上海市住房反向抵押贷款养老保险问题研究——产品定价与风险防范

一、引言 作为一项新型金融产品,住房反向抵押贷款是否具有生命力,取决于其定价是否合理。由于住房反向抵押贷款借贷期限长,影响因素复杂,如利率、房价的波动、人均预期寿命的延长、道德风险等,定价一直就是住房反向抵押贷款的难点与核心,国内外学者围绕这一问题构建了诸多模型进行定量研究。目前主要是集中在固定利率的定价上。     

固定利率住房抵押贷款定价研究——基于隐含期权视角

由于缺乏经验,我国商业银行固定利率住房抵押贷款定价存在不合理性,既影响了固定利率住房抵押贷款业务的健康发展,又导致了借贷双方风险与收益的不匹配。在市场利率服从几何布朗运动的基础上．本文从隐含期权视角出发构建固定利率住房抵押贷款单位风险收益最大化模型,并求出最优解,为商业银行固定利率住房抵押贷款定价提供理论和技术参考。     

固定利率住房抵押贷款违约行为及其定价研究

固定利率住房抵押贷款的信用风险主要是违约风险,基于理性期权的定价模型往往会低估借款人的违约概率.通过分析违约成本及非理性违约因素,可以确定借款人违约时贷款机构收回的现金流,得到固定利率住房抵押贷款定价的期望值模型,并得出模型的求解方法.     

住房抵押贷款支持证券定价模型的发展与启示

住房抵押贷款证券化发行的住房抵押贷款支持证券包含提前偿还风险和违约风险两个期权,这使得其定价要比一般债券的定价复杂得多。而我国的住房抵押贷款证券化又有着不同证券化发达国家的特点,因此研究国外定价模型的适用情景和发展对我国的实践是非常必要的。本文旨在沿着住房抵押贷款支持证券定价理论结构化和简约化模型两条主要线索的发展,对该领域的最新研究成果进行介绍和评价,并得出和我国住房抵押贷款证券化实践相关的启示。     

住房抵押贷款风险研究

我国房地产发展迅猛的同时住房抵押贷款规模也在不断扩大,这对贷款的风险管理提出了很高的要求。本文从影响贷款的两个主要因素—利率和房价入手,利用借款人的两个或有期权构建了贷款定价模型,并阐述了提前支付成本和违约成本对贷款价格的影响。同时也分析了影响贷款价格的其它摩擦性因素,并对住房抵押贷款风险提出了一些建设性意见。     

住房抵押贷款风险研究

我国房地产发展迅猛的同时住房抵押贷款规模也在不断扩大,这对贷款的风险管理提出了很高的要求。本文从影响贷款的两个主要因素—利率和房价入手,利用借款人的两个或有期权构建了贷款定价模型,并阐述了提前支付成本和违约成本对贷款价格的影响。同时也分析了影响贷款价格的其它摩擦性因素,并对住房抵押贷款风险提出了一些建设性意见。     

住房抵押贷款支持证券定价方法:发展与启示

西方MBS定价方法主要有传统定价法、计量模型定价法、期权调整利差定价法和再融资临界价法.我国在借鉴国外经验对MBS定价的过程中,应充分考虑所处定价环境的差异,采用合理的定价方法.现阶段,我国应加快完善市场利率结构和建设商业银行住房抵押贷款数据库,为MBS的科学定价创造良好条件.     

住房反向抵押改善老年人收入的定量分析

住房反向抵押贷款是一种新型的养老保障方式。用北京市的调查样本定量分析影 响老年人参与住房反向抵押贷款的因素表明,参与住房反向抵押贷款的老年人的收入改善程 度和老年人收入/住房价值的比率呈负相关性;对于老年人收入改善程度而言,住房反向抵押 贷款比卖大房换小房的效果要好。上述研究方法中的创新在于把老年人居住在自己住房里的 效用以租金的形式量化到老年人的收入中,相对全面地体现了老年人的福利状况。     

我国发展住房反向抵押贷款研究

住房反向抵押贷款（Reverse Mortgage）是一种新型的住房金融产品，也是实现以房养老的金融工具。它是指老年人以拥有产权的住房作抵押，向银行或其他金融机构借款消费，同时老人仍然保留房屋居住权，在去世后用住房还贷。由于其现金流流向与传统的抵押贷款相反，像是把住房抵押贷款业务反向来做，如同金融机构用分期付款的方式从借款人手中买房，所以在美国最先被称为“反向抵押贷款”。     

保险公司开展住房反向抵押贷款可行性简析

住房反向抵押贷款是以拥有住房的老年居民为放款对象,以房产作为抵押,在居住期间无需偿还,在贷款者死亡、卖房或者永久搬出住房时到期,以出售住房所得资金归还贷款本金、利息和各种费用的一种贷款。住房反向抵押贷款的开展可以说有特殊意义。我国如今已经进入老龄化社会,中国老龄化的特征是未富先老。所谓“未富先老”既指的是老龄化到来之际国家还很不富裕,也指的是老人的收入也很低。国家不富裕就意味着国家还不能为老人提供充分的保障,老年人在相当的程度上还得依靠自己解决养老保障的资金。这种情况下,住房反向抵押贷款可说是一块有待挖掘的养老保障“金矿”。     

Pricing commercial mortgages and their mortgage-backed securities

This article has taken considerable effort to accurately model the complexity of a commercial mortgage and its mortgage-backed security. In fact, it is the first example in the general literature on mortgage pricing to present a comprehensive set of numerical results in which the valuation of a mortgage-backed security is explicitly tied to that of the underlying mortgage. The conclusion we reach is that option pricing provides an accurate and flexible approach to valuing the complex mortgage instruments now being developed in the financial community.     

On the determinants of yield spreads between mortgage pass-through and Treasury securities

Yield spreads between mortgage pass-through and U.S. Treasury securities may reflect differences in taxation, phenomena affecting relative supply and demand, and compensation for default, call, and marketability risks on mortgage instruments. Our research empirically models differences in yields between pass-throughs and comparable-maturity Treasuries. We find that interest-rate volatility and the term structure of rates, factors often cited in the mortgage pricing literature as affecting the mortgage call premium, are the primary determinants of movements in these spreads. Moreover, these effects have grown in importance in recent years as exercise of the prepayment option has increased. We also find evidence that liquidity and credit concerns affect the pricing of pass-through securities.     

The probability of prepayment

Prepayment is a risk of holding a mortgage or derivative security. Incorrect pricing of prepayment risk leads to increased volatility and uncertainty in mortgage security markets. This article prices prepayment risk within an underlying callable bonds model. To price mortgages accurately, a probability of prepayment is required. A mortgage is a callable bond with a package of an option to prepay currently and a sequence of options to prepay up to the date of maturity. This sequence is summarized by a compound option. The probability of prepayment is determined by the prices of the current call and this compound option. These option prices depend on market interest rates and age, and on the contract terms of the originated mortgage.     

An Empirical Investigation of Alternative Contingent Claims Models for Pricing Residential Mortgages

Researchers have employed option pricing techniques to analyze mortgage financing and valuation. Alternative models (one-, two-, and three-variable models) employing different variables (short- and long-term interest rates and building value) have been designed to price mortgage securities. No prior research has addressed the question of whether the pricing accuracy of these contingent claims models improves as states increase or whether contingent claims models' valuation abilities generate reasonable estimates of primary mortgage market prices. The articles investigates the relative efficiency of each of these alternative mortgage valuation models in predicting primary market mortgage values. Our results show that a two-variable model (short rate and building value) is the most efficient. Valuation results indicate a positive pricing spread between the primary market and the theoretically estimated value.     

The valuation at origination of fixed-rate mortgages with default and prepayment

This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.     

Mortgage prepayment with an uncertain holding period

A discrete-time-option pricing model is developed to value a mortgage and its embedded prepayment option when the effective life of the mortgage is a random variable with a probability distribution of known parameters. The model can be applied when the borrower's ex ante expectation of his tenure follows any probability distribution bounded to the left at zero. The Gamma distribution is used to illustrate the model.The pricing model is further applied to determine the conditions under which financially motivated prepayment is optimal. The results show that the certainty model understates the Interest Rate Differential needed to justify prepayment (IRD) for short Expected Holding Period (EHP) borrowers and overstates the IRD for long EHP borrowers. When the EHP is relatively long, the certainty model provides relatively good estimates of IRD during the beginning years of the mortgage life. Under most other conditions, the estimates of the certainty holding period model are biased.     

Pricing mortgages: An interpretation of the models and results

Mortgages, like all debt securities, can be viewed as risk-free assets plus or minus contingent claims that can be usefully viewed as options. The most important options are: prepayment, which is a call option giving the borrower the right to buy back the mortgage at par; and default, which is a put option giving the borrower the right to sell the house in exchange for the mortgage. This article reviews and interprets the large and growing body of literature that applies recent results of option pricing models to mortgages. We also provide a critique of the models and suggest directions for future research.The Ohio State University and the National Bureau of Economic ResearchThe Urban Institute University of California at Los Angeles     

Unintended Consequences of Risk Based Pricing: Racial Differences in Mortgage Costs

The following analysis focuses on the role that risk pricing has had in the allocation and access to mortgage funds, specifically how it results in cost differences by race. Using a sample of fixed-rate first lien mortgages, we control for the risk characteristics of borrowers and assets. We find that borrowers with comparable credit quality experience significantly higher costs for mortgages in neighborhoods with a high density of minority households. Further, when the pricing differential is controlled for in a model of mortgage default, there is no support for neighborhood price differences. This finding illustrates a potential inequity that results from efficient/risk pricing in mortgage underwriting.     

A comparative study of the probability of default for global financial firms

This article presents a modification of Merton’s (1976) ruin option pricing model to estimate the implied probability of default from stock and option market prices. To test the model, we analyze all global financial firms with traded options in the US and focus on the subprime mortgage crisis period. We compare the performance of the implied probability of default from our model to the expected default frequencies based on the Moody’s KMV model and agency credit ratings by constructing cumulative accuracy profiles (CAP) and the receiver operating characteristic (ROC). We find that the probability of default estimates from our model are equal or superior to other credit risk measures studied based on CAP and ROC. In particular, during the subprime crisis our model surpassed credit ratings and matched or exceeded KMV in anticipating the magnitude of the crisis. We have also found some initial evidence that adding off-balance-sheet derivatives exposure improves the performance of the KMV model.     

Microfoundations of a mortgage prepayment function

This article focuses on the following question: how much of an interest rate decline is needed to justify refinancing a typical home mortgage? Modern option pricing theory is used to answer the question; this theory indicates that the answer depends upon several factors, which include the volatility of interest rates and the expected holding period of the borrower. The analysis suggests that the commonly espoused “rule of thumb” refinance if the interest rate declines by 200 basis points — is a fair approximation to the more precisely derived differential for many households. We also construct the prepayment behavior of a pool of mortgages in which the expected holding periods of the borrowers in the pool vary. The prepayment behavior of this simulated pool is used to generate a series of empirically testable hypotheses regarding the likely shape of an actual prepayment function and its determinants. Finally, actual prepayment data are used to estimate a hazard function that explains prepayment behavior. We find that the estimated model understates prepayment behavior relative to that predicted by the simulation model, which suggests that the simple option pricing model is not adequate to explain aggregate prepayment behavior.