Breakeven Determination of Loan Limits for Reverse Mortgages under Information Asymmetry

Since the loan limit of a reverse mortgage is a major concern for the borrower as well as the lender, this paper attempts to develop an option-based model to evaluate the loan limits of reverse mortgages. Our model can identify several crucial determinants for reverse mortgage loan limits, such as initial housing price, expected housing price growth, house price volatility, mortality distribution, and interest rates. We also pay special attention to the important implication of mortgage lenders’ informational advantage over reverse mortgage borrowers concerning housing market risk. In reverse mortgage markets, the elderly borrowers typically hold far less, relative to the lenders, or no information about the lenders’ underlying mortgage pools. Such information asymmetry leads these two categories of market participants to generate different perspectives on the risk of the collateralized properties, which can be identified to be important in determining the maximum loan amounts of reverse mortgages. We further find that the maximum loan amount of a reverse mortgage decreases in the correlation between the returns on the pooled underlying housing properties but increases with the number of the pooled mortgages.     

Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions

Equity release products are sorely needed in an aging population with high levels of home ownership. There has been a growing literature analyzing risk components and capital adequacy of reverse mortgages in recent years. However, little research has been done on the risk analysis of other equity release products, such as home reversion contracts. This is partly due to the dominance of reverse mortgage products in equity release markets worldwide. In this article we compare cash flows and risk profiles from the provider's perspective for reverse mortgage and home reversion contracts. An at-home/in long-term care split termination model is employed to calculate termination rates, and a vector autoregressive (VAR) model is used to depict the joint dynamics of economic variables including interest rates, house prices, and rental yields. We derive stochastic discount factors from the no arbitrage condition and price the no negative equity guarantee in reverse mortgages and the lease for life agreement in the home reversion plan accordingly. We compare expected payoffs and assess riskiness of these two equity release products via commonly used risk measures: Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).     

Securitization of Longevity Risk in Reverse Mortgages

Abstract

The reverse mortgage market has been expanding rapidly in developed economies in recent years. The onset of demographic transition places a rapidly rising number of households in an age window in which reverse mortgages have potential appeal. Increasing prices for residential real estate over the last decade have further stimulated interest.

Reverse mortgages involve various risks from the provider-s perspective that may hinder the further development of these financial products. This paper addresses one method of transferring and financing the risks associated with these products through the form of securitization. Securitization is becoming a popular and attractive alternative form of risk transfer of insurance liabilities. Here we demonstrate how to construct a securitization structure for reverse mortgages similar to the one applied in traditional insurance products.

Specifically, we investigate the merits of developing survivor bonds and survivor swaps for reverse mortgage products. In the case of survivor bonds, for example, we are able to compute premiums, both analytically and numerically through simulations, and to examine how the longevity risk may be transferred to the financial investors. Our numerical calculations provide an indication of the economic benefits derived from developing survivor bonds to securitize the “longevity risk component” of reverse mortgage products. Moreover, some sensitivity analysis of these economic benefits indicates that these survivor bonds provide for a promising tool for investment diversification.     

Credit History and the Performance of Prime and Nonprime Mortgages

Although nonprime lending has experienced steady or even explosive growth over the last decade very little is known about the performance characteristics of these mortgages. Using data from national secondary market institutions, this paper estimates a competing risks proportional hazard model, which includes unobserved heterogeneity. The analysis examines the performance of 30-year fixed rate owner occupied home purchase mortgages from February 1995 to the end of 1999 and compares nonprime and prime loan default and prepayment behavior. Nonprime loans are identified by mortgage interest rates that are substantially higher than the prevailing prime rate. Results indicate that nonprime mortgages differ significantly from prime mortgages: they have different risk characteristics at origination; they default at elevated levels; and they respond differently to the incentives to prepay and default. For instance, nonprime mortgages are less responsive to how much the option to call the mortgage or refinance is in the money and this effect is magnified for mortgages with low credit scores. Tests also reveal that default rates are less responsive to homeowner equity when credit scores are included in the specification.     

THE ESTIMATION OF MORTGAGE PREPAYMENT RATES

This paper uses a model in which prepayment rates on large pools of mortgages are a function of the differential between the prevailing market rate for mortgages and the contract rate at which the mortgages were originally issued. The empirical part of the paper shows a significant inverse relationship between the interest-rate differential and prepayment rates. The relationship is most elastic whenever the current market rate for mortgages is between one and three percent below the contract rate of the pool. For a given interest-rate differential, the estimated prepayment rate generally decreases and the elasticity increases as the contract rate rises.     

Advertising Expensive Mortgages

Using information on advertising and mortgages originated by subprime lenders, we study whether advertising helped consumers find cheaper mortgages. Lenders that advertise more within a region sell more expensive mortgages, measured as the excess rate of a mortgage after accounting for borrower, contract, and regional characteristics. These effects are stronger for mortgages sold to less sophisticated consumers. We exploit regional variation in mortgage advertising induced by the entry of Craigslist and other tests to demonstrate that these findings are not spurious. Analyzing advertising content reveals that initial/introductory rates are frequently advertised in a salient fashion, where reset rates are not.     

Derivative mortgage securities: An overview

Derivative mortgage securities have proliferated since planned amortization and floating rate CMO classes were introduced in late 1986. Other recently created derivative securities include reverse floaters and deep-discount bonds of CMOs, CMO residuals, and stripped and senior/subordinated passthroughs. These securities, which are derived from fixed-rate mortgages, were created to meet investor demands for maturity certainly, interest rate and prepayment hedging, and enhanced credit. The rapid growth of derivative securities reflects expansion of the investor base for fixed-rate mortgages. It also suggests that these mortgages will continue to be a viable housing finance instrument in a volatile interest rate environment. For the future, the increased creation of derivative securities will make the secondary mortgage market more efficient, facilitating the funding of fixed-rate mortgage originations.The substance of this paper was originally written in late 1987 and many of the specific data reflect that time period.     

The closing rate on residential mortgage commitments: An econometric analysis

Mortgage lenders routinely guarantee rates and points for periods of 60 days or more and hedge the inherent interest rate risk by selling the proportion of mortgages expected to close in forward markets. This article presents a model of the decision to close on the mortgage and demonstrates that the estimates of the model increase the precision of closing rate forecasts. The analysis indicates that changes in mortgage rates are important determinants of the closing rate for fixed-rate mortgages (FRM) and adjustable-rate mortgages (ARM). Other important factors include whether the mortgage is for a new purchase, for owner occupancy, and for a single-family house, and what the overall level of mortgage rates and the loan-to-value ratio are and whether the rate guarantee was granted at the application date or later.     

Originators,wholesalers, and conduits: The marginal value of the contract rate on 30-year conventional mortgages

The model we present solves for the value of an incremental change in the mortgage contract given an expectation about the time the mortgage will be outstanding and a required return for this time span. The marginal value participants in the primary mortgage market place on the contract rate of a 30-year conventional mortgage determines the array of bids for new mortgage production. Mortgagors can issue mortgages at various discounts. High discounts are associated with low contract rates, and low discounts are associated with high contract rates. This article examines the way wholesale dealers and conduits value the various contract rates associated with current production of 30-year conventional mortgages.     

Mortgage Loan Securitization and Relative Loan Performance

We compare the ex ante observable risk characteristics, the default performance, and the pricing of securitized mortgage loans to mortgage loans retained by the original lender. In our sample of loans originated between 2000 and 2007, we find that privately securitized fixed and adjustable-rate mortgages were riskier ex ante than lender-retained loans or loans securitized through the government sponsored agencies. We do not find any evidence of differential loan performance for privately securitized fixed-rate mortgages. We find evidence that privately securitized adjustable-rate mortgages performed worse than retained mortgages, although other observable factors appear to be more economically important determinants of mortgage default. We do not find any evidence of a compensating premium in the loan rates for privately securitized adjustable-rate mortgages.     

Subprime mortgage design

This paper offers evidence on the design of subprime mortgages as bridge-financing products. We show that the viability of subprime mortgages was uniquely predicated on the appreciation of house prices over short horizons. High rates of early prepayments on subprime mortgages suggest the use of prepayments as an exit option. This paper argues that high early defaults on post-2004 originations can be explained when one considers high early prepayment rates for pre-2004 originations.     

Econometric models of the Eleventh District Cost of Funds Index

The Eleventh District Cost of Funds Index (COFI) is a popular index for pricing adjustable-rate mortgages. COFI is calculated from the interest expenses incurred by thrifts when raising funds. It is a mixture of current and past interest rates on many different financial instruments. COFI can be modelled well with simple econometric models. Commonly used, simple COFI models are compared using a method developed by Hendry (1989). Some of these models, which appear to fit the data well, have nonrobust parameters, significant serial correlation, and heteroscedastic errors. These poorly specified models may lead to systematic mispricing of COFI mortgages. Once a robust econometric model is chose, the lagged adjustment of COFI to movements in interest rates can be incorporated into mortgage pricing models.     

Valuation of reverse mortgages under (limited) default risk

In this paper, we develop a consistent valuation framework for reverse mortgages based on reduced-form intensity models as used in credit risk modelling. Within our modelling framework, we explicitly calculate the probability that the total loan amount exceeds the house value at termination of the contract and derive the maximum payment(s) which can be made to the homeowner under certain constraints. We apply our results to data from the German market and discuss implications for the design of reverse mortgages from a lender's perspective.     

A model of mortgage losses and its applications for macroprudential instruments

We develop a theoretical model of mortgage loss rates that evaluates their main underlying risk factors. Following the model, loss rates are positively influenced by the house price level, the loan-to-value of mortgages, interest rates, and the unemployment rate. They are negatively influenced by the growth of house prices and the income level. The calibration of the model for the US and Switzerland demonstrates that it is able to describe the overall development of actual mortgage loss rates. In addition, we show potential applications of the model for different macroprudential instruments: stress tests, countercyclical buffer, and setting risk weights for mortgages with different loan-to-value and loan-to-income ratios.     

我国城镇住房反向抵押贷款的可行性研究

本课题运用了理论分析和演绎推理相结合的方法,在此基础上,进行大量深入调研及统计资料分析反向抵押贷款在我国城镇实施既是必要又是可行的.认为反向抵押贷款是涉及到房地产经济、社会保障、金融保险、制度经济学等学科的理论与思想方法,是对这些相关理论以反向抵押贷款为纽带的重新组合与融汇;反向抵押贷款将金融、保险、投资等不同金融工具相联接并有机融汇,形成了新的金融保险产品,实现金融保险工具创新,为我国老龄化问题提供一条崭新的思路.其研究成果具有较重要的理论价值、应用价值和现实意义.     

GSEs,Mortgage Rates,and the Long-Run Effects of Mortgage Securitization

Our paper compares mortgage securitization undertaken by government-sponsored enterprises (GSEs) with that undertaken by private firms, with an emphasis on how each type of mortgage securitization affects mortgage rates. We build a model illustrating that market structure, government sponsorship, and the characteristics of the mortgages securitized are all important determinants of mortgage rates. We find that GSEs generally—but not always—lower mortgage rates, particularly when the GSEs behave competitively, because the GSEs implicit government backing allows them to sell securities without the credit enhancements needed in the private sector. Using our simulation model, we demonstrate that when mortgages eligible for purchase by the GSEs have characteristics similar to other mortgages, the GSEs implicit government-backing generates differences in mortgage rates similar to those currently observed in the mortgage market (which range between zero and fifty basis points). However, if the mortgages purchased by GSEs are less costly to originate and securitize, and if the GSEs behave competitively, then the simulated spread in mortgage rates can be much larger than that observed in the data.     

Effects of Bankruptcy Exemptions and Foreclosure Laws on Mortgage Default and Foreclosure Rates

This study analyzes the effects of state bankruptcy asset exemptions and foreclosure laws on mortgage default and foreclosure rates across different segments of the mortgage market. We found that the effects of these legal provisions are larger for subprime than for prime mortgages and larger for adjustable rate mortgages than for fixed rate mortgages. These results demonstrate that the effect of variation in bankruptcy exemptions and foreclosure laws is most pronounced in the most risky segments of the mortgage market, which are those that have been most affected by the continuing housing slump in the United States.     

长寿风险的创新解决方案

长寿风险是指个人实际寿命高于预期寿命产生的财务风险.长寿风险给保险公司同时带来了新的挑战与机遇.近年来西方保险公司推出了各种应对长寿风险的创新解决方案,包括附保证变额年金、长期护理保险、反向抵押贷款和长寿风险证券化,对我国具有借鉴意义.本文从保险公司的新视角系统梳理了这四种创新方案,并对其优缺点和适用条件进行了比较分析...     

Pricing fixed rate mortgages: Some empirical evidence

We develop a simple model based on the hypothesis that yields in the secondary mortgage market provide a basis for pricing new loans in the primary mortgage market. The model is then expanded to include potential interest rate variations due to lender characteristics and whether the loans meet securitization requirements. The empirical results, using a two-year sample of single-family mortgage rates, conform to the predictions of the model. In particular, we find that the interest rates on FRMs in the primary market move in a one-to-one relationship with secondary market yields. We also find significantly lower interest rates on these mortgages that can be sold in the secondary market versus those that cannot, thus indicating the value of the ability to securitize mortgages.     

以地融资、地方债务与杠杆——地方融资平台的土地抵押分析

中国的高经济杠杆率和地方债务风险受到广泛关注,目前较少研究地方债务中的银行贷款,而地方融资平台的土地抵押贷款是其中重要的融资来源。本文首次利用爬虫工具获取了中国土地市场网上的土地抵押数据,并且搜集了地方融资平台名单,通过对比融资平台和非平台公司的土地抵押信息,发现地方融资平台在抵押金额和抵押率上,都显著高于非融资平台的土地抵押。我们进行了各种稳健性检验,通过采用PSM方法,降低样本选择偏误,发现结果是稳健的。此外,本文还探究了背后的政治经济学因素,发现中西部的抵押金额和抵押率显著高于东部;未到期的城投债存量越大,土地抵押越大;地方政府的经济增长压力越大,土地抵押也越大。这一定程度上意味着,融资平台获得的土地抵押较高,是出于地方政府强烈的举债动机和对信贷市场的干预,导致信贷资源的无效率配置。即使是土地抵押这种相对来说风险较小的融资渠道,依然可能蕴含着地方债务风险,这也为地方债务融资的抵押率高提供了证据。