Interest Rate Risk, Residential Mortgages and Financial Futures Markets

Residential mortgage markets in both the United States and Canada have recently been dominated by instruments such as variable-rate and short-term rollover mortgages which require borrowers to assume a greater burden of interest rate risk. An outstanding question is whether this approach to risk allocation is Pareto optimal or whether there are other more effective methods of dealing with the risk created by interest rate volatility. This study examines the potential for shifting this risk from the mortgage market to the financial futures market. After considering the rationale for expecting that neither mortgage borrowers nor lenders wish to absorb the high levels of risk present in the existing financial environment, this study discusses the hedging of interest rate risk through financial futures markets. Empirical tests are then performed to evaluate the effectiveness of U.S. futures markets for hedging positions from the U.S. mortgage market. These results indicate that the interest rate risk inherent in residential mortgages can be substantially shifted through one or more positions in the existing futures contracts and long-term, fixed-rate mortgages may still be financially feasible under conditions of interest rate volatility.     

浅析利率调整对住房抵押贷款违约风险的影响

住房贷款利率的变化对房地产价格产生着巨大影响,房地产价格又是住房抵押贷款中重要因素,与住房抵押贷款风险密切相关。违约风险是住房低押贷款风险中最基本最主要的风险,也称信用风险。论文将从理论上分析利率政策调整对住宅抵押贷款违约风险的影响,并提出相应的防范措施。     

Household Interest Rate Risk Management

I investigate household interest rate risk management by solving a life‐cycle asset allocation model that includes mortgage and bond portfolio choice. I find that most investors prefer an adjustable‐rate mortgage and thereby save on the bond risk premium that is contained in fixed‐rate mortgage payments. Only older, risk‐averse investors hold some fixed‐rate mortgage debt. Together with a position in short‐term bonds this enables them to hedge against changes in the real interest rate, while the inflation exposure of the debt and bond positions cancel out. Hedging house price changes with bonds only occurs at the end of the life cycle. Early in the life cycle short‐sale constraints prevent an effective hedge.     

The Borrower's Perceived Risk in Mortgage Choice

We investigate how borrowers perceive the risk in the adjustable rate mortgage (ARM) versus fixed rate mortgage (FRM) choice. We develop a mortgage choice model where the coefficient on the long‐term bond risk premium is conditional on the borrower's perceived risk. We show that the perceived risk fluctuates over time according to the short‐term interest rate level and housing market conditions. We find that when the short‐term rate level is high (low), the borrowers perceive low (high) risk of a short‐term rate rise, thus opting for ARMs (FRMs). Also, during a down housing market they become more risk‐averse perceiving higher risk in choosing ARMs. The perceived risk level alters the borrowers’ sensitivity to the long‐term bond risk premium.     

UK Fixed Rate Repayment Mortgage and Mortgage Indemnity Valuation

We use a mean-reverting interest rate model and a lognormal house price diffusion model to evaluate British fixed rate repayment mortgage contracts with (embedded) default and prepayment options. The model also provides values for capped mortgage indemnity guarantees and the corresponding (residual) lender's coinsurance. Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed-form solution, an explicit finite difference method is used for the valuation (and sensitivity) results, with solution improvements to deal with error bounds. Then we provide graphical representations of each mortgage component as a function of house prices and interest rate levels, along with interpretations of the analysis. We calculate precisely the lender's (residual) exposure to house price risk, given the borrower's options, house and interest rate uncertainty, and customary mortgage indemnity insurance for high loan/collateral ratio mortgages.     

Modelling reverse mortgages

This paper suggests a framework for analyzing reverse mortgages in a fixed interest rate environment as well as a variable interest rate environment. To analyze the risk and potential profit of a reverse mortgage, we propose to calculate the expected present value of profit and the probability of loss as indicators of the viability of the loan. Using Singapore data, we provide some estimates of these quantities for various levels of annuity payment under different circumstances.The author is from the Department of Economics and Statistics, National University of Singapore. He wishes to thank Chan Wai Sum, Thomas Herzog, Lim Kian Guan (the previous chief editor), Tan Kin Lian and Albert Tsui for their invaluable comments on the earlier drafts of the paper. All errors and shortcomings, however, remain his responsibility.     

The Accuracy of Senior Households’ Estimates of Home Values: Application to the Reverse Mortgage Decision

Using a unique data set of more than 14,000 senior homeowners in the United States, this study compares self‐assessed home values to arm's length contemporaneous appraisals. In a sample of seniors who received counseling for a reverse mortgage, the absolute value of the assessment error averages 18.9% of appraised value and it is biased upwards by 13.4%. When adjusted to reflect the general population of seniors, the size and bias of the average error fall to 16.1% and 4.2%. Both the bias and the size of the error tend to be lower for households with higher income and credit scores but it is greater for black households. In our sample period of 2009–2011, house prices were falling. The greater the rate of price reduction, the greater is the upward bias and size of the assessment error. When seniors who applied for a reverse mortgage learn that they overvalued their home, their probability of closing the loan falls.     

The Integration of Mortgage Markets and Capital Markets

In this paper, we develop a model to predict the impact of deregulation in the form of relaxing interest rate control on the integration between the mortgage credit market and the general credit market. The model is tested through the examination of the long-term Granger-like equilibrium relationship between mortgage interest rates and general interest rates in the pre-1980 regulated vs. the post-1980 deregulated periods. It is shown that the level of regulation, in the form of targeting general interest rate levels, contributes to the segmentation of the mortgage market from the capital market. To test this model, we compare the relationship between mortgage interest rates and general interest rates around 1980 where major control on interest rate levels in capital markets was lifted. Using Engle and Granger's procedure to overcome the estimation problem from nonstationarity in the interest rate series, we are able to find that the two interest rates were cointegrated after 1980 but not before. More importantly, it appears that the two markets were already integrated before the full development of the secondary mortgage markets between 1984 and 1987. Therefore, we conclude that the bulk of the integration between the mortgage and capital markets was completed as a result of the removal of interest rate controls around 1980, in contrast with previous studies that find integration occurred during the mid-1980s primarily as a result of the rapid development of the secondary mortgage markets.     

Managing the Short-Term Interest Rate Exposure Inherent in Adjustable Rate Mortgage Loans

This paper develops a model for determining the level of, and changes over time in, the short-term interest rate exposure contained in adjustable rate mortgage loans (ARMs). Results of the study indicate that movements in the underlying adjustment index can create both upward-movement or downward-movement interest rate risk for lenders whose ARMs carry rate adjustment limits. The model presented here is useful for designing hedging strategies for ARM loans, and for analyzing the impact of new originations on the interest rate exposure of the ARM portfolio.     

Regressive Interest Rate Expectations and Mortgage Instrument Choice in the United Kingdom Housing Market

The paper considers the choice of mortgage instrument when the rate of interest is fixed for a short duration, with reversion to a variable (bullet) rate mortgage contract. The research is the first direct test for regressive interest rate expectations using United Kingdom data while testing for wealth and portfolio effects. The econometric modeling uses a variety of nonparametric and parametric techniques to control for classification error in the dependent variable. There is evidence that households adopt regressive interest rate expectations. The lack of statistical significance of wealth and portfolio effects confirms the short run cash flow perspective of United Kingdom mortgage choices.     

What drives screening incentives in nonbank mortgage originators?

Nonbank mortgage originators, which operate through the originate-to-distribute (OTD) model, account for more than half of all the mortgage origination in the United States. However, less is known about which factors drive the quality of mortgage originations through nonbanks. I show that an exogenous shock that reduced collateral risk for funding intermediaries of nonbank mortgage originators led to a greater issuance of riskier mortgages that culminated in 10–30% higher ex post defaults. These results show how the quality of mortgage origination in the OTD model of nonbanks is affected by the collateral risk borne by their funding intermediaries. Overall, the results highlight funding intermediaries' monitoring incentives as one of the factors that drive the quality of mortgage originations through nonbanks.     

A Comparison of the Reinvestment Risk of the Price Level Adjusted Mortgage and the Standard Fixed Payment Mortgage

The purpose of this paper is to increase the understanding of the risk of the indexed mortgage, commonly referred to as the price level adjusted mortgage (PLAM). This is accomplished by comparing, analytically, the reinvestment risk of the PLAM and the standard fixed-payment mortgage (FPM) under conditions of stochastic inflation and real interest rates. The conclusion is that the PLAM has less reinvestment risk. From the viewpoint of an investor concerned with periodically reinvesting payment streams, the PLAM is the superior mortgage.     

Optimal Mortgage Refinancing with Stochastic Interest Rates

The purpose of this paper is to develop a dynamic model of mortgage refinancing in a contingent claim framework that simultaneously solves for the borrower's optimal mortgage refinancing strategy, the value of the refinancing call option, the value of the mortgage liability to the borrower, and the market (lender) value of the fixed-rate contract. We also calculate the minimum differential between the contract rate on the existing mortgage and the current interest rate that is required to trigger an optimal mortgage refinancing.     

A Model of Localized Mortgage Lending Behavior*

Loan administration costs and the costs of search for information about risk are found to be determinants of spatial interest rate differentials. These costs are independent of dollar loan size; therefore, rational lending policies can produce higher interest rates (or lower term to maturity) in low-income communities. But the premium (lower maturity) should be related to lower loan size and risk differentials. Public policy should be directed toward compiling and verifying an information bank which would allow lenders to search efficiently for information about risk. An empirical methodology designed to test for mortgage deficiency in minority areas was developed through case studies. This indicated the utility of specifying the supply and demand for mortgages at the neighborhood level of aggregation. Trends in neighborhood property values were identified as important and overlooked measures of lending risk. Further exploration of the hypothesis that Spanish-speaking areas are mortgage deficient is suggested by the cases.     

Hedging Forward Mortgage Loan Commitments: The Option of Futures and a Future for Options

The purpose of this paper is to analyze theoretically the problem of how mortgage lending institutions assume the interest rate risks inherent in the granting of fixed-rate mortgage loan commitments.
Two approaches to hedge this risk are analyzed. First, the use of the GNMA futures market is evaluated from the standpoint of how it might be used to hedge against mortgage commitment risks. Secondly, the use of an appropriate pricing model—the Black-Scholes option pricing model—is offered as a proxy for establishing the market value of a fixed-rate mortgage commitment. This model is extended and empirically estimated for several hypothetical environments.
The paper demonstrates a basic flaw in the GNMA futures market as a hedge against mortgage commitments. Once this is established, the use of the options pricing approach is offered as a more rational approach for hedging these risks.     

A Contingent Claims Analysis of Price Level-Adjusted Mortgages

This paper examines the performance of alternative mortgage instruments in an environment of stochastic price fluctuations. The two most widely discussed contracts that deal with inflation are the adjustable-rate mortgage (ARM) and the price level-adjusted mortgage (PLAM). The former compensates for inflation by paying the nominal interest rate, which contains a component reflecting the rate of inflation. Nonetheless, even without explicit nominal amortization, this results in real amortization and hence a tilting effect. In addition, the inflation component of the nominal interest rate is shown to reflect only anticipated and not actual inflation, and so the real value of an ARM fluctuates due to unanticipated inflation. A PLAM suffers from none of these defects. To the extent that one is interested in a mortgage whose properties reflect the underlying real environment, the price level-adjusted mortgage is the ideal instrument.     

Valuing the Mortgage Borrower's Prepayment Option

This paper investigates the value of the prepayment option that normally accompanies a fixed-rate mortgage. Using the two-state option-pricing model developed by Bartter and Rendleman, the paper presents simulations of prepayment option values using several sets of interest rate parameters. The sensitivity of the value of the option to changes in various aspects of the mortgage contract is assessed. Prepayments are not priced separately in the market from the underlying mortgage, so the paper investigates how the inclusion of a prepayment option affects the contract interest rate. Finally, there is reason to believe that any option-pricing model will overestimate the value of a mortgage prepayment option. The size of this bias is assessed indirectly and is found to be rather small.     

Pay Me Now or Pay Me Later: Alternative Mortgage Products and the Mortgage Crisis

Mortgage contract design has been identified as a contributory factor in the recent market crisis. Here we examine alternative mortgage products (including interest‐only and other deferred amortization structures) and develop a game theoretic model of contract choice given uncertain future income and house prices across different types of borrowers. Results imply that deferred amortization contracts are more likely to be selected in housing markets with greater expected price appreciation and by households with greater risk tolerance; moreover, such products necessarily entail greater default risk, especially among lower‐income households who are aggressive in housing consumption levels. Empirical tests of model predictions generally provide support for the theory.     

The Termination of Subprime Hybrid and Fixed‐Rate Mortgages

Adjustable‐rate and hybrid loans have been a larger component of subprime mortgage lending in the mortgage market than prime lending. The typical adjustable‐rate loan in subprime is a hybrid of fixed and adjustable characteristics in which the first 2 years are fixed and the remaining 28 years adjustable. Hybrid loans terminate at elevated probabilities even before the first adjustment date. Hybrid loan terminations are sensitive to interest rates and teaser rates (payment shocks). Default probabilities increase dramatically when payment shocks are mixed with low or no equity in the home. This is the mixture of events that helped to trigger the 2007/2008 subprime mortgage crisis.     

Mortgage Refinancing with Asymmetric Information

Information asymmetry exists between the lender and the borrower regarding the holding period of the mortgaged real estate; the lender does not know how long the borrower plans to own the house. This information asymmetry allows the cost of obtaining a mortgage to deviate from its value to the borrower. As a result, the exercise price of the option to refinance becomes the cost to the borrower of obtaining a new mortgage instead of the outstanding balance of the existing mortgage as used in previous models. The option to refinance is a sequential option; after the borrower refinances, a new option is obtained to refinance again in the future. A mortgage refinancing model is developed taking information asymmetry and sequential refinancing into account. The model is used to solve for (1) the value to the borrower of a callable mortgage and (2) the minimum interest rate differential between the contract rate of the existing mortgage and the market interest rate needed to justify refinancing.