatilities taken as the base case of this paper. The reason, of course, is that, given the opportunity to terminate in the future, borrowers rationally delay current default until their payoff is well in the money a

40、nd the house has substantially dropped in price. Beyond this case where default is insured but inadequately so, the lender also must worry about default that occurs after insurance has ceased. For insurance coverage to cease, the house price must have risen: but just as there is upward volatility, s

41、o there is downward volatility, and if this subsequently results in default, all liability goes to the lender. Finally, private mortgage insurance refuses to cover the catastrophic falls in property values associated with major natural disasters. All these possibilities of loss are of consequence to

42、 the lender and need to be evaluated. The point of this paper is that the option-pricing methodology provides the means for calculating such probability distributions, and the techniques traditional role in pricing mortgages is but one aspect of its usefulness to lending institutions.外文题目: Catastrop

43、hic Default and Credit Risk for Lending Institutions出 处:Journal of Financial Services Research作 者: JAMES B. KAU and DONALD C. KEENAN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

44、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

45、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&L危机等的悲惨经历已经充分表明,众多的借贷机构继续有明显的灾难性事件发生,这暴露了当地的内在问题。某种明显的无能或者贷方多元化非意愿的价值观导致了信用风险,必须留有一份自己的利息以及部分研究人员。对于获得的理解,不仅是抵押贷款出租人赔偿责任的预期花费,也是对整个分布情况内的可能责任。 本文摘要认为,现在已经被广泛接受了贷款只是另一个金融合同,所以,可以由期权-价格的方法进行定价。对于违约的解决方案是当涉及借款人的经济利益时,给提供借款人多一份选择以及可能发生时间的较精确分

46、析。任何采用自然期权定价法的报告可以显示,评估这些模型驱动,我们便能获得市场违约价值,抵押保险和银行的责任。然而,原因仅仅表明,对于总体市场价值评估的深入研究可以获得更加深刻的理解,从新颖的角度看,生成的市场成本分布平均值上移的事件在贷方之责任。通常的评估期权定价的计算不涉及到概率计算。虽然是对借款者违约或不违约的精确抵押贷款价值正确的评估,这个信息一定是可得到的,仅仅需要提取过程中的重抵押贷款。在第二部分解释这样做的程序,随后在第三部分是对小几率但较大的悲惨事件进行抵押的样本进行的数值分析。2.模型A.经济环境和灾害 当我们提到的所有关键方面的模型,考虑的空间要求我们少花点时间特性的抵押贷款

47、,例如提前还款,灾难性违约,这仅由我们的中央间接关注承担。任何固定利率贷款(FRM)的关键要素是摊销贷款连同选项预缴或违约。第一个两个特点是期限结构的特殊性和敏感性,而决定违约的因素取决于房子自身的价值。所以,我们选择进化点利率和房价代表不确定的经济环境。最常规的变革(考克斯,英格索尔, 罗斯,1985年)利率的演变是假定依据平均值-回归的随机过程。 定期扩散部分房价格也假设为最标准的形式,进行一个比例-增长对数正态过程(莫顿,1973年)然而,代表灾难性事件的到来,或者发生超过典型的运动的房价下跌,我们也倚普耳松过程(莫顿, 考克斯,罗斯1976年;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