Securitization of Longevity Risk Using Percentile Tranching

Securitizations that transfer risk to the financial markets are a potential solution to longevity risk in the annuity business. The classical Lee–Carter model is applied to generate the future stochastic survival distribution. A method to design inverse survivor bonds using percentile tranches and to calculate the security prices is presented. The percentile tranche method is a simple and practical way for the issuer to design and price the security. This method can serve to identify the risk–yield relationship, which can provide investors with clear insight regarding the appropriate choice of tranches.     

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: Pricing Survivor Bonds With Wang Transform in the Lee-Carter Framework

Longevity risk is a major issue for insurers and pension funds, especially in the selling of annuity products. In that respect, securitization of this risk could offer great opportunities for hedging. This article proposes to design survivor bonds which could be issued directly by insurers. In order to guaranty some transparency in the product, the survivor bond is based on a public mortality index. The classical Lee‐Carter model for mortality forecasting is used to price a risky coupon survivor bond based on this index.     

A Bayesian Multivariate Risk-Neutral Method for Pricing Reverse Mortgages

In this article, we propose a Bayesian multivariate framework to price reverse mortgages that involve several risks in both insurance and financial sectors (e.g., mortality rates, interest rates, and house prices). Our method is a multivariate extension of the Bayesian risk-neutral method developed by Kogure and Kurachi. We apply the proposed method to Japanese data to examine the possibility for a successful introduction of reverse mortgages into Japan. The results suggest a promising future for this new market.     

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.     

商业银行抵押贷款折扣率风险管理研究

折扣率是商业银行抵押贷款风险管理的核心要素。如何科学合理地确定折扣率,是有效发挥押品风险缓释作用的重要因素。本文在对折扣率现有计量方法进行归纳、总结的基础上,重点介绍了单一押品折扣率模型、基于内部评级法的折扣率模型、基于加权平均法的传统计算方法、VaR评估模型以及监管要求的其他方法,同时结合部分实际处置数据和评估案例,利用VaR方法中的参数法和非参数法进行了介绍性实证分析,并针对当前部分商业银行折扣率计量风险敏感性不足、计量依据和规范性有待强化等问题,提出了构建商业银行内部押品计量体系、强化折扣率计量验证管理、完善押品风险数据库建设和加强押品存续期管理等具体政策建议。     

Determining an Optimal Principal Limit Factor for Reverse Mortgages under Economics-Based Models

The Journal of Real Estate Finance and Economics - Determining an optimal principal limit factor (PLF) is important for a reverse mortgage (RM) contract because it mainly influences the development...     

Measuring Basis Risk in Longevity Hedges

Abstract

In examining basis risk in index longevity hedges, it is important not to ignore the dependence between the population underlying the hedging instrument and the population being hedged. We consider four extensions to the Lee-Carter model that incorporate such dependence: Both populations are jointly driven by the same single time-varying index, the two populations are cointegrated, the populations depend on a common age factor, and there is an augmented common factor model in which a population-specific time-varying index is added to the common factor model with the property that it will tend toward a certain constant level over time. Using data from the female populations of Canada and the United States, we show the augmented common factor model is preferred in terms of both goodness-of-fit and ex post forecasting performance. This model is then used to quantify the basis risk in a longevity hedge of 65-year old Canadian females structured using a portfolio of q-forward contracts predicated on U.S. female population mortality. The hedge effectiveness is estimated at 56% on the basis of longevity value-at-risk and 81.61% on the basis of longevity risk reduction.     

Demographic Issues in Longevity Risk Analysis

Fundamental to the modeling of longevity risk is the specification of the assumptions used in demographic forecasting models that are designed to project past experience into future years, with or without modifications based on expert opinion about influential factors not represented in the historical data. Stochastic forecasts are required to explicitly quantify the uncertainty of forecasted cohort survival functions, including uncertainty due to process variance, parameter errors, and model misspecification errors. Current applications typically ignore the latter two sources although the potential impact of model misspecification errors is substantial. Such errors arise from a lack of understanding of the nature and causes of historical changes in longevity and the implications of these factors for the future. This article reviews the literature on the nature and causes of historical changes in longevity and recent efforts at deterministic and stochastic forecasting based on these data. The review reveals that plausible alternative sets of forecasting assumptions have been derived from the same sets of historical data, implying that further methodological development will be needed to integrate the various assumptions into a single coherent forecasting model. Illustrative calculations based on existing forecasts indicate that the ranges of uncertainty for older cohorts' survival functions will be at a manageable level. Uncertainty ranges for younger cohorts will be larger and the need for greater precision will likely motivate further model development.     

Spatial Variation in Reverse Mortgages Usage: House Price Dynamics and Consumer Selection

Reverse mortgages have been obtained by nearly one million senior households. In the future, the number of eligible households will grow substantially, about 80 % are homeowners, and many of them have substantial equity in their home. We study state-level variations in rate of originations of HUD’s Home Equity Conversion Mortgage (HECM) product. Our focus is on the impact of house prices on the origination rate. We test the hypothesis that in states where real house prices are volatile and the current level is above the long term norm, seniors rationally anticipate future reductions in house prices and lock-in their housing equity gains by obtaining a reverse mortgage. We test alternative hypotheses, the first being that seniors living in states with high rates of house price appreciation increase their use of HECMs as a means to convert an illiquid wealth capital gain into a more liquid asset. A second alternative hypothesis is that the intertemporal changes in originations of HECMs were a result of changes in the supply of mortgage originators. Our empirical work supports the hypothesis that seniors used HECMs to insure against house price declines, but we find no evidence in support of the alternative hypotheses.     

Familial Risk for Exceptional Longevity

One of the most glaring deficiencies in the current assessment of mortality risk is the lack of information concerning the impact of familial longevity. In this article we update estimates of sibling relative risk of living to extreme ages using data from more than 1700 sibships, and we begin to examine the trend for heritability for different birth-year cohorts. We also build a network model that can be used to compute the increased chance for exceptional longevity of a subject, conditional on his or her family history of longevity. The network includes familial longevity from three generations and can be used to understand the effects of paternal and maternal longevity on an individual's chance to live to an extreme age.     

Sharing Longevity Risk: Why Governments Should Issue Longevity Bonds

Government-issued longevity bonds would allow longevity risk to be shared efficiently and fairly between generations. In exchange for paying a longevity risk premium, the current generation of retirees can look to future generations to hedge their systematic longevity risk. Longevity bonds will lead to a more secure pension savings market, together with a more efficient annuity market. By issuing longevity bonds, governments can aid the establishment of reliable longevity indices and key price points on the longevity risk term structure and help the emerging capital market in longevity-linked instruments to build on this term structure with liquid longevity derivatives.     

The Effects of Purchases of Mortgages and Securitization by Government Sponsored Enterprises on Mortgage Yield Spreads and Volatility

In this paper, we investigate the effects of GSE (government sponsored enterprise) activities on mortgage yield spreads and volatility. Using various regression procedures (i.e., vector error correction (VEC) and GARCH models) and controlling for default and prepayment risk, we find that securitizations and purchases of mortgages by GSEs reduce mortgage yield spreads and volatility. In particular, we find that the yield spread between conforming and 10-year constant maturity treasury (CMT) rates decreases by 8.0 bp per $1billion increase in the level of GSE securitizations. Similarly, if GSEs increase mortgage purchases, the yield spread decreases 10.5 bp per $1billion increase of purchases. In addition, we hypothesize and find that GSE activities have a spillover effect to the non-conforming mortgage market; via investor substitutions, GSE purchases and securitizations of conforming loans reduce non-conforming loan rates. Thus, the measured influence of GSE activities is biased downward when measured using the spread of non-conforming loans over conforming loan rates. We also find that purchases of mortgages by GSEs significantly reduce mortgage yield volatility. In sum, our findings show that GSE activities reduce and stabilize mortgage market rates.     

Anatomy of an ARM: The Interest-Rate Risk of Adjustable-Rate Mortgages

This article analyzes the dynamics of the commonly used indices for adjustable rate mortgages and systematically compares the effects of their time-series properties on the interest-rate sensitivity of adjustable-rate mortgages. Our ARM valuation methodology allows us simultaneously to capture the effects of index dynamics, discrete coupon adjustment, mortgage prepayment, and both lifetime and periodic caps and floors. We can, moreover, either calculate an optimal prepayment strategy for mortgage holders or use an empirical prepayment function. We find that the different dynamics of the major ARM indices lead to significant variation in the interest-rate sensitivities of loans based on different indices. We also find that changing assumptions about contract features, such as loan caps and coupon reset frequency, has a significant, and in some cases unexpected, impact on our results.