Fixed-rate Mortgages Research Articles

The Impact of Interest Rates and The Housing Market on The UK Economy

The Chancellor has asked Professor David Miles to examine the UK market for longer‐term fixed rate mortgages. This paper by Adrian Cooper, which is part of a study commissioned by the Miles Review, presents the results of a series of simulations using the OEF Model of the UK economy to investigate the contribution of the housing market to macroeconomic volatility and the implications of changing the structure of mortgage finance from the current variable rate system linked to short‐term interest rates to a fixed rate system linked to long rates. The main findings are that the housing market has been a contributor to past volatility in the UK economy, and that moving to a fixed rate structure would reduce the impact of a change in interest rates on key macroeconomic indicators.

The Structural Relation Between Mortgage and Market Interest Rates

This paper analyzes the dynamic relationship between primary and secondary mortgage markets and the short‐term and long‐term market interest rates. Using a series of monthly data on fixed rate mortgage rates and GNMA rates, we explore the dependence and speed of adjustment in these primary and secondary mortgage rates to each other as well as to the long and short‐term government rates. The results indicate that residential mortgage rates in general, appear to follow the long‐term rate and are not very sensitive to movements in the short‐term interest rate.

International Real Estate Review

The prepayment risk of adjustable rate mortgages, unlike that of fixed rate mortgages, greatly depends on the decision of mortgagors to move. Given that housing also serves as an investment asset for the owner, it is hypothesised that the expected capital returns of housing are likely to affect his decision to move and hence, prepay. This paper aims to test the capital gains hypothesis using Singapore’s housing market as a case study. In addition, this paper also explores how the expected returns from alternative types of housing affect the decision of households to move/prepay. The expected returns of housing are computed in accordance with the definitions of the Rational Expectation Hypothesis, Adaptive Expectation Hypothesis, and Exogenous Expectation Hypothesis, which are well established in macroeconomic literature and the explanation of cycles. The results showed that the expected returns of public housing formed under the assumptions of rational and adaptive expectation hypothesis are significant. The rational expected return for private housing, however, does not have a significant relationship with the decision of mortgagors to move/prepay, although the adapted expected return for private housing is not significantly related to the households' length of stay.

Fixed-Rate Endowment Mortgage and Mortgage Indemnity Valuation

Fixed rate endowment mortgages differ from fixed rate repayment mortgages primarily because, in the event of early termination, the amount owed by the borrower is a function of the evolution of the term structure of interest rates, whereas for a repayment mortgage it is pre-determined. We use a contingent claims framework for valuing the embedded options in certain British fixed-rate endowment mortgages, with a (capped) mortgage indemnity guarantee (MIG). We assume a mean-reverting interest rate and a lognormal house price diffusion process to arrive at a partial differential equation as the basis of the contingent claims and include conventional mortgage terms such as arrangement fees and prepayment penalties. This methodology provides a template for the borrower, lender and insurer to compare mortgage terms, including the fairness of contract rates, fees and any MIG premiums required, when borrowing more than 75% of the house value at origination. Given the conventional terms and the diffusion processes, we assume the parties have common expectations for some diffusion parameters, including expected future rate and price volatilities. Also we assume that borrowers are 'economic actors' regarding default and prepayment options, and that factors such as mobility, divorce, unemployment, and transaction costs are deterministic and can be ignored in this model, along with moral hazard problems between the insurer and the lender. 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. We provide graphical representations (and interpretations) of each mortgage component as a function of house prices and interest rate levels. After empirical studies on the input parameters, each mortgage component may be compared with 'market values'. This model may also be useful as a 'mark-to-value' proxy for all parties, as expected parameters change (especially interest rate and house price levels, and expected future volatilities), for purposes of determining 'value added accounting', appropriate reserves, and indeed for setting premiums and business decisions. Finally, we compare endowment and repayment mortgages for different levels of loan-to-value ratios, interest rate and house price volatility.

A Fixed-Rate Mortgage Valuation Model in Three State Variables

This article investigates the effect of a two-factor interest rate process on the value of the mortgage and its inherent options including the right to default. Our complete three-state model for a mortgage derivative asset is used to make comparisons with the standard two-state model with the option to default or prepay. With slight modification, this model is applicable to other types of mortgages and mortgage-backed securities, and to derivative securities in general. The authors demonstrate that a two-state model with a one-factor term structure and a three-state model with a two-factor term structure value a mortgage substantially differently. The results suggest that valuing defaultable mortgages requires a three-state option pricing model to avoid mispricing.

Active-Passive Decomposition in Burnout Modeling

To model the effect of mortgage prepayment burnout, the author decomposes mortgage pools into active (potentially refinancing) and passive (prepaying at a turnover speed) components. This two-component model is not only powerful enough to replicate the burnout effect, but also perfectly tractable for a much wider range of mortgage valuation and modeling problems than once thought. Once parameters of the model are known at origination, one can reconstruct the current burnout stage using only the age and the observed pool factor, without retroactive analysis of past prepayment incentives. Or, assuming no change in interest rates, one can compute the average life and the life speeds for the entire mortgage pool, and therefore fit the broker forecasts. Unlike the mortgage pool itself, the two modeled components are path-independent for unstructured fixed-rate mortgage pass-throughs, which facilitates time-efficient pricing methods and avoids Monte-Carlo simulations.

Adjustable and Fixed Rate Mortgages as a Screening Mechanism for Default Risk

This paper studies how borrowers with different levels of default risk would self-select between fixed rate mortgages (FRMs) and adjustable rate mortgages (ARMs). We show that under asymmetric information, where the risk type of a borrower is private information to the borrower and not known by the lender, the unique equilibrium may be a separating equilibrium in which the high-risk (low-risk) borrowers choose ARMs (FRM's). Thus, the borrower's mortgage choice will serve as a signal of default risk, enabling lenders to screen high-risk and low-risk borrowers. It is possible for the separating equilibrium to yield positive economic profits for lenders in a competitive market. It is also possible to have a unique pooling equilibrium where all borrowers choose either FRMs or ARMs. The model implies that an increase in the proportion of high risks will increase the likelihood of a separating equilibrium where both mortgage types are offered. Also, a uniform downward shift in the expected change in the interest rate or an increase in borrowers' current or future incomes make ARMs more attractive for both types of borrowers.

Determinants of the ARM Share of FHA and Conventional Lending

Loan-choice research has generally examined the determinants of fixed-rate mortgage (FRM) versus ARM lending in the single-family conventional market. Little attention has been paid to the significant differences in ARM lending between the GSE conforming and jumbo markets, as well as differences in the FHA market. For example, the ARM share of jumbo originations is generally two to three times that of the conforming market. This article extends past analysis by examining the determinants of ARM market share in the conventional conforming, jumbo, and FHA markets. Mortgage-pricing variables and the slope of the Treasury yield curve, a proxy for expectations of the time path of ARM indexes, were generally found to be significant. Further, the geographic shift in FHA lending toward the California market since 1992 was found to explain a significant part of the increase in the ARM share of FHA originations during the mid-1990s.

Prepayment Risk in Adjustable Rate Mortgages Subject to Initial Year Discounts: Some New Evidence

This paper uses microlevel data to examine recent prepayment performance of adjustable rate mortgages (ARMs) employing the competing risk methodology developed by Deng, Quigley and Van Order (2000). We find support for the teaser rate and adjustment date effects implied by the theoretical model of Kau et al. (1993). In addition, we find that teased ARMs bear prepayment risk related to their discount, contrary to results reported by VanderHoff (1996) and Green and Shilling (1997). Finally, and contrary to the usual finding for fixed‐rate mortgages, we find that loan age has a negative effect on prepayment risk for ARMs, consistent with the phenomenon that borrowers with high mobility and/or propensity to refinance exit the pool early.

A Study of RASC Subprime Loan Prepayments, Delinquencies, and Losses

Subprime first-lien mortgages are securitized through the residential assets securities corporation. While they manifest differences with respect to loan age, credit grade, loan-to-value ratio, and vintage, both fixed-rate and adjustable-rate rasc mortgages exhibit positive convexity similar to that of the rest of the subprime market. There is some flexibility built into the credit underwriting guidelines through compensating factors related to (for example) delinquency versus debt-to-income ratios. This article describes collateral and performance differences in detail.

Are Multiple Hedging Instruments Better than One?

The authors examine the effectiveness of the ten–year, the five–year, and the two–year treasury note futures contracts in hedging the price risk of fixed–rate mortgage–backed securities. The ten–year treasury note futures contract offers superior hedging opportunities across all six coupon MBS examined. Using multiple instruments simultaneously results in minor improvements with–in sample. In out of–sample experiments, however, the use of a single instrument provides better hedging performance than the use of multiple instruments.

CMOs, Duration Risk and a New Mortgage

This article is the winner of the Real Estate Finance manuscript prize (sponsored by the Fannie Mae Foundation) presented at the 1999 American Real Estate Society Annual Meeting.This article presents an alternative mortgage that retains the fixed-rate feature of a fixed-rate mortgage (FRM), but accelerates the principal amortization when interest rates rise, exposing the buyer to less duration risk in a rising interest rate environment. This mortgage, labeled the adjustable amortization mortgage (AAM), is shown to have lessened interest rate risk for the buyer as well as lower default risk, suggesting that it should be priced higher (at a lower rate of interest) than the typical FRM. It is also shown that mortgage-backed securities collateralized by an AAM have much less price volatility than mortgage-backed securities backed by FRMs.

The Residential Mortgage Supply Function of Commercial Banks

The paper develops a residential supply function for approved fixed-rate mortgages in US commercial banks as a first step to explain differences in origination patterns among groups of borrowers. It models the lender's decision to offer the borrower a risk-adjusted loan bundle relative to the terms on the credit application. The model includes multiple dependent variables that are risk-adjusted simultaneously to reflect accurately the loan officer's decision. Canonical correlation factor analysis is used to capture the lender's simultaneous decision. The loan-price ratio and contract interest rate are the most important variables in the lender supply function.

Home mortgage analysis for cultivating crucial spreadsheet and model development skills

Abstract Accounting practitioners and academics have identified spreadsheet and model development skills as important for accounting graduates to possess. We present an adaptable mortgage analysis project that provides a practical setting in which students can develop critical spreadsheet modeling skills while demonstrating knowledge of several important principles of accounting and finance. The developed spreadsheet model is designed in a structured manner to permit changing the necessary financial terms and facilitates performing sensitivity analysis on critical variables. The analysis requires an informed decision be made between employing a fixed rate mortgage or an adjustable rate mortgage (ARM) for financing a home purchase. Important theoretical skills required to arrive at an acceptable solution include understanding of present value concepts, effective rate method of interest calculation, and amortization of principle balance. The student must also verify proficiency with the necessary theoretical and practical skills of effective spreadsheet design and model development

Secondary Mortgage Market Pedagogy: The Central Role of Prepayments

Executive Summary. This article presents a different approach to teaching secondary mortgage market concepts. Focusing on prepayments allows the instructor to illustrate and reinforce a rich variety of concepts: risk-return tradeoffs and efficient markets, servicing risks, the use of econometric models in providing information to investors and the importance of duration concepts to mortgage investors. Reviewing the history of the development of mortgage derivatives also illustrates the process of financial engineering—as prepayment risk and other risks in holding fixed-rate mortgages were explicitly recognized, new mortgage-backed securities were created to manage these risks.

A Closed Form Formula for Valuing Mortgages

We develop a closed form formula for the value of a fixed-rate residential mortgage that includes the provision that the borrower can prepay at any time with no penalty. The value of the mortgage equals the expectation, under the risk neutral probability measure, of the future cash flows. We model future cash flows by estimating an empirical model of prepayment behavior. A second change of measure leads to a closed form expression for the expectation. The closed form values explain most of the time series variation in MBS prices. The closed form formula significantly shortens the time to calculate mortgage values and durations and can be a useful tool for portfolio management and hedging.

Valuing Prepayment and Default in a Fixed‐Rate Mortgage: A Bivariate Binomial Options Pricing Technique

This paper uses a bivariate binomial options pricing technique to value the prepayment and default options in a fixed-rate mortgage. The American style options are dependent on two stochastic variables: (1) house price, (2) one year spot rate. The paper uses the standard lognormal process for house price and the CIR square-root process for interest rates. By forcing the two underlying state variables to undergo transformations, two new uncorrelated variables with constant volatilities are established. With constant volatilities, a computationally simple bivariate binomial tree is formed which greatly reduces the complexity of working with two state variables and is pedagogicallyuseful. Using this procedure, the price of any real estate contingent claim whose value is dependent on the one year spot rate and house price can be determined. Results are compared with those from a finite difference model.

Mortgage Choice: What's the Point?

This article shows that, in the presence of transaction costs payable by borrowers on refinancing, it is possible to construct a separating equilibrium in which borrowers with differing mobility select fixed rate mortgages (FRMs) with different combinations of coupon rate and points. We also show that, in the absence of such costs, no such equilibrium is possible. This provides a possible explanation for the large menus of FRMs typically encountered by potential borrowers, and suggests that the menu available at the time of origination should be an important predictor of future prepayment. We numerically implement the model, developing the first contingent claims mortgage valuation algorithm that can quantify the effect of self‐selection on real contracts in a realistic interest rate setting. The algorithm allows investors to account for self‐selection when valuing mortgages and mortgage‐backed securities. It also, for the first time, allows lenders to determine the optimal points/coupon rate schedule to offer to a specified set of potential borrowers, given the current level of interest rates.

An analytical comparison of the durations and price sensitivities of fixed-rate, constant payment and constant amortization mortgages

Both open-form and closed-form formulas are developed to compute duration for two types of fixed-rate mortgages: the level or constant payment mortgage and the constant amortization mortgage. Because holding periods are often less than maturity, duration formulas are also developed for mortgages that are paid prior to maturity. The duration formulas are used to compare the risk and price behavior of the two types of mortgages. Under any scenario, the constant amortization mortgage exhibits less interest rate risk than the constant payment mortgage. The durations of both mortgage types are monotonically increasing functions of maturity when the mortgages are held to maturity. When the mortgages are subject to prepayment, however, durations may, under certain circumstances decline with original maturity.

Demographic versus Option-Driven Mortgage Terminations

This study examines mortgage termination behavior at the household level, including fixed-rate mortgage terminations due to call, default, and mobility behavior. It exploits information in the American Housing Survey to examine national cross sections of 6119 and 4160 owner households. While accounting for the influence of interest rate movements in motivating termination—the call option influence—the study uses two sequential panels to investigate the modifying effect of household financial, demographic, and location characteristics upon termination behavior. Although we find the effect of the call option (systematic effect) to be highly significant in explaining terminations in a declining interest rate environment, we also find that demographic and locational effects (diversifiable) are potentially at least as significant. This result suggests that incomplete diversification over the nonsystematic factors of demography and location could cause significant variation in termination rates.